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Quadrature Coherence Scale of Linear Combinations of Gaussian Functions in Phase Space (2402.04404v3)

Published 6 Feb 2024 in quant-ph

Abstract: The quadrature coherence scale (QCS) is a recently introduced measure that was shown to be an efficient witness of nonclassicality. It takes a simple form for pure and Gaussian states, but a general expression for mixed states tends to be prohibitively unwieldy. In this paper, we introduce a method for computing the quadrature coherence scale of quantum states characterized by Wigner functions expressible as linear combinations of Gaussian functions. Notable examples within this framework include cat states, GKP states, and states resulting from Gaussian transformations, measurements, and breeding protocols. In particular, we show that the quadrature coherence scale serves as a valuable tool for examining the scalability of nonclassicality in the presence of loss. Our findings lead us to put forth a conjecture suggesting that, subject to 50% loss or more, all pure states lose any QCS-certifiable nonclassicality. We also consider the quadrature coherence scale as a measure of quality of the output state of the breeding protocol.

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References (100)
  1. Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47:777–780, May 1935.
  2. John Stewart Bell. On the Einstein Podolsky Rosen paradox. Physics, 1(3):195–200, 1964.
  3. John S. Bell. On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys., 38:447–452, Jul 1966.
  4. The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics, 17(1):59–87, 1967.
  5. Bas C. van Fraassen. The Charybdis of Realism: Epistemological Implications of Bell’s Inequality. Synthese, 52(1):25–38, 1982.
  6. Artur K. Ekert. Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett., 67:661–663, Aug 1991.
  7. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Physical Review Letters, 70:1895–1899, Mar 1993.
  8. Peter W. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Review, 41(2):303–332, 1999.
  9. Lov K Grover. A fast quantum mechanical algorithm for database search. In Proceedings of the twenty-eighth annual ACM symposium on Theory of computing, pages 212–219, 1996.
  10. Quantum-enhanced measurements: Beating the standard quantum limit. Science, 306(5700):1330–1336, 2004.
  11. Jonathan P. Dowling. Quantum optical metrology – the lowdown on high-N00N states. Contemporary Physics, 49(2):125–143, 2008.
  12. Johan Åberg. Catalytic coherence. Phys. Rev. Lett., 113:150402, Oct 2014.
  13. The extraction of work from quantum coherence. New Journal of Physics, 18(2):023045, feb 2016.
  14. Experimental generation of squeezed cat states with an operation allowing iterative growth. Phys. Rev. Lett., 114:193602, May 2015.
  15. Generating grid states from Schrödinger-cat states without postselection. Phys. Rev. A, 97:022341, Feb 2018.
  16. Transcoherent states: Optical states for maximal generation of atomic coherence. Physical Review X Quantum, 1:020306, Oct 2020.
  17. Cohering and decohering power of quantum channels. Phys. Rev. A, 92:032331, Sep 2015.
  18. Frozen quantum coherence. Phys. Rev. Lett., 114:210401, May 2015.
  19. A note on coherence power of n-dimensional unitary operators. Quantum Info. Comput., 16(15–16):1282–1294, nov 2016.
  20. Cohering power of quantum operations. Physics Letters A, 381(19):1670–1676, 2017.
  21. Johan Aberg. Quantifying Superposition. arXiv e-prints, pages quant–ph/0612146, December 2006.
  22. Quantifying coherence. Physical Review Letters, 113:140401, Sep 2014.
  23. Measuring quantum coherence with entanglement. Phys. Rev. Lett., 115:020403, Jul 2015.
  24. Trace-distance measure of coherence. Phys. Rev. A, 93:012110, Jan 2016.
  25. Alternative framework for quantifying coherence. Phys. Rev. A, 94:060302, Dec 2016.
  26. Alexey E. Rastegin. Quantum-coherence quantifiers based on the Tsallis relative α𝛼\alphaitalic_α entropies. Phys. Rev. A, 93:032136, Mar 2016.
  27. Mark Hillery. Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation. Phys. Rev. A, 93:012111, Jan 2016.
  28. Davide Girolami. Observable measure of quantum coherence in finite dimensional systems. Phys. Rev. Lett., 113:170401, Oct 2014.
  29. Directly measuring the degree of quantum coherence using interference fringes. Phys. Rev. Lett., 118:020403, Jan 2017.
  30. Experimental demonstration of observability and operability of robustness of coherence. Phys. Rev. Lett., 120:230504, Jun 2018.
  31. Experimental quantification of coherence of a tunable quantum detector. Phys. Rev. Lett., 125:060404, Aug 2020.
  32. Experimental progress on quantum coherence: Detection, quantification, and manipulation. Advanced Quantum Technologies, 4(9):2100040, 2021.
  33. Optimal estimation of quantum coherence by bell state measurement: A case study. Entropy, 25(10), 2023.
  34. Operational resource theory of coherence. Phys. Rev. Lett., 116:120404, Mar 2016.
  35. Colloquium: Quantum coherence as a resource. Reviews of Modern Physics, 89:041003, Oct 2017.
  36. Operational resource theory of quantum channels. Phys. Rev. Res., 2:012035, Feb 2020.
  37. Quadrature coherence scale driven fast decoherence of bosonic quantum field states. Phys. Rev. Lett., 124:090402, Mar 2020.
  38. Measuring nonclassicality of bosonic field quantum states via operator ordering sensitivity. Phys. Rev. Lett., 122:080402, Feb 2019.
  39. Interferometric measurement of the quadrature coherence scale using two replicas of a quantum optical state. Phys. Rev. A, 108:023730, Aug 2023.
  40. Measuring the quadrature coherence scale on a cloud quantum computer. Phys. Rev. A, 107:042610, Apr 2023.
  41. Quantum computation over continuous variables. Phys. Rev. Lett., 82:1784–1787, Feb 1999.
  42. Efficient classical simulation of continuous variable quantum information processes. Phys. Rev. Lett., 88:097904, Feb 2002.
  43. A. Mari and J. Eisert. Positive Wigner functions render classical simulation of quantum computation efficient. Phys. Rev. Lett., 109:230503, Dec 2012.
  44. Mattia Walschaers. Non-Gaussian quantum states and where to find them. PRX Quantum, 2:030204, Sep 2021.
  45. Fast simulation of bosonic qubits via Gaussian functions in phase space. PRX Quantum, 2:040315, Oct 2021.
  46. Simulation of quantum optics by coherent state decomposition. Optica Quantum, 1(2):78–93, Dec 2023.
  47. E. Schrödinger. Die gegenwärtige situation in der quantenmechanik. Naturwissenschaften, 23(48):807–812, Nov 1935.
  48. Wojciech Hubert Zurek. Sub-Planck structure in phase space and its relevance for quantum decoherence. Nature, 412(6848):712–717, 2001.
  49. Macroscopically distinct quantum-superposition states as a bosonic code for amplitude damping. Phys. Rev. A, 59:2631–2634, Apr 1999.
  50. All-optical generation of states for “encoding a qubit in an oscillator”. Opt. Lett., 35(19):3261–3263, Oct 2010.
  51. B. M. Terhal and D. Weigand. Encoding a qubit into a cavity mode in circuit qed using phase estimation. Phys. Rev. A, 93:012315, Jan 2016.
  52. Encoding a qubit in an oscillator. Phys. Rev. A, 64:012310, Jun 2001.
  53. Gaussian quantum information. Rev. Mod. Phys., 84:621–669, May 2012.
  54. Anaelle Hertz. Exploring continuous-variable entropic uncertainty relations and separability criteria in quantum phase space. PhD thesis, 2018.
  55. Correlation functions for coherent fields. Phys. Rev., 140:B676–B682, Nov 1965.
  56. Negativity of the Wigner function as an indicator of non-classicality. Journal of Optics B: Quantum and Semiclassical Optics, 6(10):396–404, aug 2004.
  57. Mark Hillery. Nonclassical distance in quantum optics. Phys. Rev. A, 35:725–732, Jan 1987.
  58. A. Bach and U. Luxmann-Ellinghaus. The simplex structure of the classical states of the quantum harmonic oscillator. Commun. Math. Phys., 107, 1986.
  59. Mark Hillery. Total noise and nonclassical states. Phys. Rev. A, 39:2994–3002, Mar 1989.
  60. Ching Tsung Lee. Theorem on nonclassical states. Phys. Rev. A, 52:3374–3376, Oct 1995.
  61. G. S. Agarwal and K. Tara. Nonclassical character of states exhibiting no squeezing or sub-poissonian statistics. Phys. Rev. A, 46:485–488, Jul 1992.
  62. N. Lütkenhaus and Stephen M. Barnett. Nonclassical effects in phase space. Phys. Rev. A, 51:3340–3342, Apr 1995.
  63. Hilbert-Schmidt distance and non-classicality of states in quantum optics. Journal of Modern Optics, 47(4):633–654, 2000.
  64. Quantifying nonclassicality of one-mode Gaussian states of the radiation field. Phys. Rev. Lett., 88:153601, Mar 2002.
  65. Th. Richter and W. Vogel. Nonclassicality of quantum states: A hierarchy of observable conditions. Phys. Rev. Lett., 89:283601, Dec 2002.
  66. Computable measure of nonclassicality for light. Phys. Rev. Lett., 94:173602, May 2005.
  67. Unified nonclassicality criteria. Phys. Rev. A, 92:011801, Jul 2015.
  68. J. Sperling and W. Vogel. Convex ordering and quantification of quantumness. Physica Scripta, 90(7):074024, june 2015.
  69. Converting nonclassicality into entanglement. Phys. Rev. Lett., 116:080402, Feb 2016.
  70. Moorad Alexanian. Non-classicality criteria: Glauber–Sudarshan P function and Mandel parameter. Journal of Modern Optics, 65(1):16–22, 2018.
  71. Ranjith Nair. Nonclassical distance in multimode bosonic systems. Phys. Rev. A, 95:063835, Jun 2017.
  72. Quantifying nonclassicality by characteristic functions. Phys. Rev. A, 95:053825, May 2017.
  73. Operational resource theory of continuous-variable nonclassicality. Phys. Rev. X, 8:041038, Dec 2018.
  74. Nonclassicality as a quantifiable resource for quantum metrology. Phys. Rev. Lett., 122:040503, Feb 2019.
  75. Convex resource theory of non-Gaussianity. Phys. Rev. A, 97:062337, Jun 2018.
  76. Thermal-difference states of light: Quantum states of heralded photons. Phys. Rev. A, 100:053831, Nov 2019.
  77. Quantifying nonclassicality via Wigner-Yanase skew information. Phys. Rev. A, 100:032116, Sep 2019.
  78. Probing nonclassicality with matrices of phase-space distributions. Quantum, 4:343, October 2020.
  79. Relating the entanglement and optical nonclassicality of multimode states of a bosonic quantum field. Phys. Rev. A, 102:032413, Sep 2020.
  80. Decoherence and nonclassicality of photon-added and photon-subtracted multimode Gaussian states. Phys. Rev. A, 107:043713, Apr 2023.
  81. On the design of photonic quantum circuits, 2023.
  82. The matrix cookbook, nov 2012. Version 20121115.
  83. Quantum error correction with the Gottesman-Kitaev-Preskill code. PRX Quantum, 2:020101, Jun 2021.
  84. Fault-tolerant quantum computation with static linear optics. PRX Quantum, 2:040353, Dec 2021.
  85. Autonomous quantum error correction of Gottesman-Kitaev-Preskill states, 2023.
  86. Progress towards practical qubit computation using approximate Gottesman-Kitaev-Preskill codes. Phys. Rev. A, 101:032315, Mar 2020.
  87. Radim Filip. Gaussian quantum adaptation of non-Gaussian states for a lossy channel. Phys. Rev. A, 87:042308, Apr 2013.
  88. Nicolas C. Menicucci. Fault-tolerant measurement-based quantum computing with continuous-variable cluster states. Phys. Rev. Lett., 112:120504, Mar 2014.
  89. Non-Gaussian and Gottesman–Kitaev–Preskill state preparation by photon catalysis. New Journal of Physics, 21(11):113034, nov 2019.
  90. Conversion of Gaussian states to non-Gaussian states using photon-number-resolving detectors. Phys. Rev. A, 100:052301, Nov 2019.
  91. Measurement-based generation and preservation of cat and grid states within a continuous-variable cluster state. Quantum, 6:769, July 2022.
  92. Gottesman-Kitaev-Preskill qubit synthesizer for propagating light. npj Quantum Information, 9(1):98, 2023.
  93. Quantum nondemolition measurements with optical parametric amplifiers for ultrafast universal quantum information processing. PRX Quantum, 4:010333, Mar 2023.
  94. Propagating Gottesman-Kitaev-Preskill states encoded in an optical oscillator. arXiv e-prints, page arXiv:2309.02306, September 2023.
  95. Seeding Gaussian boson samplers with single photons for enhanced state generation. arXiv e-prints, page arXiv:2311.03432, November 2023.
  96. Machine learning for efficient generation of universal hybrid quantum computing resources. arXiv e-prints, page arXiv:2310.03130, October 2023.
  97. Generation of Flying Logical Qubits using Generalized Photon Subtraction with Adaptive Gaussian Operations. arXiv e-prints, page arXiv:2401.07287, January 2024.
  98. Proposal for a loophole-free violation of bell’s inequalities with a set of single photons and homodyne measurements. New Journal of Physics, 16(5):053001, may 2014.
  99. Enlargement of optical schrödinger’s cat states. Nat, Potonis, 11:379–382, May 2017.
  100. Relating the Glauber-Sudarshan, Wigner and Husimi quasiprobability distributions operationally through the quantum limited amplifier and attenuator channels, 2023.
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