Non-Markovian Evolution: a Quantum Walk Perspective

Kumar, N. Pradeep; Banerjee, Subhashish; Srikanth, R.; Jagadish, Vinayak; Petruccione, Francesco

doi:10.1142/s1230161218500142

Cited by 66 publications

(64 citation statements)

References 63 publications

(77 reference statements)

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“…www.nature.com/scientificreports/ OUN model, as characterized here, helps to prolong the time to ESD 40 and also counteracts decoherence in quantum walk 37 . This should pave the way for more such examples which could have an impact on broadening the scope of memory in quantum phenomena.…”

Section: Scientific Reports |mentioning

confidence: 86%

“…Two examples may be pointed out. In the OUN model, this effect was made use of 40 to study its impact on the prolongation of the time to entanglement sudden death (ESD); while in 37 , the analogous nature in the OUN and PLN models is shown to counteract decoherence for quantum walks. In both these examples, the weaker-than-CP-indivisible effect acts as a memory resource.…”

Section: Scientific Reportsmentioning

confidence: 99%

“…As our next example, we consider random telegraph noise (RTN), which is a very well studied pure dephasing process, known to be non-Markovian according to information back-flow and CP-divisibility criteria 37,47 . The Kraus operators characterizing this process has a functional form similar to that of PLN and OUN with the function p(t) in Eq.…”

Section: Random Telegraph Noise (Rtn): P-indivisible Dephasingmentioning

confidence: 99%

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Temporal self-similarity of quantum dynamical maps as a concept of memorylessness

Utagi

Srikanth

Banerjee

2020

Sci Rep

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The problem of defining quantum non-Markovianity has proven elusive, with various in-equivalent criteria put forth to address it. The concept of CP-indivisibility and the hierarchy of stronger divisibility criteria going up to P-indivisibility, capture a fundamental aspect of memory in quantum non-Markovianity. In practice, however, there can be a memory-like influence associated with divisible channels in the form of weakening, if not reversing, the effects of decoherence. Arguably, such a facet of memory relates to CP-indivisibility as quantum discord relates to entanglement. We concretize this weaker notion of non-Markovianity by identifying it with deviation from “temporal self-similarity”, the property of a system dynamics whereby the propagator between two intermediate states is independent of the initial time $$t_0$$ t 0 . We illustrate this idea through examples, and propose a geometric quantification of temporal self-similarity, and show how our approach complements the divisibility-based criterion of quantum non-Markovianity.

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Section: Scientific Reports |mentioning

confidence: 86%

Section: Scientific Reportsmentioning

confidence: 99%

Section: Random Telegraph Noise (Rtn): P-indivisible Dephasingmentioning

confidence: 99%

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Temporal self-similarity of quantum dynamical maps as a concept of memorylessness

Utagi

Srikanth

Banerjee

2020

Sci Rep

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“…The performance of Lindbladian channels, such as the squeezed generalized amplitude damping (SGAD) channel [36] and the Unruh channel [37] have been studied using these parameters [24]. Here, these are used to characterize the two non-Markovian channels, RTN [38][39][40] and NMD [41]. The non-Markovianity in these two channels can be witnessed by using QFI-flow.…”

Section: Introductionmentioning

confidence: 99%

Facets of quantum information under non-Markovian evolution

2019

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We consider two non-Markovian models: Random Telegraph Noise (RTN) and non-Markovian dephasing (NMD). The memory in these models is studied from the perspective of quantum Fisher information flow. This is found to be consistent with the other well known witnesses of non-Markovianity. The two noise channels are characterized quantum information theoretically by studying their gate and channel fidelities. Further, the quantum coherence and its balance with mixedness is studied. This helps to put in perspective the role that the two noise channels can play in various facets of quantum information processing and quantum communication.

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“…Effects of non-Markovian structured environment on quantum coherence and correlation has been theoretically and experimentally studied [17][18][19][20][21]. A number of measures of deviation from Markovianity have been proposed recently, where "Non-Markovianity" is recognized as the departure from monotonic behavior of certain measures under strictly Markovian dynamics [22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Evolution of coherence and non-classicality under global environmental interaction

Bhattacharya

Banerjee

Pati

2018

Quantum Inf Process

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A master equation has been constructed for a global system-bath interaction both in the absence as well as presence of non-Markovian noise. For the memoryless case, it has been exactly solved for a paradigmatic class of two qubit states in high and zero temperature thermal environment. For the non-Markovian model, it has been solved for zero temperature bath. The evolution of quantum coherence and entanglement has been observed in presence of the above mentioned interactions. We show that the global part of the system-bath interaction compensates for the decoherence, resulting in slow down of coherence and entanglement decay. For an appropriately defined limiting case, both coherence and entanglement show freezing behaviour for the high temperature bath. In case of zero temperature bath, the mentioned interaction not only stabilizes the non-classical correlations, but also enhances them for a finite period. For the memory dependent case, we have seen that the global interaction enhances the back-flow of information from environment to the system, as it enhances the regeneration of coherence and entanglement. Also we have studied the generation of Quantum Fisher information by the mentioned process. An intuitive measure of non-classicality based on non-commutativity of quantum states has been considered. Bounds on generated quantum Fisher information has been found in terms of quantumness and coherence. This gives us a novel understanding of Quantum Fisher information as a measure of non-classicality.

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Non-Markovian Evolution: a Quantum Walk Perspective

Cited by 66 publications

References 63 publications

Temporal self-similarity of quantum dynamical maps as a concept of memorylessness

Temporal self-similarity of quantum dynamical maps as a concept of memorylessness

Facets of quantum information under non-Markovian evolution

Evolution of coherence and non-classicality under global environmental interaction

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