2000 character limit reached
Unveiling the nonclassicality within quasi-distribution representations through deep learning
Published 26 Dec 2023 in quant-ph | (2312.16055v2)
Abstract: To unequivocally distinguish genuine quantumness from classicality, a widely adopted approach focuses on the negative values of a quasi-distribution representation as compelling evidence of nonclassicality. Prominent examples include the dynamical process nonclassicality characterized by the canonical Hamiltonian ensemble representation (CHER) and the nonclassicality of quantum states characterized by the Wigner function. However, to construct a multivariate joint quasi-distribution function with negative values from experimental data is typically highly cumbersome. Here we propose a computational approach utilizing a deep generative model, processing three marginals, to construct the bivariate joint quasi-distribution functions. We first apply our model to tackle the challenging problem of the CHERs, which lacks universal solutions, rendering the problem ground-truth (GT) deficient. To overcome the GT deficiency of the CHER problem, we design optimal synthetic datasets to train our model. While trained with synthetic data, the physics-informed optimization enables our model to capture the detrimental effect of the thermal fluctuations on nonclassicality, which cannot be obtained from any analytical solutions. This underscores the reliability of our approach. This approach also allows us to predict the Wigner functions subject to thermal noises. Our model predicts the Wigner functions with a prominent accuracy by processing three marginals of probability distributions. Our approach also provides a significant reduction of the experimental efforts of constructing the Wigner functions of quantum states, giving rise to an efficient alternative way to realize the quantum state tomography.
- L. E. Ballentine, “The statistical interpretation of quantum mechanics,” Rev. Mod. Phys. 42, 358 (1970).
- W. H. Zurek, “Decoherence, einselection, and the quantum origins of the classical,” Rev. Mod. Phys. 75, 715 (2003).
- K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: Discord and related measures,” Rev. Mod. Phys. 84, 1655 (2012).
- A. Aspect, P. Grangier, and G. Roger, “Experimental tests of realistic local theories via bell’s theorem,” Phys. Rev. Lett. 47, 460 (1981).
- B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682 (2015).
- M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
- L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
- J. S. Bell, “On the einstein podolsky rosen paradox,” Physics 1, 195 (1964).
- A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777 (1935).
- N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419 (2014).
- E. P. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749 (1932).
- A. Kenfack and K. Życzkowski, “Negativity of the wigner function as an indicator of non-classicality,” J. Opt. B Quantum Semicl. Opt. 6, 396 (2004).
- R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766 (1963).
- E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277 (1963).
- N. Lambert, C. Emary, Y.-N. Chen, and F. Nori, “Distinguishing quantum and classical transport through nanostructures,” Phys. Rev. Lett. 105, 176801 (2010).
- S. Rahimi-Keshari, T. Kiesel, W. Vogel, S. Grandi, A. Zavatta, and M. Bellini, “Quantum process nonclassicality,” Phys. Rev. Lett. 110, 160401 (2013).
- E. J. O’Reilly and A. Olaya-Castro, ‘‘Non-classicality of the molecular vibrations assisting exciton energy transfer at room temperature,” Nat. Commun. 5, 3012 (2014).
- K. K. Sabapathy, “Process output nonclassicality and nonclassicality depth of quantum-optical channels,” Phys. Rev. A 93, 042103 (2016).
- A. Smirne, D. Egloff, M. G. Díaz, M. B. Plenio, and S. F. Huelga, “Coherence and non-classicality of quantum markov processes,” Quantum Sci. Technol. 4, 01LT01 (2019).
- S. Milz, D. Egloff, P. Taranto, T. Theurer, M. B. Plenio, A. Smirne, and S. F. Huelga, “When is a non-markovian quantum process classical?” Phys. Rev. X 10, 041049 (2020).
- A. Seif, Y.-X. Wang, and A. A. Clerk, “Distinguishing between quantum and classical markovian dephasing dissipation,” Phys. Rev. Lett. 128, 070402 (2022).
- H.-B. Chen, P.-Y. Lo, C. Gneiting, J. Bae, Y.-N. Chen, and F. Nori, “Quantifying the nonclassicality of pure dephasing,” Nat. Commun. 10, 3794 (2019).
- H.-B. Chen and Y.-N. Chen, “Canonical hamiltonian ensemble representation of dephasing dynamics and the impact of thermal fluctuations on quantum-to-classical transition,” Sci. Rep. 11, 10046 (2021).
- M.-C. Lin, P.-Y. Lo, F. Nori, and H.-B. Chen, “Precession-induced nonclassicality of the free induction decay of nv centers by a dynamical polarized nuclear spin bath,” J. Phys.: Condens. Matter 34, 505701 (2022).
- C. M. Kropf, C. Gneiting, and A. Buchleitner, “Effective dynamics of disordered quantum systems,” Phys. Rev. X 6, 031023 (2016).
- H.-B. Chen, C. Gneiting, P.-Y. Lo, Y.-N. Chen, and F. Nori, “Simulating open quantum systems with hamiltonian ensembles and the nonclassicality of the dynamics,” Phys. Rev. Lett. 120, 030403 (2018).
- H.-B. Chen, ‘‘Effects of symmetry breaking of the structurally-disordered hamiltonian ensembles on the anisotropic decoherence of qubits,” Sci. Rep. 12, 2869 (2022).
- D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, “Measurement of the wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum,” Phys. Rev. Lett. 70, 1244 (1993).
- G. Breitenbach, S. Schiller, and J. Mlynek, “Measurement of the quantum states of squeezed light,” Nature 387, 471 (1997).
- A. I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, “Quantum state reconstruction of the single-photon fock state,” Phys. Rev. Lett. 87, 050402 (2001).
- S. Deléglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, “Reconstruction of non-classical cavity field states with snapshots of their decoherence,” Nature 455, 510 (2008).
- C. Flühmann and J. P. Home, “Direct characteristic-function tomography of quantum states of the trapped-ion motional oscillator,” Phys. Rev. Lett. 125, 043602 (2020).
- L. G. Lutterbach and L. Davidovich, “Method for direct measurement of the wigner function in cavity qed and ion traps,” Phys. Rev. Lett. 78, 2547 (1997).
- K. Banaszek, C. Radzewicz, K. Wódkiewicz, and J. S. Krasiński, “Direct measurement of the wigner function by photon counting,” Phys. Rev. A 60, 674 (1999).
- P. Bertet, A. Auffeves, P. Maioli, S. Osnaghi, T. Meunier, M. Brune, J. M. Raimond, and S. Haroche, “Direct measurement of the wigner function of a one-photon fock state in a cavity,” Phys. Rev. Lett. 89, 200402 (2002).
- B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon schrödinger cat states,” Science 342, 607 (2013).
- F.-R. Winkelmann, C. A. Weidner, G. Ramola, W. Alt, D. Meschede, and A. Alberti, “Direct measurement of the wigner function of atoms in an optical trap,” J. Phys. B: At. Mol. Opt. Phys. 55, 194004 (2022).
- S. Ahmed, C. Sánchez Muñoz, F. Nori, and A. F. Kockum, “Quantum state tomography with conditional generative adversarial networks,” Phys. Rev. Lett. 127, 140502 (2021).
- G. D. Lin, X. Dou, S. Kuriki, and J.-S. Huang, “Recent developments on the construction of bivariate distributions with fixed marginals,” J. Stat. Distrib. App. 1, 14 (2014).
- T. T. Takeuchi, “Constructing a bivariate distribution function with given marginals and correlation: application to the galaxy luminosity function,” Mon. Not. Roy. Astron. Soc. 406, 1830 (2010).
- F. Cicalese, L. Gargano, and U. Vaccaro, “Minimum-entropy couplings and their applications,” IEEE Trans. Inf. Theory 65, 3436 (2019).
- S. H. Ong, R. C. Gupta, T. Ma, and S. Z. Sim, “Bivariate conway–maxwell poisson distributions with given marginals and correlation,” J. Stat. Theory Pract. 15, 10 (2021).
- K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2016) pp. 770–778.
- H.-N. Xiong, P.-Y. Lo, W.-M. Zhang, D. H. Feng, and F. Nori, “Non-markovian complexity in the quantum-to-classical transition,” Sci. Rep. 5, 13353 (2015).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.
