Simple and maximally robust processes with no classical common-cause or direct-cause explanation

Marcello Nery1, Marco Túlio Quintino2,3, Philippe Allard Guérin3,2,4, Thiago O. Maciel5,6, and Reinaldo O. Vianna1

1Departamento de Física, Universidade Federal de Minas Gerais, Av. Pres. Antonio Carlos 6627 - Belo Horizonte, MG, Brazil - 31270-901.
2Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
3Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
4Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, N2L 2Y5, Canada
5Departamento de Física, Universidade Federal de Santa Catarina, Florianópolis, SC, 88040-900, Brazil
6Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ 21941-972, Brazil

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Abstract

Guided by the intuition of coherent superposition of causal relations, recent works presented quantum processes without classical common-cause and direct-cause explanation, that is, processes which cannot be written as probabilistic mixtures of quantum common-cause and quantum direct-cause relations (CCDC). In this work, we analyze the minimum requirements for a quantum process to fail to admit a CCDC explanation and present "simple" processes, which we prove to be the most robust ones against general noise. These simple processes can be realized by preparing a maximally entangled state and applying the identity quantum channel, thus not requiring an explicit coherent mixture of common-cause and direct-cause, exploiting the possibility of a process to have both relations simultaneously. We then prove that, although all bipartite direct-cause processes are bipartite separable operators, there exist bipartite separable processes which are not direct-cause. This shows that the problem of deciding weather a process is direct-cause process $\textit{is not}$ equivalent to entanglement certification and points out the limitations of entanglement methods to detect non-classical CCDC processes. We also present a semi-definite programming hierarchy that can detect and quantify the non-classical CCDC robustnesses of every non-classical CCDC process. Among other results, our numerical methods allow us to show that the simple processes presented here are likely to be also the maximally robust against white noise. Finally, we explore the equivalence between bipartite direct-cause processes and bipartite processes without quantum memory, to present a separable process which cannot be realized as a process without quantum memory.

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Cited by

[1] Christina Giarmatzi and Fabio Costa, "Witnessing quantum memory in non-Markovian processes", arXiv:1811.03722.

[2] Simon Milz and Kavan Modi, "Quantum Stochastic Processes and Quantum non-Markovian Phenomena", PRX Quantum 2 3, 030201 (2021).

[3] 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).

[4] Yu Guo, Philip Taranto, Bi-Heng Liu, Xiao-Min Hu, Yun-Feng Huang, Chuan-Feng Li, and Guang-Can Guo, "Experimental Demonstration of Instrument-Specific Quantum Memory Effects and Non-Markovian Process Recovery for Common-Cause Processes", Physical Review Letters 126 23, 230401 (2021).

[5] Marco Túlio Quintino and Daniel Ebler, "Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality", arXiv:2109.08202.

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