Quantifying non-Markovianity via conditional mutual information

Huang, Zhiqiang; Guo, Xiao-Kan

doi:10.1103/physreva.104.032212

Cited by 10 publications

(7 citation statements)

References 32 publications

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“…Interestingly, in this new framework of Quantum Darwinism, one can consider also the scaling of the conditional mutual information I(S : F l |F k ) [18]. This form of conditional mutual information also makes appearance in our recent work on quantum non-Markovianity [20,21]. We therefore expect to study the connections between Quantum Darwinism and quantum (non-)Markovianity from a new perspective, in light of these new results.…”

Section: Introductionmentioning

confidence: 94%

“…It is well-known by now that the quantum non-Markovianity of open quantum dynamics can be quantified by the information backflow from environment to system, or the increase in distinguishability of system's states [41]. Recently, we have shown in [20] that the backflow of quantum mutual information can be equivalently reformulated as the backflow of conditional mutual information in a system-environment-ancilla setting. Here, we shall consider the backflow of conditional mutual information in the new setting of Quantum Darwinism.…”

Section: Relation To Backflow Of Correlationmentioning

confidence: 99%

“…In the system-environment-ancilla setting of [20], we require the ancilla-system initial state is maximally entangled, i.e. I(A : S) ρi = 2H A = 2 ln d A .…”

Section: Relation To Backflow Of Correlationmentioning

confidence: 99%

“…where √ P ŝ = ŝ|s . In this case, AS-state is entangled, and the observer A keeps all the classical information about S. We have in fact returned to the systemenvironment-ancilla setting of [20]. After the time evolution of SE by U SE (or under the quantum channel Λ S→E ), we have…”

Section: Relation To Backflow Of Correlationmentioning

confidence: 99%

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On the relation between quantum Darwinism and approximate quantum Markovianity

Guo¹,

Huang²

2022

Preprint

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Section: Introductionmentioning

confidence: 94%

Section: Relation To Backflow Of Correlationmentioning

confidence: 99%

“…In the system-environment-ancilla setting of [20], we require the ancilla-system initial state is maximally entangled, i.e. I(A : S) ρi = 2H A = 2 ln d A .…”

Section: Relation To Backflow Of Correlationmentioning

confidence: 99%

Section: Relation To Backflow Of Correlationmentioning

confidence: 99%

See 2 more Smart Citations

On the relation between quantum Darwinism and approximate quantum Markovianity

Guo¹,

Huang²

2022

Preprint

Self Cite

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“…To systematically investigate the impact of memory on the learning task, it is crucial to quantify the degree of non-Markovianity of the sequence for a given value of k beyond the binary distinction between Markovian and non-Markovian. Yet de ning a practical measure that quanti es conclusively the degree of non-Markovianity is a non-trivial task [44,45] and subject of ongoing research mainly done in the eld of open quantum systems [46][47][48][49][50].…”

Section: The Waiting Time Distribution Of the Trap Controls The Memor...mentioning

confidence: 99%

The impact of memory on learning sequence-to-sequence tasks

Seif¹,

Loos²,

Tucci³

et al. 2022

Preprint

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The recent success of neural networks in machine translation and other elds has drawn renewed attention to learning sequence-to-sequence (seq2seq) tasks. While there exists a rich literature that studies classi cation and regression using solvable models of neural networks, learning seq2seq tasks is signi cantly less studied from this perspective. Here, we propose a simple model for a seq2seq task that gives us explicit control over the degree of memory, or non-Markovianity, in the sequences -the stochastic switching-Ornstein-Uhlenbeck (SSOU) model. We introduce a measure of non-Markovianity to quantify the amount of memory in the sequences. For a minimal autoregressive (AR) learning model trained on this task, we identify two learning regimes corresponding to distinct phases in the stationary state of the SSOU process. These phases emerge from the interplay between two di erent time scales that govern the sequence statistics. Moreover, we observe that while increasing the memory of the AR model always improves performance, increasing the non-Markovianity of the input sequences can improve or degrade performance. Finally, our experiments with recurrent and convolutional neural networks show that our observations carry over to more complicated neural network architectures.

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Facets of Correlated Non‐Markovian Channels

Sabale,

Dash,

Kumar

et al. 2024

Annalen der Physik

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The domain of correlated non‐Markovian channels are investigated, exploring the potential memory arising from the correlated action of channels and the inherent memory due to non‐Markovian dynamics. The impact of channel correlations is studied using different non‐Markovianity indicators and measures. In addition, the dynamical aspects of correlated non‐Markovian channels, including entanglement dynamics as well as changes in the volume of accessible states, are explored. The analysis is presented for both unital and non‐unital correlated channels. A new correlated channel constructed with modified Ornstein–Uhlenbeck noise (OUN) is also presented and explored. Further, the geometrical effects of the non‐Markovianity of the correlated non‐Markovian channels are discussed with a study of change in the volume of the accessible states. The link between the correlation factor and error correction success probability is highlighted.

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Quantifying non-Markovianity via conditional mutual information

Cited by 10 publications

References 32 publications

On the relation between quantum Darwinism and approximate quantum Markovianity

On the relation between quantum Darwinism and approximate quantum Markovianity

The impact of memory on learning sequence-to-sequence tasks

Facets of Correlated Non‐Markovian Channels

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