Kvantuminformatika és a Kvantummechanika Alapjai Kutatócsoport
https://wigner.hu/hu
hu2022_Quantum information and Complex Systems Research Group
https://wigner.hu/hu/node/2531
<span class="field field--name-title field--type-string field--label-hidden">2022_Quantum information and Complex Systems Research Group</span>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><h4><strong>2022</strong></h4>
<p><strong>Nonlocal Boxes.</strong> — We have developed a Web Application Programming Interface (API) that is capable of implementing no-signaling correlations between pairs of parties [<a href="https://wigner.hu/nonlocalbox">1</a>,<a href="https://arxiv.org/abs/2212.06769">2</a>]. Certainly it does not include particular measurements on entangled particles; the correlations are realized via communication with a central server. In this way, however, scenarios based on such correlations that involve quantum measurements and entanglement, like the Bell-CHSH experiment or device-independent quantum cryptographic protocols can be simulated using the API, making it a useful tool for protocol design and a basis for computer applications to help in experience-based teaching of nonclassical correlations. The development of the API has inspired our research resulting the first known two-party protocol in which using nonlocal boxes in different causal order is important [<a href="https://m2.mtmt.hu/gui2/?mode=browse¶ms=publication;33048972">3</a>]. Currently a mobile application to support the teaching of Bell-type scenarios is being developed.</p>
<p><strong>Energy gap of transverse-field Ising chains. </strong>— Based on a relationship with continuous-time random walks discovered by Iglói, Turban, and Rieger, we derived exact lower and upper bounds on the lowest energy gap of open transverse-field Ising chains, which are explicit in the parameters and are generally valid for arbitrary sets of couplings and fields. Applying the bounds to a random Ising chain with coupling-field correlations, a model which is relevant for adiabatic quantum computing, we determined the critical dynamical exponent of the model and revealed the existence of logarithmic corrections at special points [<a href="https://m2.mtmt.hu/gui2/?mode=browse¶ms=publication;33072949">4</a>].</p>
<p><strong>Wasserstein distance and quantum Fisher information. </strong>— A classical Wasserstein distance is a metric between probability distributions μ and ν, induced by the problem of optimal mass transportation. It reflects the minimal effort that is required in order to morph the mass of μ into the mass distribution of ν. Methods based on the theory of optimal transport and advantageous properties of Wasserstein metrics have achieved great success in several important fields of pure mathematics. The non-commutative generalization, the so-called quantum optimal transport, has been at the center of attention, as it led to the definition of several new and very useful notions in quantum physics. One of the key results of quantum optimal transport is the definition of the quantum Wasserstein distance. It has the often desirable feature that it is not necessarily maximal for two quantum states orthogonal to each other, which is beneficial, for instance, when performing learning on quantum data. Some of the properties of the new quantities are puzzling, yet point to profound relations between seemingly unrelated fields of quantum physics. For instance, the quantum Wasserstein distance order 2 of the quantum state from itself can be nonzero, while in the classical case the self-distance is always zero. In particular, the quantum Wasserstein distance has been defined based on a quantum channel formalism, and it has been shown that the square of the self-distance is equal to the Wigner-Yanase skew information of the quantum state. We obtained new quantities by restricting the optimization to separable states in the above definitions [<a href="https://arxiv.org/abs/2209.09925">5</a>]. We showed that, in this case, the square of the self-distance equals the quantum Fisher information times a constant. The quantum Fisher information is a central quantity of quantum metrology, a field that is concerned with metrological tasks in which the quantumness of the system plays an essential role. This way we connected quantum optimal transport to quantum entanglement theory.</p>
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<p class="text-align-center"><em>Figure 1. Geometric representation of the quantum Wasserstein distance between a pure state and a mixed state for operator H<sub>1</sub>. The square of the distance is the sum of three terms of which two can be nonzero even if we calculate the distance of the state from itself, i.e, we calculate self-distance.</em></p>
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<span class="field field--name-created field--type-created field--label-hidden">k, 02/21/2023 - 13:30</span>
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<div class="field__item"><time datetime="2023-02-21T12:00:00Z" class="datetime">k, 02/21/2023 - 12:00</time>
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Tue, 21 Feb 2023 12:30:52 +0000Dovicsin-Péntek Csilla Klára2531 at https://wigner.hu2021_Quantum information and complex systems
https://wigner.hu/hu/node/2233
<span class="field field--name-title field--type-string field--label-hidden">2021_Quantum information and complex systems</span>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><h4><strong>2021</strong></h4>
<p><strong>Entanglement entropy scaling in random singlet states.</strong> — We considered random singlet phases of antiferromagnetic spin chains, in which the leading-order logarithmic divergence of the entanglement entropy, as well as the closely related leading term in the distribution of singlet lengths are well known by the strong-disorder renormalization group (SDRG) method. We addressed the question of how large the sub-leading terms of the above quantities are. By an analytical calculation performed along a special SDRG trajectory, we identified a series of integer powers of 1/l in the singlet-length distribution. This was confirmed by a numerical SDRG analysis which showed non-universal coefficients of the sub-leading term and also revealed terms with half-integer powers. We also presented how the singlet lengths originating in the SDRG approach can be interpreted and calculated in the XX chain from the one-particle states of the equivalent free-fermion model <a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.104.054209">[1]</a>.</p>
<p>We considered a sublattice-symmetric free-fermion model on a one-dimensional lattice with random, power-law decaying hopping amplitudes, and addressed the question how far an analogue of the random-singlet state (RSS) is valid for this model. For this purpose, we studied the effective central charge characterizing the logarithmic divergence of the entanglement entropy (EE) and the prefactor of the distribution of distances between localization centers on the two sublattices, which must fulfill a consistency relation for a RSS. We found by exact diagonalization an overall logarithmic divergence of EE with an effective central charge varying with the decay exponent α of the hopping amplitudes. The consistency relation of RSS is violated for α≤2, while for α>2 it is possibly valid. The EE was also calculated by the SDRG method numerically. We constructed and applied an efficient minimal SDRG scheme, which turned out to be an accurate approximation of the traditional scheme <a href="https://arxiv.org/abs/2110.01985">[2]</a>.</p>
<p><strong>Quantum optical description of high order multiphoton processes</strong>.— In the frame of nonrelativistic quantumelectrodynamics, we have constructed a general theoretical model for nonperturbatively treating the interaction of an atomic electron with the quantized radiation field, which may contain high-intensity components [3]. In the course of eliminating the minimal coupling terms of the quantized field, the interaction with the radiation is condensed to a space-translated “multiphoton effective potential”, which represent the vortices of multiphoton interaction (for an illustration see Figure 1). In our formalism the system “electron + (strong) laser mode(s) + mode(s) of the scattered radiation” has a natural basis set of entangled Coulomb-Volkov type states, whose photon part is in a multimode squeezed coherent state. According to this result, our model may also serve as a proper “microscopic background” of various strong-field phenomena, like above-threshold ionization (ATI) or high-harmonic generation (HHG). The derived strong-field Kramers-Heisenberg formula inherently desribes the optional appearance of the Cooper minimum in the HHG spectrum. The presented formalism may contibute to a more fundamental level of the theoretical description and understanding of photon-electron interactions in high-intensity radiation fields<a href="https://www.mdpi.com/2304-6732/8/7/269"> [3].</a></p>
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<p><br />
Figure 1. This 3D figure illustrates the temporal evolution of the expectation value of the multiphoton effective potential (laser-dressed Coulomb potential with ) in Heisenberg picture. We have taken , and for the inducing Ti:Sa laser parameters, in which case the amplitude of the free electron oscillation is 9 times larger than the Bohr radius, and assumed a Gaussian envelope , which corresponds to 2.3 cyles full temporal width at half maximum. For a better visualization, we have chosen for the cylindrical coordinate. This figure illustrates, that the effective potential vanishes before and after the external pulse, in contrast to the usual Kramers-Henneberger space translated potential.</p>
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<p><strong>Optical realization of a chaotic quantum protocol.</strong> — Iterated quantum protocols with measurement-based selection lead to deterministic chaos for the evolving pure state representing an ensemble of qubits. Deterministic chaos for the pure quantum state may lead to ergodic evolution in the sense that initial states from any small area on the Bloch sphere will cover the whole sphere after a finite number of iterations. We realized two steps of an ergodic protocol in a photonic experiment, where initial qubit states were encoded in the polarization and path degrees of freedom of down-converted photons stemming from a parametric process. We numerically analyzed the effect of noise on the time evolution and showed that the protocol, described by a Lattès map, remains quasi-ergodic for any initial state if the initial noise is small. The tomographic reconstruction of the quantum states throughout the evolution was consistent with simulations and thus the ergodicity of the quantum dynamics was demonstrated <a href="https://iopscience.iop.org/article/10.1088/1367-2630/ac15b4">[4]</a>.</p>
<p><strong>Optical realization of quantum walks on fractal graphs.</strong> — Photon propagation through an array of coupled waveguides arranged in various fractal patterns serves as a useful ‘optical simulator’ for revealing insights into quantum transport in complex scenarios. An independent research group tested recurrence for continuus-time quantum walks on Sierpiński gaskets and carpets in an optical experiment, corresponding to our earlier work. We have highlighted the importance of this developement <a href="https://www.nature.com/articles/s41566-021-00868-x">[5]. </a>The ability to experimentally implement quantum walks on complicated graphs may accelerate the design and testing of artificial 2D materials and algorithms based on quantum walks.</p>
<p><strong>Electron-phonon entanglement in 1D systems.</strong> — We investigated the entanglement between electrons and phonons in a one dimensional system. The electron subsystem has been described by the Luttinger theory. We investigated the entanglement entropy, the negativity and the mutual information. The entanglement negativity increases with the electron-phonon coupling strength and diverges with the Wentzel-Bardeen singularity. The mutual information decrease with the temperature and reaches a constant nonzero value in the high temperature limit, wich is the consequence of the infinite linear electron spectrum of the Luttinger model. The negativity decrease with the temperature, and becomes exactly zero above a temperature limit. The temperature limit depends on the system size. If the electron-electron interaction is screened enough the limit temperature remains finite. This means, in certain coupled electron phonon systems the electrons and the phonons become non-entangled over a limit temperature [6].</p>
<p><strong>Quantum entanglement and its use it quantum metrology.</strong> — We worked on detecting entanglement in cold gases <a href="https://arxiv.org/abs/2104.05663">[7]</a>. Our conditions have been tested in systems that create Dicke states. The condition detects bipartite entanglement between two spatially separated part of the ensemble. We also present criteria that detect Einstein-Podolsky-Rosen (EPR) steering in such systems. Our criteria are resistant to the usual imperfections of the experiments, such as the nonzero variance of the particle number and the fact that not the entire state lives in the spatial mode in the Bose-Einstein condensate.<br />
We also worked on the relation of entanglement and metrology via the formalism using the quantum Fisher information <a href="https://arxiv.org/abs/2002.12409">[8]</a>. We presented a family of weakly entangle quantum states, called bound entangled states, that are more useful for metrology than separable states. In the limit of large dimensions, they are maximally useful. The family of states is known analytically, thus we can carry our calculations for large systems. Before, presented in a previous publication, we found similar states numerically, but could consider only relatively small systems.</p>
<p>We also worked on uncertainty relations with the quantum Fisher information, using the knowledge that the quantum Fisher information is the convex roof of the variance times four <a href="https://arxiv.org/abs/2109.06893">[9]</a>. Starting from the Robertson-Schrödinger relation, we present further uncertainties with the convex roof of the bound. We gain new insights on the Cramér-Rao bound. We strengthen the Robertson-Schrödinger uncertainty with a concave roof of the bound. We also present a novel uncertainty that is the sum of two variances and a quantum Fisher information term bounded by a constant. Finally, we show that the violation of some entanglement criteria implies that the quantum state is more useful than certain relevant subsets of separable states.</p>
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<p>References.</p>
<p>[1] DOI: 10.1103/PhysRevB.104.054209</p>
<p>[2] <a href="https://arxiv.org/abs/2110.01985">https://arxiv.org/abs/2110.01985</a></p>
<p>[3] <a href="https://doi.org/10.3390/photonics8070269">https://doi.org/10.3390/photonics8070269</a></p>
<p>Varró S, Quantum optical aspects of high-harmonic generation. Photonics 2021, 8 (7), 269.</p>
<p>[4] DOI: 10.1088/1367-2630/ac15b4</p>
<p>[5] <a href="https://doi.org/10.1038/s41566-021-00868-x">https://doi.org/10.1038/s41566-021-00868-x</a><br />
Tamás Kiss and Igor Jex, Photons walk on fractal graphs, Nature Photonics 15, 638 (2021)</p>
<p>[6] Gergő Roósz and Carsten Timm Phys. Rev. B 104, 035405 (2021)</p>
<p>[7] G. Vitagliano, M. Fadel, I. Apellaniz, M. Kleinmann, B. Lücke, C. Klempt, G. Tóth, Detecting Einstein-Podolsky-Rosen steering and bipartite entanglement in split Dicke states, arXiv:2104.05663.</p>
<p>[8] K. F. Pál, G. Tóth, E. Bene, T. Vértesi, Bound entangled singlet-like states for quantum metrology, Phys. Rev. Res. 3, 023101 (2021); arXiv:2002.12409. DOI: 10.1103/PhysRevResearch.3.023101</p>
<p>[9] G. Tóth and F. Fröwis, Uncertainty relations with the variance and the quantum Fisher information based on convex decompositions of density matrices, Phys. Rev. Res., in press; arXiv:2109.06893.</p>
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<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="https://wigner.hu/hu/user/124" typeof="schema:Person" property="schema:name" datatype="" content="13566@wigner.mta.hu" xml:lang="">Dovicsin-Pénte…</span></span>
<span class="field field--name-created field--type-created field--label-hidden">cs, 05/26/2022 - 12:44</span>
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<div class="field__item"><time datetime="2022-05-26T12:00:00Z" class="datetime">cs, 05/26/2022 - 12:00</time>
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Thu, 26 May 2022 10:44:01 +0000Dovicsin-Péntek Csilla Klára2233 at https://wigner.hu2020_Quantum Information and Complex Systems
https://wigner.hu/hu/node/1713
<span class="field field--name-title field--type-string field--label-hidden">2020_Quantum Information and Complex Systems</span>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><h4><strong>2020</strong></h4>
<p><strong>Topological delocalization in the completely disordered two-dimensional quantum walk.</strong> — In low dimensional quantum systems, spatial disorder generically leads to Anderson localization, inhibiting spatial spread of wavefunctions. This also occurs in two-dimensional quantum walks, versatile toy models for periodically driven quantum systems. We have found <a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.102.224202">[1]</a> that increasing spatial disorder to the maximum possible value (Haar random coin operators), leads to a delocalization: a diffusive spread of an initially localized wavepacket instead of Anderson localizaiton. This delocalization happens because maximal disorder places the quantum walk to a critical point between different anomalous Floquet-Anderson insulating topological phases. We have previously observed topological delocalization in a simpler quantum walk, using time-evolution of the wavefunctions and level spacing statistics. We have now calculated the topological invariants of disordered quantum walks using scattering theory, substantiating the topological interpretation of the delocalization, and finding its signatures in the finite-size scaling of transmission. We have shown criticality of the Haar random quantum walk by calculating the critical exponent η in three different ways and found η ≈ 0.52 as in the integer quantum Hall effect. Our results showcase how theoretical ideas and numerical tools from solid-state physics can help us understand spatially random quantum walks.</p>
<img alt="Kvantuminformatika1" data-entity-type="file" data-entity-uuid="b25d29e4-61cc-46e0-91e6-dc8cedabe958" src="https://wigner.hu/sites/default/files/inline-images/kvantuminformatika.png" width="600" class="align-center" />
<p class="text-align-center"><em><strong>Figure 1.</strong> Position distribution of the Haar random quantum walk after 10000 timesteps</em></p>
<p><strong>Ex ante versus ex post equilibria in classical Bayesian games with a nonlocal resource. </strong>— The relation of nonclassical correlations such those of Einstein-Podolsky-Rosen type to the classical theory of Bayesian games is getting an increasing research attention. As a contribution to this line of research we have analyzed the difference between the so-called ex ante and ex post equilibria in classical Bayesian games played with the assistance of a nonlocal (quantum or no-signaling) resource. In physics, the playing of these games is known as performing bipartite Bell-type experiments. By analyzing the Clauser-Horn-Shimony-Holt game, we have found a constructive procedure to find two-person Bayesian games with a nonlocal (ie, no-signaling, and, in many cases, quantum) advantage. Most games of this kind known from the literature can be constructed along this principle. Our construction can be applied to find further scenarios and protocols in which quantum correlations can be useful if realized. In addition we have found that the already known scenarios share the property that their relevant ex ante equilibria are ex post equilibria as well. We have found, however, a different type of game, based on the Bell theorem by Vértesi and Bene, which does not have the latter property: The ex ante and ex post equilibria differ. <a href="https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.022505">[2]</a></p>
<p><strong>Complete classification of trapping coins for quantum walks on the two-dimensional square lattice.</strong> — One of the unique features of discrete-time quantum walks is called trapping, meaning the inability of the quantum walker to completely escape from its initial position, although the system is translationally invariant. The effect is dependent on the dimension and the explicit form of the local coin. A four-state discrete-time quantum walk on a square lattice is defined by its unitary coin operator, acting on the four-dimensional coin Hilbert space. The well-known example of the Grover coin leads to a partial trapping, i.e., there exists some escaping initial state for which the probability of staying at the initial position vanishes. On the other hand, some other coins are known to exhibit strong trapping, where such an escaping state does not exist. We present a systematic study of coins leading to trapping, explicitly construct all such coins for discrete-time quantum walks on the two-dimensional square lattice, and classify them according to the structure of the operator and the manifestation of the trapping effect. We distinguish three types of trapping coins exhibiting distinct dynamical properties, as exemplified by the existence or nonexistence of the escaping state and the area covered by the spreading wave packet. <a href="https://journals.aps.org/pra/abstract/10.1103/PhysRevA.102.012207">[3]</a></p>
<p><strong>Optimization of multiplexed single-photon sources operated with photon-number-resolving detectors.</strong> — Detectors inherently capable of resolving photon numbers have undergone a significant development recently, and this is expected to affect multiplexed periodic single-photon sources where such detectors can find their applications. We analyze various spatially and time-multiplexed periodic single-photon source arrangements with photon-number-resolving detectors, partly to identify the cases when they outperform those with threshold detectors. We develop a full statistical description of these arrangements in order to optimize such systems with respect to maximal single-photon probability, taking into account all relevant loss mechanisms. The model is suitable for the description of all spatial and time multiplexing schemes. Our detailed analysis of symmetric spatial multiplexing identifies a particular range of loss parameters in which the use of the new type of detectors leads to an improvement. Photon number resolution opens an additional possibility for optimizing the system in that the heralding strategy can be defined in terms of actual detected photon numbers. Our results show that this kind of optimization opens an additional parameter range of improved efficiency. Moreover, this higher efficiency can be achieved by using less multiplexed units, i.e., smaller system size as compared to threshold-detector schemes. We also extend our investigation to certain time-multiplexed schemes of actual experimental relevance. We find that the highest single-photon probability is 0.907 that can be achieved by binary bulk time multiplexers using photon-number-resolving detectors. <a href="https://journals.aps.org/pra/abstract/10.1103/PhysRevA.102.013513">[4]</a></p>
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<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="https://wigner.hu/hu/user/124" typeof="schema:Person" property="schema:name" datatype="" content="13566@wigner.mta.hu" xml:lang="">Dovicsin-Pénte…</span></span>
<span class="field field--name-created field--type-created field--label-hidden">cs, 02/18/2021 - 08:54</span>
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<div class="field__item"><time datetime="2020-01-02T12:00:00Z" class="datetime">cs, 01/02/2020 - 12:00</time>
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Thu, 18 Feb 2021 07:54:54 +0000Dovicsin-Péntek Csilla Klára1713 at https://wigner.hu2019_Quantum Information and Foundations of Quantum Mechanics Group
https://wigner.hu/hu/node/1472
<span class="field field--name-title field--type-string field--label-hidden">2019_Quantum Information and Foundations of Quantum Mechanics Group</span>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><h4><strong>2019</strong></h4>
<p><b>Mesurement-induced nonlinear transformations.</b> — By involving two or more identical copies of qubits in the same state, it is possible to induce nonlinear quantum state transformations by applying an entangling unitary operation pairwise, combined with a postselection scheme conditioned on the measurement result obtained on one of the qubits of the pair. Such maps play a central role in distillation protocols used for quantum key distribution. We determined that such protocols may exhibit sensitive, quasi-chaotic evolution not only for pure initial states but also for mixed states, i.e., the complex dynamical behavior is not destroyed by small initial uncertainty. We showed that the appearance of sensitive, complex dynamics associated with a fractal structure in the parameter space of the system has the character of a phase transition. The purity of the initial state plays the role of the control parameter, and the dimension of the fractal structure is independent of the purity value after passing the phase transition point (Fig.1). The critical purity coincides with the purity of a repelling fixed point of the dynamics, and we show that all the pre-images of states from the close neighborhood of pure chaotic initial states have purity larger than this. Initial states from this set can be considered as quasi-chaotic .</p>
<img alt="S-Q2019-1" data-entity-type="file" data-entity-uuid="2c794d2f-5f51-4509-8a78-8542c59c520a" src="https://wigner.hu/sites/default/files/inline-images/S-Q2019-1.png" width="600" class="align-center" />
<p><i><b>Figure 1.</b> The fractal dimension D<sub>bc</sub> of the border between the different convergence regions as a function of the initial purity. The error bars indicate the range of numerically calculated values D<sub>bc</sub>. The black squares correspond to the mean value of the 37 data points for each initial purity. For initial purities above 0.78, D<sub>bc</sub> is fluctuating around the average value 1.561 (solid line). For P < 0.76, where the structure is no longer a fractal, D<sub>bc</sub> equals 1 within the statistical error of the numerical method.</i></p>
<p>We experimentally realized a nonlinear quantum protocol for single-photon qubits with linear optical elements and appropriate measurements. Quantum nonlinearity was induced by postselecting the polarization qubit based on a measurement result obtained for the spatial degree of freedom of the single photon which played the role of a second qubit. Initially, both qubits were prepared in the same quantum state and an appropriate two-qubit unitary transformation entangled them before the measurement of the spatial part. We analyzed the result by quantum state tomography of the polarization degree of freedom. We then demonstrated the usefulness of the protocol for quantum state discrimination by iteratively applying it to either of two slightly different quantum states which rapidly converged to different orthogonal states by the iterative dynamics .</p>
<p><b>Nonlinear optical processes.</b> — We implemented the pseudospectral method for the Finite Difference Frequency Domain method (FDFD) and hence the resulting method is called Pseudospectral Frequency Domain method (PSFD). We compared the PSFD method with the FDFD method in terms of the numerical phase velocity and anisotropy. The main advantage of our method compared to finite differences is the significantly larger accuracy at the same grid resolution. We extended our method for the nonlinear process (NL-PSFD) of Second Harmonic Generation (SHG). We showed how a plane wave source at oblique incidence can be implemented and we discussed its performance for tilted Quasi-Phase Matched (QPM) grating. Finally, we proposed a specific method deduced from NL-PSFD for large volume simulation where only second order nonlinearity is structured spatially, and simulated a two-dimensional nonlinear photonic crystal (Fig.2) .</p>
<img alt="S-Q2019-2" data-entity-type="file" data-entity-uuid="5bc7950e-5d6c-4cdb-b41d-3694aa9ce7e5" src="https://wigner.hu/sites/default/files/inline-images/S-Q2019-2.png" width="400" class="align-center" />
<p><i><b>Figure 2.</b> SHG process in a 2D nonlinear photonic crystal. The domain inversion is carried out on a centered rectangular lattice, in a circular pattern. The left part of the figure shows the incoming fundamental wave, the middle represents the nonlinear photonic crystal, while the right part shows the generated second harmonic wave.</i></p>
<p><b>Topological quantum gates.</b> — Topological properties of quantum systems could provide protection of information against environmental noise, and thereby drastically advance their potential in quantum information processing. Most proposals for topologically protected quantum gates are based on many-body systems, e.g., fractional quantum Hall states, exotic superconductors, or ensembles of interacting spins, bearing an inherent conceptual complexity. We proposed and studied a topologically protected quantum gate, based on a one-dimensional single-particle tight-binding model, known as the Su-Schrieffer-Heeger chain. The proposed Y gate acts in the two-dimensional zero-energy subspace of a Y junction assembled from three chains, and is based on the spatial exchange of the defects supporting the zero-energy modes. With numerical simulations, we demonstrated that the gate is robust against hopping disorder but is corrupted by disorder in the on-site energy. Then we show that this robustness is topological protection, and that it arises as a joint consequence of chiral symmetry, time-reversal symmetry, and the spatial separation of the zero-energy modes bound to the defects. This setup will most likely not lead to a practical quantum computer; nevertheless it does provide valuable insight to aspects of topological quantum computing as an elementary minimal model. Since this model is noninteracting and nonsuperconducting, its dynamics can be studied experimentally, e.g., using coupled optical waveguides .</p>
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<span class="field field--name-created field--type-created field--label-hidden">sze, 05/27/2020 - 13:43</span>
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<div class="field__item"><time datetime="2019-01-02T12:00:00Z" class="datetime">sze, 01/02/2019 - 12:00</time>
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Wed, 27 May 2020 11:43:12 +0000Dovicsin-Péntek Csilla Klára1472 at https://wigner.hu2018_Quantum Information and Foundations of Quantum Mechanics Group
https://wigner.hu/hu/node/942
<span class="field field--name-title field--type-string field--label-hidden">2018_Quantum Information and Foundations of Quantum Mechanics Group</span>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><h4><strong>2018</strong></h4>
<p><strong>Measurement-induced nonlinear transformations </strong>— We considered the task of deciding whether an unknown qubit state falls in a prescribed neighborhood of a reference state. If several copies of the unknown state are given and we can apply a unitary operation pairwise on them combined with a postselection scheme conditioned on the measurement result obtained on one of the qubits of the pair, the resulting transformation is a deterministic, nonlinear, chaotic map in the Hilbert space. We derived a class of these transformations capable of orthogonalizing nonorthogonal qubit states after a few iterations. These nonlinear maps orthogonalize states which correspond to the two different convergence regions of the nonlinear map. Based on the analysis of the border (the so-called Julia set) between the two regions of convergence, we showed that it is always possible to find a map capable of deciding whether an unknown state is within a neighborhood of fixed radius around a desired quantum state. We analyzed which one- and two-qubit operations would physically realize the scheme. It is possible to find a single two-qubit unitary gate for each map or, alternatively, a universal special two-qubit gate together with single-qubit gates in order to carry out the task. We note that it is enough to have a single physical realization of the required gates due to the iterative nature of the scheme.<br />
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<img alt="kt1" data-entity-type="file" data-entity-uuid="5b9378ec-93ad-4296-a5cb-a67970c96a2e" height="297" src="https://wigner.hu/sites/default/files/inline-images/KT1.jpg" width="441" /><br />
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<em><strong>Figure 1.</strong> The decomposition of the relevant map f into the subsequent actions of a contracting two-qubit operation and a single-qubit unitary operation. (a) The effect of the decomposition on the complex plane (projection of the Bloch sphere), representing the initial states of the qubit. States within the solid circle are matched. (b) The same decomposition represented on the Bloch sphere.</em><br />
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<strong>Quantum walks </strong>— Measurements on a quantum particle unavoidably affect its state, since the otherwise unitary evolution of the system is interrupted by a nonunitary projection operation. To probe measurement-induced effects in the state dynamics using a quantum simulator, the challenge is to implement controlled measurements on a small subspace of the system and continue the evolution from the complementary subspace. A powerful platform for versatile quantum evolution is represented by photonic quantum walks because of their high control over all relevant parameters. However, measurement-induced dynamics in such a platform have not yet been realized. We participated in the implementation (at the University of Paderborn) of controlled measurements in a discrete-time quantum walk based on time-multiplexing. This was achieved by adding a deterministic outcoupling of the optical signal to include measurements constrained to specific positions resulting in the projection of the walker’s state on the remaining ones. With this platform and coherent input light, we experimentally simulated measurement-induced single-particle quantum dynamics. We demonstrated the difference between dynamics with only a single measurement at the final step and those including measurements during the evolution. To this aim, we studied recurrence as a figure of merit, that is, the return probability to the walker’s starting position, which was measured in the two cases. We tracked the development of the return probability over 36 time steps and observed the onset of both recurrent and transient evolution as an effect of the different measurement schemes, a signature which only emerges for quantum systems. Our simulation of the observed one-particle conditional quantum dynamics does not require a genuine quantum particle but was demonstrated with coherent light.<br />
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<img alt="kt2" data-entity-type="file" data-entity-uuid="ab8d0e4a-e0cd-42bf-9ba0-84e22b497bcc" height="283" src="https://wigner.hu/sites/default/files/inline-images/KT2.jpg" width="439" /><br />
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<em><strong>Figure 2.</strong> Schematic of the experimental setup of the time-multiplexed quantum walk with active in- and outcoupling realized by two EOMs (electro-optical modulators). The active control of the switches allows to implement in the time domain both the continual and reset measurement schemes. HWP, half-wave plate; PBS, polarizing beam splitter; SMF, single-mode fiber; SNSPDs, superconducting nanowire single-photon detectors.</em> <br />
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<strong>Ro-vibrational quantum states in molecules</strong> — We determined the internal-axis system (IAS) of molecules with a large amplitude internal motion (LAM) by integrating the kinematic equation of the IAS by Lie-group and Lie-algebraic methods. Numerical examples on hydrogen peroxide, nitrous acid, and acetaldehyde demonstrate the methods. By exploiting the special product structure of the solution matrix, we devised simple methods for calculating the transformation to the rho-axis system (RAS) along with the value of the parameter ρ characterizing a RAS rotational-LAM kinetic energy operator. The parameter ρ so calculated agrees exactly with that one obtained by the Floquet method as shown in the example of acetaldehyde. We gave geometrical interpretation of ρ. We numerically demonstated the advantageous property of the RAS over the IAS in retaining simple periodic boundary conditions.<br />
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<strong>Nanophotonics </strong>— Nonlinear second harmonic wave generation (SHG) has been thoroughly examined in one dimension both analytically and numerically. Recently, the application of advanced domain poling techniques enabled the fabrication of two-dimensional (2D) patterns of the sign of the nonlinear coefficient in certain nonlinear crystals, such as LiNbO3 and LiTaO3 . This method can be used to achieve quasi phase matching in SHG and hence amplification of the second harmonic fields in 2D. We have worked out a true vectorial numerical method for the simulation of SHG by extending the finite difference frequency domain method (FDFD). Our nonlinear method (NL-FDFD) operates directly on the electromagnetic fields, uses two meshes for the simulation (for ω and 2ω fields), and handles the nonlinear coupling as an interaction between the two meshes. Final field distributions can be obtained by a small number of iteration steps. NL-FDFD can be applied in arbitrarily structured linear media with an arbitrarily structured χ^(2) component both in the small conversion efficiency and the pump depleted cases.<br />
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<img alt="kt3" data-entity-type="file" data-entity-uuid="e15fd337-6bd1-4dfd-9950-ff5d117d8f4e" height="461" src="https://wigner.hu/sites/default/files/inline-images/KT3.jpg" width="358" /><br />
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<em><strong>Figure 3.</strong> Magnitude of the Ez field components for (a) fundamental wave (b) second harmonic wave at the resonant frequency for five arrays of cylinders. We show here the result of a model calculation: the underlying dielectric structure consists of periodic arrays of nonlinear cylinders, it is infinite in the x-direction and there are five periods in the y-direction. The fundamental wave propagates in the positive y-direction, and it can be tilted from normal incidence. At certain angles and frequencies the structure exhibits double resonance: the reflectivity is close to unity both for the fundamental and for the second harmonic wave</em><br />
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<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="https://wigner.hu/hu/user/171" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">Werovszky Veronika</span></span>
<span class="field field--name-created field--type-created field--label-hidden">k, 08/06/2019 - 13:31</span>
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<div class="field__item"><time datetime="2018-01-02T12:00:00Z" class="datetime">k, 01/02/2018 - 12:00</time>
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Tue, 06 Aug 2019 11:31:05 +0000Werovszky Veronika942 at https://wigner.hu2017_Quantum Information and Foundations of Quantum Mechanics Group
https://wigner.hu/hu/node/1471
<span class="field field--name-title field--type-string field--label-hidden">2017_Quantum Information and Foundations of Quantum Mechanics Group</span>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><h4><strong>2017</strong></h4>
<p><strong>Measurement-induced non-linear transformations.</strong> — We proposed a cavity quantum electrodynamical scenario for implementing a Schrödinger microscope capable of amplifying differences between non-orthogonal atomic quantum states. The scheme involves an ensemble of identically prepared two-level atoms interacting pairwise with a single mode of the radiation field as described by the Tavis-Cummings model (Fig. 1).</p>
<p><img alt="quantuminformatics1" data-entity-type="file" data-entity-uuid="6caed67e-9d89-40ad-8ebe-e762ad647b4a" height="307" src="https://wigner.hu/sites/default/files/inline-images/quantuminformatics1.png" width="410" /></p>
<p><em><strong>Figure 1. </strong>Illustration of the scheme. Two two-level atoms in the same state interact with the cavity field prepared in a coherent state. Before the interaction, a unitary gate is applied to one of the atoms, and after the interaction and the projection of the field onto the initial coherent state, this same atom is projected onto its ground state. Finally, the other atom is left in a non-linearly transformed state.</em></p>
<p>We showed that by repeated measurements of the cavity field and of one atom within each pair, a measurement-induced non-linear quantum transformation of the relevant atomic states can be realized. The intricate dynamical properties of this non-linear quantum transformation, which exhibits measurement-induced chaos, allow approximate orthogonalization of atomic states by purification after a few iterations of the protocol and, thus, the application of the scheme for quantum state discrimination.</p>
<p><strong>Topological phases.</strong> — We discovered topological features of the Hofstadter butterfly spectra of periodically driven systems. The butterfly is the fractal spectrum of energy eigenstates of a quantum lattice system in a magnetic field. It was discovered numerically (1976, predating the word "fractal"), analyzed analytically (contributing to the topological understanding of the quantum Hall effect), and it is about to be observed experimentally on laser-trapped cold atoms and in graphene. We found that in periodically driven systems, where the drive is very far from just a perturbation, the Hofstadter butterfly can "take flight", i.e., can "wind" in quasienergy (Fig. 2). This behaviour is closely related to a recently discovered topological invariant unique to such non-perturbatively driven systems, and gives us a way to numerically evaluate and perhaps experimentally observe this invariant in an efficient way.</p>
<p><img alt="quantuminformatics2" data-entity-type="file" data-entity-uuid="33eccd05-0e5d-4aa2-abb9-40ac9c6d20a8" height="359" src="https://wigner.hu/sites/default/files/inline-images/quantuminformatics2.jpg" width="359" /></p>
<p><em><strong>Figure 2.</strong> The spectrum of quasienergies of a periodically driven system (quantum walk) can wind as a function of applied magnetic field. The winding is quantized, and reveals a bulk topological invariant of the system.</em></p>
<p>Ro-vibrational quantum states in molecules. — Recently, a general expression for Eckart-frame Hamilton operators has been obtained by the gateway Hamiltonian method. The kinetic energy operator in this general Hamiltonian is nearly identical to that of the Eckart-Watson operator even when curvilinear vibrational coordinates are employed. Its different realizations correspond to different methods of calculating Eckart displacements. There are at least two different methods for calculating such displacements: rotation and projection. In our work, the application of Eckart Hamiltonian operators constructed by rotation and projection was numerically demonstrated in calculating vibrational energy levels. The numerical examples confirm that there is no need for rotation to construct an Eckart ro-vibrational Hamiltonian. The application of the gateway method is advantageous even when rotation is used since it obviates the need for differentiation of the matrix rotating into the Eckart frame. Simple geometrical arguments explain that there are infinitely many different methods for calculating Eckart displacements. The geometrical picture also suggests that a unique Eckart displacement vector may be defined as the shortest (mass-weighted) Eckart displacement vector among Eckart displacement vectors corresponding to configurations related by rotation. Its length, as shown analytically and demonstrated by numerical examples, is equal to or less than that of the Eckart displacement vector one can obtain by rotation to the Eckart frame.</p>
<p><strong>Nanophotonics. </strong>— We have worked out a true vectorial numerical method for the simulation of the non-linear second harmonic generation process by extending the finite difference frequency domain method (FDFD). Our non-linear method (NL-FDFD) operates directly on the electromagnetic fields, uses two meshes for the simulation (for ω and 2ω fields) and handles the non-linear coupling as an interaction between the two meshes. Final field distributions can be obtained by a small number of iteration steps. NL-FDFD can be applied in arbitrarily structured linear media with an arbitrarily structured χ (2) component both in the small-conversion-efficiency and the pump-depleted cases.</p></div>
<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="https://wigner.hu/hu/user/124" typeof="schema:Person" property="schema:name" datatype="" content="13566@wigner.mta.hu" xml:lang="">Dovicsin-Pénte…</span></span>
<span class="field field--name-created field--type-created field--label-hidden">v, 05/27/2018 - 13:40</span>
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<div class="field__item"><time datetime="2017-01-02T12:00:00Z" class="datetime">h, 01/02/2017 - 12:00</time>
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Sun, 27 May 2018 11:40:38 +0000Dovicsin-Péntek Csilla Klára1471 at https://wigner.hu