Emergent classicality in general multipartite states and channels

Xiao-Liang Qi and Daniel Ranard

Department of Physics, Stanford University, Stanford, CA 94305-4060, USA

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

In a quantum measurement process, classical information about the measured system spreads throughout the environment. Meanwhile, quantum information about the system becomes inaccessible to local observers. Here we prove a result about quantum channels indicating that an aspect of this phenomenon is completely general. We show that for any evolution of the system and environment, for everywhere in the environment excluding an $O(1)$-sized region we call the "quantum Markov blanket," any locally accessible information about the system must be approximately classical, i.e. obtainable from some fixed measurement. The result strengthens the earlier result of Brandão et al. ($\textit{Nat. comm. 6:7908}$) in which the excluded region was allowed to grow with total environment size. It may also be seen as a new consequence of the principles of no-cloning or monogamy of entanglement. Our proof offers a constructive optimization procedure for determining the "quantum Markov blanket" region, as well as the effective measurement induced by the evolution. Alternatively, under channel-state duality, our result characterizes the marginals of multipartite states.

Why do quantum-mechanical systems often appear to behave classically at large scales? Part of the answer lies in decoherence: when a quantum system interacts with an environment, often the environment effectively “measures” the system. Afterward, local observers in the environment can only learn classical information about the system. This phenomenon might seem to depend on the exact form of the system-environment interaction. However, we prove that an aspect of this phenomenon is general to all quantum evolutions. The structure of quantum mechanics itself ensures that most observers can only learn compatible, classical information about any system.

We prove a general result about quantum states and channels that guarantees the above classicality. More precisely, we show that whenever a subsystem interacts with an environment, almost all local observers in the environment can only learn classical information about the system. This result also provides a new quantitative form of two well-known principles: no-cloning, i.e. the inability to clone quantum information, and monogamy of entanglement, i.e. the inability of one system to be highly entangled with multiple others.

Our proof also offers an optimization procedure for determining the effective measurement made by the environment. This procedure could be used to analyze the emergence of classicality in numerically tractable systems like spin chains. Taking advantage of our general results, future work might also identify the more specific conditions under which the quantum dynamics allow an effective classical description.

► BibTeX data

► References

[1] Harold Ollivier, David Poulin, and Wojciech H Zurek. Environment as a witness: Selective proliferation of information and emergence of objectivity in a quantum universe. Physical review A, 72 (4): 042113, 2005. 10.1103/​PhysRevA.72.042113.
https:/​/​doi.org/​10.1103/​PhysRevA.72.042113

[2] Robin Blume-Kohout and Wojciech H Zurek. Quantum darwinism: Entanglement, branches, and the emergent classicality of redundantly stored quantum information. Physical review A, 73 (6): 062310, 2006. 10.1103/​PhysRevA.73.062310.
https:/​/​doi.org/​10.1103/​PhysRevA.73.062310

[3] C Jess Riedel and Wojciech H Zurek. Quantum darwinism in an everyday environment: Huge redundancy in scattered photons. Physical review letters, 105 (2): 020404, 2010. 10.1103/​PhysRevLett.105.020404.
https:/​/​doi.org/​10.1103/​PhysRevLett.105.020404

[4] Wojciech H Zurek. Quantum darwinism, classical reality, and the randomness of quantum jumps. Physics today, 67 (10): 44, 2014. 10.1063/​PT.3.2550.
https:/​/​doi.org/​10.1063/​PT.3.2550

[5] Michael Zwolak, C Jess Riedel, and Wojciech H Zurek. Amplification, redundancy, and quantum chernoff information. Physical review letters, 112 (14): 140406, 2014. 10.1103/​PhysRevLett.112.140406.
https:/​/​doi.org/​10.1103/​PhysRevLett.112.140406

[6] C Jess Riedel, Wojciech H Zurek, and Michael Zwolak. Objective past of a quantum universe: Redundant records of consistent histories. Physical Review A, 93 (3): 032126, 2016. 10.1103/​PhysRevA.93.032126.
https:/​/​doi.org/​10.1103/​PhysRevA.93.032126

[7] Fernando G. Sl. L. Brandao, Marco Piani, and Horodecki. Pawel. Generic emergence of classical features in quantum darwinism. Nature Communications, 6, Aug 2015. 10.1038/​ncomms8908.
https:/​/​doi.org/​10.1038/​ncomms8908

[8] Judea Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 1988. ISBN 1558604790. 10.1016/​C2009-0-27609-4.
https:/​/​doi.org/​10.1016/​C2009-0-27609-4

[9] Mark M. Wilde. Quantum Information Theory. Cambridge University Press, New York, NY, USA, 1st edition, 2013. ISBN 1107034256, 9781107034259. 10.1017/​9781316809976.
https:/​/​doi.org/​10.1017/​9781316809976

[10] Michael Horodecki, Peter W Shor, and Mary Beth Ruskai. Entanglement breaking channels. Reviews in Mathematical Physics, 15 (06): 629–641, 2003. 10.1142/​S0129055X03001709.
https:/​/​doi.org/​10.1142/​S0129055X03001709

[11] JK Korbicz, Paweł Horodecki, and Ryszard Horodecki. Quantum-correlation breaking channels, broadcasting scenarios, and finite markov chains. Physical Review A, 86 (4): 042319, 2012. 10.1103/​PhysRevA.86.042319.
https:/​/​doi.org/​10.1103/​PhysRevA.86.042319

[12] William Matthews, Stephanie Wehner, and Andreas Winter. Distinguishability of quantum states under restricted families of measurements with an application to quantum data hiding. Communications in Mathematical Physics, 291 (3): 813–843, 2009. 10.1007/​s00220-009-0890-5.
https:/​/​doi.org/​10.1007/​s00220-009-0890-5

[13] Fernando GSL Brandao, Matthias Christandl, and Jon Yard. Faithful squashed entanglement. Communications in Mathematical Physics, 306 (3): 805, 2011. 10.1007/​s00220-011-1302-1.
https:/​/​doi.org/​10.1007/​s00220-011-1302-1

[14] Fernando GSL Brandao and Aram W Harrow. Quantum de finetti theorems under local measurements with applications. Communications in Mathematical Physics, 353 (2): 469–506, 2017. 10.1007/​s00220-017-2880-3.
https:/​/​doi.org/​10.1007/​s00220-017-2880-3

[15] Fernando GSL Brandao and Aram W Harrow. Product-state approximations to quantum states. Communications in Mathematical Physics, 342 (1): 47–80, 2016. 10.1007/​s00220-016-2575-1.
https:/​/​doi.org/​10.1007/​s00220-016-2575-1

[16] David Sutter. Approximate quantum markov chains. In Approximate Quantum Markov Chains, pages 75–100. Springer, 2018. 10.1007/​978-3-319-78732-9_5.
https:/​/​doi.org/​10.1007/​978-3-319-78732-9_5

[17] Michael A Nielsen and Dénes Petz. A simple proof of the strong subadditivity inequality. arXiv preprint quant-ph/​0408130, 2004. URL https:/​/​arxiv.org/​abs/​quant-ph/​0408130.
arXiv:quant-ph/0408130

[18] Omar Fawzi and Renato Renner. Quantum conditional mutual information and approximate markov chains. Communications in Mathematical Physics, 340 (2): 575–611, 2015. 10.1007/​s00220-015-2466-x.
https:/​/​doi.org/​10.1007/​s00220-015-2466-x

[19] Mari Carmen Bañuls, J Ignacio Cirac, and Matthew B Hastings. Strong and weak thermalization of infinite nonintegrable quantum systems. Physical review letters, 106 (5): 050405, 2011. 10.1103/​PhysRevLett.106.050405.
https:/​/​doi.org/​10.1103/​PhysRevLett.106.050405

[20] Giacomo Mauro D'Ariano, Paoloplacido Lo Presti, and Paolo Perinotti. Classical randomness in quantum measurements. Journal of Physics A: Mathematical and General, 38 (26): 5979, 2005. 10.1088/​0305-4470/​38/​26/​010.
https:/​/​doi.org/​10.1088/​0305-4470/​38/​26/​010

[21] Maximilian Schlosshauer. Quantum decoherence. Physics Reports, 831: 1–57, 2019. 10.1016/​j.physrep.2019.10.001.
https:/​/​doi.org/​10.1016/​j.physrep.2019.10.001

[22] Wojciech Hubert Zurek. Decoherence, einselection, and the quantum origins of the classical. Reviews of modern physics, 75 (3): 715, 2003. 10.1103/​RevModPhys.75.715.
https:/​/​doi.org/​10.1103/​RevModPhys.75.715

[23] Caterina Foti, Teiko Heinosaari, Sabrina Maniscalco, and Paola Verrucchi. Whenever a quantum environment emerges as a classical system, it behaves like a measuring apparatus. Quantum, 3: 179, 2019. 10.22331/​q-2019-08-26-179.
https:/​/​doi.org/​10.22331/​q-2019-08-26-179

[24] Jarosław K Korbicz, Edgar A Aguilar, Piotr Ć wikliński, and P Horodecki. Generic appearance of objective results in quantum measurements. Physical Review A, 96 (3): 032124, 2017. 10.1103/​PhysRevA.96.032124.
https:/​/​doi.org/​10.1103/​PhysRevA.96.032124

[25] Patrick J Coles, Li Yu, Vlad Gheorghiu, and Robert B Griffiths. Information-theoretic treatment of tripartite systems and quantum channels. Physical Review A, 83 (6): 062338, 2011. 10.1103/​PhysRevA.83.062338.
https:/​/​doi.org/​10.1103/​PhysRevA.83.062338

[26] Teiko Heinosaari, Takayuki Miyadera, and Mário Ziman. An invitation to quantum incompatibility. Journal of Physics A: Mathematical and Theoretical, 49 (12): 123001, 2016. 10.1088/​1751-8113/​49/​12/​123001.
https:/​/​doi.org/​10.1088/​1751-8113/​49/​12/​123001

[27] Carlton M Caves, Christopher A Fuchs, and Rüdiger Schack. Unknown quantum states: the quantum de finetti representation. Journal of Mathematical Physics, 43 (9): 4537–4559, 2002. 10.1063/​1.1494475.
https:/​/​doi.org/​10.1063/​1.1494475

[28] Ke Li and Graeme Smith. Quantum de finetti theorem under fully-one-way adaptive measurements. Physical review letters, 114 (16): 160503, 2015. 10.1103/​PhysRevLett.114.160503.
https:/​/​doi.org/​10.1103/​PhysRevLett.114.160503

[29] Masato Koashi and Andreas Winter. Monogamy of quantum entanglement and other correlations. Physical Review A, 69 (2): 022309, 2004. 10.1103/​PhysRevA.69.022309.
https:/​/​doi.org/​10.1103/​PhysRevA.69.022309

[30] Paul A. Knott, Tommaso Tufarelli, Marco Piani, and Gerardo Adesso. Generic emergence of objectivity of observables in infinite dimensions. Phys. Rev. Lett., 121: 160401, Oct 2018. 10.1103/​PhysRevLett.121.160401.
https:/​/​doi.org/​10.1103/​PhysRevLett.121.160401

[31] Eugenia Colafranceschi, Ludovico Lami, Gerardo Adesso, and Tommaso Tufarelli. Refined diamond norm bounds on the emergence of objectivity of observables. Journal of Physics A: Mathematical and Theoretical, 53 (39): 395305, 2020. 10.1088/​1751-8121/​aba469.
https:/​/​doi.org/​10.1088/​1751-8121/​aba469

[32] Guillaume Aubrun, Ludovico Lami, Carlos Palazuelos, Stanisław J Szarek, and Andreas Winter. Universal gaps for xor games from estimates on tensor norm ratios. Communications in Mathematical Physics, pages 1–46, 2020. 10.1007/​s00220-020-03688-2.
https:/​/​doi.org/​10.1007/​s00220-020-03688-2

[33] Ludovico Lami, Carlos Palazuelos, and Andreas Winter. Ultimate data hiding in quantum mechanics and beyond. Communications in Mathematical Physics, 361 (2): 661–708, 2018. 10.1007/​s00220-018-3154-4.
https:/​/​doi.org/​10.1007/​s00220-018-3154-4

Cited by

[1] Thao P. Le and Alexandra Olaya-Castro, "Witnessing non-objectivity in the framework of strong quantum Darwinism", Quantum Science and Technology 5 4, 045012 (2020).

[2] Akram Touil, Bin Yan, Davide Girolami, Sebastian Deffner, and Wojciech H. Zurek, "Eavesdropping on the Decohering Environment: Quantum Darwinism, Amplification, and the Origin of Objective Classical Reality", arXiv:2107.00035.

[3] Thao P. Le, Piotr Mironowicz, and Paweł Horodecki, "Blurred quantum Darwinism across quantum reference frames", Physical Review A 102 6, 062420 (2020).

[4] Wojciech Hubert Zurek, "Emergence of the Classical from within the Quantum Universe", arXiv:2107.03378.

[5] Mark Girard, Martin Plávala, and Jamie Sikora, "Jordan products of quantum channels and their compatibility", Nature Communications 12, 2129 (2021).

[6] Eugenia Colafranceschi, Ludovico Lami, Gerardo Adesso, and Tommaso Tufarelli, "Refined diamond norm bounds on the emergence of objectivity of observables", Journal of Physics A Mathematical General 53 39, 395305 (2020).

[7] Rene Allerstorfer, Harry Buhrman, Florian Speelman, and Philip Verduyn Lunel, "New Protocols and Ideas for Practical Quantum Position Verification", arXiv:2106.12911.

[8] Alexandre Feller, Guillaume CÅ`uret Cauquil, and Benjamin Roussel, "Einselection from incompatible decoherence channels", Physical Review A 101 6, 062107 (2020).

The above citations are from SAO/NASA ADS (last updated successfully 2021-10-24 16:31:01). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2021-10-24 16:30:59).