Data processing inequality and open quantum systems: Beyond Markov states

Turkmen, Aysenur; Verçin, A.; Yilmaz, Serap

doi:10.1103/physreva.96.042112

Cited by 3 publications

(2 citation statements)

References 23 publications

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“…Summing the Equations (19,20,21,22), using the strong subadditivity of quantum entropy [27], (23) and solving for (15,16,17,18), we have the desired inequality.…”

Section: Theorem 1 (Quantum Markov Monogamy Inequality)mentioning

confidence: 99%

“…With rising interest in quantum information theory, classical data processing inequalities were extended to the regime of quantum processes [12], setting an appropriate approach to define new constraints on quantum Markovian processes. Indeed, intense research has been undertaken in this direction since then [13][14][15][16][17][18][19][20]. Naturally, further information-theoretic constraints imposed by quantum Markovian processes is of great interest and it is the main problem addressed in this paper.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Markov monogamy inequalities

Capela,

Céleri,

Chaves

et al. 2021

Preprint

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Markovianity lies at the heart of classical communication problems. This in turn makes the information-theoretic characterization of Markovian processes worthwhile. Data processing inequalities are ubiquitous in this sense, assigning necessary conditions for all Markovian processes. We address here the problem of the information-theoretic analysis of constraints on Markovian processes in the quantum regime. Firstly, we show the existence of a novel class of quantum data processing inequalities called here quantum Markov monogamy inequalities. This new class of necessary conditions on quantum Markovian processes is inspired by its counterpart for classical Markovian processes, and thus providing a strong link between classical and quantum constraints on Markovianity. Secondly, we show the relevance of such inequalities by considering an example of non-Markovian behaviour witnessed by a monogamy inequality, nevertheless, do not violating any of the remaining data processing inequalities. Lastly, we show how this inequalities can be used to witness non-Markovianity at the level of the process tensor formalism.

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“…Summing the Equations (19,20,21,22), using the strong subadditivity of quantum entropy [27], (23) and solving for (15,16,17,18), we have the desired inequality.…”

Section: Theorem 1 (Quantum Markov Monogamy Inequality)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum Markov monogamy inequalities

Capela,

Céleri,

Chaves

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

Quantum Markov monogamy inequalities

et al. 2022

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Quantum Error Correction in the Presence of Initial System-Environment Correlations

Turkmen

Verçin

2020

Open Syst. Inf. Dyn.

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Quantum error correction is studied in a framework consisting of an open quantum system and its environment, jointly subjected to a unitary action, and an interaction-free reference system. It has been shown that coherent information between the initially correlated open system and reference system is conserved in the transmission stage of any quantum communication process, provided that the tripartite input is any pure Markov state and the overall evolution preserves its form. This conservation constitutes the necessary and sufficient condition for accomplishment of perfect error correction by a recovery channel even in the presence of initial system-environment correlations. Explicit expressions of the recovery operators and examples of the joint unitary evolution preserving the form of inputs are given for all classes of pure Markov states.

show abstract

Data processing inequality and open quantum systems: Beyond Markov states

Cited by 3 publications

References 23 publications

Quantum Markov monogamy inequalities

Quantum Markov monogamy inequalities

Quantum Markov monogamy inequalities

Quantum Error Correction in the Presence of Initial System-Environment Correlations

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