Completely Positive Divisibility Does Not Mean Markovianity

Milz, Simon; Kim, M. S.; Pollock, Felix A.; Modi, Kavan

doi:10.1103/physrevlett.123.040401

Cited by 117 publications

(100 citation statements)

References 76 publications

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“…For the latter, it is also possible to quantify the violation of quantum regression theorem [58]. For the correspondence to classical Markovianity, a recent series of papers [55][56][57] exploited the concepts of process tensor and causal break. k ; A k−1:0 ).…”

mentioning

confidence: 99%

Non-Markovian quantum dynamics: What does it mean?

Li¹,

Guo²,

Piilo³

2019

EPL

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During the last ten years, the studies on non-Markovian open system dynamics has become increasingly popular and having contributions from diverse set of research communities. This interest has arisen due to fundamental problematics how to define and quantify memory effects in the quantum domain, how to exploit and develop applications based on them, and also due to the question what are the ultimate limits for controlling open system dynamics. We give here a simple theoretical introduction to the basic approaches to define and quantify quantum non-Markovianity -also highlighting their connections and differences. In addition to the importance of the development for open quantum systems studies, we also discuss the implications of the progress for other fields including, e.g., formal studies of stochastic processes and quantum information science, and conclude with possible future directions the recent developments open.

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mentioning

confidence: 99%

Non-Markovian quantum dynamics: What does it mean?

Li¹,

Guo²,

Piilo³

2019

EPL

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“…Memory effects are not an exclusive feature of quantum dynamics, being also present in classical physics. Our understanding regarding quantum non-Markovian behavior has markedly increased in the last few years [28][29][30]. Therefore, moving forward with this design, the question regarding the quantumness of the time-correlations generated in the output beam should be experimentally addressed by a measure of quantum non-Markovianity or by means of a Leggett-Garg inequality [31].…”

Section: Discussionmentioning

confidence: 99%

Quantum Memristors in Frequency-Entangled Optical Fields

et al. 2020

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A quantum memristor is a resistive passive circuit element with memory engineered in a given quantum platform. It can be represented by a quantum system coupled to a dissipative environment, in which a system-bath coupling is mediated through a weak measurement scheme and classical feedback on the system. In quantum photonics, such a device can be designed from a beam splitter with tunable reflectivity, which is modified depending on the results of measurements in one of the outgoing beams. Here, we show that a similar implementation can be achieved with frequencyentangled optical fields and a frequency mixer that, working similarly to a beam splitter, produces state superpositions. We show that the characteristic hysteretic behavior of memristors can be reproduced when analyzing the response of the system with respect to the control, for different experimentally-attainable states. Since memory effects in memristors can be exploited for classical and neuromorphic computation, the results presented in this work provides the first steps of a novel route towards constructing quantum neural networks in quantum photonics.

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“…However, for n ≥ 4, Markovianity implies new kinds of monogamy constraints for the correlations in the Markov chain, violations of which can be seen as a device-independent test [20][21][22] of the non-Markovianity of the underlying process. Interestingly, arXiv:1910.04236v1 [quant-ph] 9 Oct 2019 by employing an operational definition of divisibility [23], we show that such condition is sufficient for a process satisfying all data processing and monogamy inequalities. Furthermore, we show how the violation of these new constraints can also be connected with the quantification of causal influences [16,24,25] among the variables.…”

Section: Introductionmentioning

confidence: 92%

“…If we also have access to p(Y, Z) then we can compute Γ Z:Y and check if Γ Z:X = Γ Z:Y Γ Y:X . The latter condition is stronger than the former because Γ Z:X represents the actual process Y → Z (see [23] for details).…”

Section: Inequalities For Divisible Processesmentioning

confidence: 99%

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Monogamy of temporal correlations: Witnessing non-Markovianity beyond data processing

Capela

Céleri

Modi

et al. 2020

Phys. Rev. Research

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The modeling of natural phenomena via a Markov process -a process for which the future is independent of the past, given the present-is ubiquitous in many fields of science. Within this context, it is of foremost importance to develop ways to check from the available empirical data if the underlying mechanism is indeed Markovian. A paradigmatic example is given by data processing inequalities, the violation of which is an unambiguous proof of the non-Markovianity of the process. Here, our aim is twofold. First we show the existence of a monogamy-like type of constraints, beyond data processing, respected by Markov chains. Second, to show a novel connection between the quantification of causality and the violation of both data processing and monogamy inequalities. Apart from its foundational relevance in the study of stochastic processes we also consider the applicability of our results in a typical quantum information setup, showing it can be useful to witness the non-Markovianity arising in a sequence of quantum non-projective measurements.

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Completely Positive Divisibility Does Not Mean Markovianity

Cited by 117 publications

References 76 publications

Non-Markovian quantum dynamics: What does it mean?

Non-Markovian quantum dynamics: What does it mean?

Quantum Memristors in Frequency-Entangled Optical Fields

Monogamy of temporal correlations: Witnessing non-Markovianity beyond data processing

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