Witnessing quantum memory in non-Markovian processes

Christina Giarmatzi1,2 and Fabio Costa1

1Centre for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, QLD 4072 Australia
2University of Technology Sydney, Centre for Quantum Software and Information, Ultimo NSW 2007, Australia

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

Abstract

We present a method to detect quantum memory in a non-Markovian process. We call a process Markovian when the environment does not provide a memory that retains correlations across different system-environment interactions. We define two types of non-Markovian processes, depending on the required memory being classical or quantum. We formalise this distinction using the process matrix formalism, through which a process is represented as a multipartite state. Within this formalism, a test for entanglement in a state can be mapped to a test for quantum memory in the corresponding process. This allows us to apply separability criteria and entanglement witnesses to the detection of quantum memory. We demonstrate the method in a simple model where both system and environment are single interacting qubits and map the parameters that lead to quantum memory. As with entanglement witnesses, our method of witnessing quantum memory provides a versatile experimental tool for open quantum systems.

The study of open quantum systems is a vast field within quantum physics that concerns the interaction between some system and its environment. Its great importance lies on the fact that every experimental realization of a quantum process faces the possibility of noise coming from the environment. Although in small quantum devices the noise is assumed to be uncorrelated (Markovian) this assumption fails as the size and complexity increases, and the various system-environment interactions become correlated (non-Markovian). These non-Markovian processes can be simulated only by adding an external memory that carries the correlations across the different interactions. The memory required to reproduce the process can be quantum or classical, and being able to distinguish between the two types of non-Markovian noise would lead to different ways of finding its source or correcting for it. Therefore, it is desirable to have efficient methods to decide whether an environment carries a classical or quantum memory.

In this work, we provide a first rigorous definition of classical memory in a non-Markovian process and we present a method that detects that a process is non-Markovian with quantum memory. We do this by mapping our problem to the well known problem of entanglement. We apply our method to an example of a non-Markovian process and present our results of detecting a quantum memory.

► BibTeX data

► References

[1] H. P. Breuer and F. Petruccione, Oxford University Press, Oxford (2002).
https:/​/​doi.org/​10.1093/​acprof:oso/​9780199213900.001.0001

[2] F. Arute, K. Arya, R. Babbush et al., Nature 574, 505 (2019).
https:/​/​doi.org/​10.1038/​s41586-019-1666-5

[3] J. Preskill, Quantum 2, 79 (2018).
https:/​/​doi.org/​10.22331/​q-2018-08-06-79

[4] J. Morris, F. A. Pollock and K. Modi, Non-markovian memory in ibmqx4, (2019), arXiv:1902.07980 [quant-ph].
arXiv:1902.07980

[5] J. Piilo, S. Maniscalco, K. Härkönen et al., Phys. Rev. Lett. 100, 180402 (2008).
https:/​/​doi.org/​10.1103/​PhysRevLett.100.180402

[6] M. M. Wolf and J. I. Cirac, Communications in Mathematical Physics 279, 147 (2008).
https:/​/​doi.org/​10.1007/​s00220-008-0411-y

[7] H.-P. Breuer, E.-M. Laine and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009).
https:/​/​doi.org/​10.1103/​PhysRevLett.103.210401

[8] A. Rivas, S. F. Huelga and M. B. Plenio, Phys. Rev. Lett. 105, 050403 (2010).
https:/​/​doi.org/​10.1103/​PhysRevLett.105.050403

[9] S. C. Hou, X. X. Yi, S. X. Yu et al., Phys. Rev. A 83, 062115 (2011).
https:/​/​doi.org/​10.1103/​PhysRevA.83.062115

[10] D. Chruściński and S. Maniscalco, Phys. Rev. Lett. 112, 120404 (2014).
https:/​/​doi.org/​10.1103/​PhysRevLett.112.120404

[11] Á. Rivas, S. F. Huelga and M. B. Plenio, Reports on Progress in Physics 77, 094001 (2014).
https:/​/​doi.org/​10.1088/​0034-4885/​77/​9/​094001
http:/​/​stacks.iop.org/​0034-4885/​77/​i=9/​a=094001

[12] H.-P. Breuer, E.-M. Laine, J. Piilo et al., Rev. Mod. Phys. 88, 021002 (2016).
https:/​/​doi.org/​10.1103/​RevModPhys.88.021002

[13] L. Li, M. J. Hall and H. M. Wiseman, Physics Reports 759, 1 (2018).
https:/​/​doi.org/​10.1016/​j.physrep.2018.07.001

[14] I. de Vega and D. Alonso, Reviews of Modern Physics 89, 015001 (2017).
https:/​/​doi.org/​10.1103/​RevModPhys.89.015001

[15] J. H. Shapiro, G. Saplakoglu, S.-T. Ho et al., J. Opt. Soc. Am. B 4, 1604 (1987).
https:/​/​doi.org/​10.1364/​JOSAB.4.001604

[16] C. M. Caves and G. J. Milburn, Phys. Rev. A 36, 5543 (1987).
https:/​/​doi.org/​10.1103/​PhysRevA.36.5543

[17] H. M. Wiseman and G. J. Milburn, Phys. Rev. Lett. 70, 548 (1993).
https:/​/​doi.org/​10.1103/​PhysRevLett.70.548

[18] A. A. Budini, Phys. Rev. A 64, 052110 (2001).
https:/​/​doi.org/​10.1103/​PhysRevA.64.052110

[19] D. Zhou, A. Lang and R. Joynt, Quantum Inf. Process. 9, 727 (2010).
https:/​/​doi.org/​10.1007/​s11128-010-0165-2

[20] P. Bordone, F. Buscemi and C. Benedetti, Fluctuation Noise Lett. 11, 1242003 (2012).
https:/​/​doi.org/​10.1142/​S0219477512420035

[21] A. Bodor, L. Diósi, Z. Kallus et al., Phys. Rev. A 87, 052113 (2013).
https:/​/​doi.org/​10.1103/​PhysRevA.87.052113

[22] J.-S. Xu, K. Sun, C.-F. Li et al., Nature Communications 4, 2851 (2013).
https:/​/​doi.org/​10.1038/​ncomms3851

[23] B. Vacchini, Phys. Rev. A 87, 030101 (2013).
https:/​/​doi.org/​10.1103/​PhysRevA.87.030101

[24] A. A. Budini, Phys. Rev. A 97, 052133 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.97.052133

[25] A. Shaji and E. Sudarshan, Physics Letters A 341, 48 (2005).
https:/​/​doi.org/​10.1016/​j.physleta.2005.04.029

[26] P. Pechukas, Phys. Rev. Lett. 73, 1060 (1994).
https:/​/​doi.org/​10.1103/​PhysRevLett.73.1060

[27] P. Štelmachovičand V. Bužek, Phys. Rev. A 64, 062106 (2001).
https:/​/​doi.org/​10.1103/​PhysRevA.64.062106

[28] D. Schmid, K. Ried and R. W. Spekkens, Phys. Rev. A 100, 022112 (2019).
https:/​/​doi.org/​10.1103/​PhysRevA.100.022112

[29] G. Lindblad, Comm. Math. Phys. 65, 281 (1979).
https:/​/​projecteuclid.org:443/​euclid.cmp/​1103904877

[30] L. Accardi, A. Frigerio and J. T. Lewis, Publications of the Research Institute for Mathematical Sciences 18, 97 (1982).
https:/​/​doi.org/​10.2977/​prims/​1195184017

[31] G. Chiribella, G. M. D'Ariano and P. Perinotti, Phys. Rev. A 80, 022339 (2009).
https:/​/​doi.org/​10.1103/​PhysRevA.80.022339

[32] F. A. Pollock, C. Rodríguez-Rosario, T. Frauenheim et al., Physical Review A 97, 012127 (2018a).
https:/​/​doi.org/​10.1103/​PhysRevA.97.012127

[33] O. Oreshkov, F. Costa and Č. Brukner, Nat. Commun. 3, 1092 (2012), arXiv:1105.4464 [quant-ph].
https:/​/​doi.org/​10.1038/​ncomms2076
arXiv:1105.4464

[34] O. Oreshkov and C. Giarmatzi, New Journal of Physics 18, 093020 (2016).
https:/​/​doi.org/​10.1088/​1367-2630/​18/​9/​093020
http:/​/​stacks.iop.org/​1367-2630/​18/​i=9/​a=093020

[35] A. Peres, Physical Review Letters 77, 1413 (1996).
https:/​/​doi.org/​10.1103/​PhysRevLett.77.1413

[36] A. C. Doherty, P. A. Parrilo and F. M. Spedalieri, Physical Review A 69, 022308 (2004).
https:/​/​doi.org/​10.1103/​PhysRevA.69.022308

[37] Y. Nesterov and A. Nemirovskii, Interior Point Polynomial Algorithms in Convex Programming, Studies in Applied Mathematics (Society for Industrial and Applied Mathematics, 1987).

[38] E. Davies and J. Lewis, Comm. Math. Phys. 17, 239 (1970).
https:/​/​doi.org/​10.1007/​BF01647093

[39] A. Jamiołkowski, Rep. Math. Phys 3, 275 (1972).
https:/​/​doi.org/​10.1016/​0034-4877(72)90011-0

[40] M.-D. Choi, Linear Algebra Appl. 10, 285 (1975).
https:/​/​doi.org/​10.1016/​0024-3795(75)90075-0

[41] D. Kretschmann and R. F. Werner, Phys. Rev. A 72, 062323 (2005).
https:/​/​doi.org/​10.1103/​PhysRevA.72.062323

[42] F. Costa and S. Shrapnel, New Journal of Physics 18, 063032 (2016).
https:/​/​doi.org/​10.1088/​1367-2630/​18/​6/​063032

[43] C. Giarmatzi and F. Costa, npj Quantum Information 4, 17 (2018).
https:/​/​doi.org/​10.1038/​s41534-018-0062-6

[44] F. A. Pollock, C. Rodríguez-Rosario, T. Frauenheim et al., Physical Review Letters 120, 040405 (2018b).
https:/​/​doi.org/​10.1103/​PhysRevLett.120.040405

[45] J. Kołodyński, S. Rana and A. Streltsov, Physical Review A 101, 020303 (2020).
https:/​/​doi.org/​10.1103/​PhysRevA.101.020303

[46] D. Chruściński and S. Maniscalco, Physical Review Letters 112, 120404 (2014).
https:/​/​doi.org/​10.1103/​PhysRevLett.112.120404

[47] M. Araújo, C. Branciard, F. Costa et al., New J. Phys. 17, 102001 (2015).
https:/​/​doi.org/​10.1088/​1367-2630/​17/​10/​102001

[48] E. M. Rains, arXiv:9707002 [quant-ph].
arXiv:quant-ph/9707002

[49] V. Vedral and M. B. Plenio, Phys. Rev. A 57, 1619 (1998).
https:/​/​doi.org/​10.1103/​PhysRevA.57.1619

[50] C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs et al., Phys. Rev. A 59, 1070 (1999).
https:/​/​doi.org/​10.1103/​PhysRevA.59.1070

[51] M. Nery and M. T. Quintino and P. A. Guérin and T. O. Maciel and R. O. Vianna arXiv:2101.11630 [quant-ph].
arXiv:2101.11630

[52] G. Rubino, L. A. Rozema, A. Feix et al., Science Advances 3 (2017), 10.1126/​sciadv.1602589.
https:/​/​doi.org/​10.1126/​sciadv.1602589

[53] K. Goswami, C. Giarmatzi, M. Kewming et al., Phys. Rev. Lett. 121, 090503 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.121.090503

[54] I. Ernst, Z. Physik 31, 253 (1925).

[55] V. Vedral, Reviews of Modern Physics 74, 197 (2002).
https:/​/​doi.org/​10.1103/​RevModPhys.74.197

[56] S. Milz, M. S. Kim, F. A. Pollock et al., Phys. Rev. Lett. 123, 040401 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.123.040401

[57] S. Milz, F. Sakuldee, F. A. Pollock et al., Quantum 4, 255 (2020).
https:/​/​doi.org/​10.22331/​q-2020-04-20-255

[58] D. Chruściński, A. Kossakowski and A. Rivas, Phys. Rev. A 83, 052128 (2011).
https:/​/​doi.org/​10.1103/​PhysRevA.83.052128

[59] C. Giarmatzi, Github page.
http:/​/​github.com/​Christina-Giar/​SDP2_non_markov

Cited by

[1] Pedro Figueroa-Romero, Kavan Modi, Robert J. Harris, Thomas M. Stace, and Min-Hsiu Hsieh, "Randomized Benchmarking for Non-Markovian Noise", PRX Quantum 2 4, 040351 (2021).

[2] Joshua Morris, Felix A. Pollock, and Kavan Modi, "Quantifying non-Markovian Memory in a Superconducting Quantum Computer", Open Systems & Information Dynamics 29 02, 2250007 (2022).

[3] Huan-Yu Ku, Hao-Cheng Weng, Yen-An Shih, Po-Chen Kuo, Neill Lambert, Franco Nori, Chih-Sung Chuu, and Yueh-Nan Chen, "Hidden nonmacrorealism: Reviving the Leggett-Garg inequality with stochastic operations", Physical Review Research 3 4, 043083 (2021).

[4] Nina Megier, Manuel Ponzi, Andrea Smirne, and Bassano Vacchini, "Memory Effects in Quantum Dynamics Modelled by Quantum Renewal Processes", Entropy 23 7, 905 (2021).

[5] K. Goswami, C. Giarmatzi, C. Monterola, S. Shrapnel, J. Romero, and F. Costa, "Experimental characterization of a non-Markovian quantum process", Physical Review A 104 2, 022432 (2021).

[6] U. Shrikant and Prabha Mandayam, "Quantum non-Markovianity: Overview and recent developments", Frontiers in Quantum Science and Technology 2, 1134583 (2023).

[7] Simon Milz, Cornelia Spee, Zhen-Peng Xu, Felix Pollock, Kavan Modi, and Otfried Gühne, "Genuine multipartite entanglement in time", SciPost Physics 10 6, 141 (2021).

[8] Philip Taranto, Marco Túlio Quintino, Mio Murao, and Simon Milz, "Characterising the Hierarchy of Multi-time Quantum Processes with Classical Memory", Quantum 8, 1328 (2024).

[9] Matheus Capela, Harshit Verma, Fabio Costa, and Lucas C. Céleri, "Reassessing thermodynamic advantage from indefinite causal order", Physical Review A 107 6, 062208 (2023).

[10] Pedro Figueroa–Romero, Felix A. Pollock, and Kavan Modi, "Markovianization with approximate unitary designs", Communications Physics 4 1, 127 (2021).

[11] Stefano Martina, Stefano Gherardini, and Filippo Caruso, "Machine learning classification of non-Markovian noise disturbing quantum dynamics", Physica Scripta 98 3, 035104 (2023).

[12] Graeme D. Berk, Simon Milz, Felix A. Pollock, and Kavan Modi, "Extracting quantum dynamical resources: consumption of non-Markovianity for noise reduction", npj Quantum Information 9 1, 104 (2023).

[13] Marcello Nery, Marco Túlio Quintino, Philippe Allard Guérin, Thiago O. Maciel, and Reinaldo O. Vianna, "Simple and maximally robust processes with no classical common-cause or direct-cause explanation", Quantum 5, 538 (2021).

[14] Lucas B. Vieira, Simon Milz, Giuseppe Vitagliano, and Costantino Budroni, "Witnessing environment dimension through temporal correlations", Quantum 8, 1224 (2024).

[15] Daniel Burgarth, Paolo Facchi, Davide Lonigro, and Kavan Modi, "Quantum non-Markovianity elusive to interventions", Physical Review A 104 5, L050404 (2021).

[16] Fabio Costa, "A no-go theorem for superpositions of causal orders", Quantum 6, 663 (2022).

[17] Matheus Capela, Lucas C. Céleri, Rafael Chaves, and Kavan Modi, "Quantum Markov monogamy inequalities", Physical Review A 106 2, 022218 (2022).

[18] Neil Dowling, Pedro Figueroa-Romero, Felix A. Pollock, Philipp Strasberg, and Kavan Modi, "Relaxation of Multitime Statistics in Quantum Systems", Quantum 7, 1027 (2023).

[19] Satoshi Yoshida, Akihito Soeda, and Mio Murao, "Universal construction of decoders from encoding black boxes", Quantum 7, 957 (2023).

[20] I.A. Aloisio, G.A.L. White, C.D. Hill, and K. Modi, "Sampling Complexity of Open Quantum Systems", PRX Quantum 4 2, 020310 (2023).

[21] Charlotte Bäcker, Konstantin Beyer, and Walter T. Strunz, "Local Disclosure of Quantum Memory in Non-Markovian Dynamics", Physical Review Letters 132 6, 060402 (2024).

[22] Simon Milz, M. S. Kim, Felix A. Pollock, and Kavan Modi, "Completely Positive Divisibility Does Not Mean Markovianity", Physical Review Letters 123 4, 040401 (2019).

[23] C. -F. Li, G. -C. Guo, and J. Piilo, "Non-Markovian quantum dynamics: What does it mean?", EPL (Europhysics Letters) 127 5, 50001 (2019).

[24] Chu Guo, Kavan Modi, and Dario Poletti, "Tensor-network-based machine learning of non-Markovian quantum processes", Physical Review A 102 6, 062414 (2020).

[25] Roope Uola, Tristan Kraft, and Alastair A. Abbott, "Quantification of quantum dynamics with input-output games", Physical Review A 101 5, 052306 (2020).

[26] Graeme D. Berk, Andrew J. P. Garner, Benjamin Yadin, Kavan Modi, and Felix A. Pollock, "Resource theories of multi-time processes: A window into quantum non-Markovianity", arXiv:1907.07003, (2019).

[27] Philip Taranto, "Memory effects in quantum processes", International Journal of Quantum Information 18 2, 1941002-574 (2020).

[28] Graeme D. Berk, Andrew J. P. Garner, Benjamin Yadin, Kavan Modi, and Felix A. Pollock, "Resource theories of multi-time processes: A window into quantum non-Markovianity", Quantum 5, 435 (2021).

[29] Simon Milz, Dominic Jurkschat, Felix A. Pollock, and Kavan Modi, "Delayed-choice causal order and nonclassical correlations", Physical Review Research 3 2, 023028 (2021).

[30] Adrián A. Budini, "Detection of bidirectional system-environment information exchanges", Physical Review A 103 1, 012221 (2021).

[31] Kavan Modi, "George Sudarshan and Quantum Dynamics", Open Systems and Information Dynamics 26 3, 1950013 (2019).

[32] Pedro Figueroa-Romero, "Equilibration and Typicality in Quantum Processes", arXiv:2102.02289, (2021).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-24 20:17:34) and SAO/NASA ADS (last updated successfully 2024-05-24 20:17:35). The list may be incomplete as not all publishers provide suitable and complete citation data.