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

Utagi, Shrikant; Srikanth, R.; Banerjee, Subhashish

doi:10.1038/s41598-020-72211-3

Cited by 45 publications

(45 citation statements)

References 49 publications

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“…OUN noisy channel even though Markovian from the perspective of the CP-divisibility criteria, is non-Markovian [32,37]. The decoherence function of OUN is [38],…”

Section: Cp-divisible Phase Damping Channel;mentioning

confidence: 99%

“…This raises the question of whether there is a quantum concept of memory that is better indicated by the quantum speed limit. In this context, here we consider the quantification of memory as a deviation from 'temporal self-similarity' [32], which roughly refers to the idea of the form of the intermediate map being independent of the initial time. It is known to be equivalent to the dynamical semigroup, and thus provides a concept of non-Markovianity weaker than non-divisibility and information backflow.…”

Section: Introductionmentioning

confidence: 99%

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The effect of quantum memory on quantum speed limit time

Paulson,

Banerjee,

Srikanth

2021

Preprint

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Quantum speed limit time defines the limit on the minimum time required for a quantum system to evolve between two states. Investigation of bounds on speed limit time of quantum system under non-unitary evolution is of fundamental interest, as it reveals interesting connections to quantum (non-)Markovianity. Here, we discuss the characteristics of quantum speed limit time as a function of quantum memory, quantified as the deviation from temporal self-similarity of quantum dynamical maps for CP-divisible as well as indivisible maps. This provides an operational meaning to CPdivisible (non-)Markovianity.I.

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“…OUN noisy channel even though Markovian from the perspective of the CP-divisibility criteria, is non-Markovian [32,37]. The decoherence function of OUN is [38],…”

Section: Cp-divisible Phase Damping Channel;mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The effect of quantum memory on quantum speed limit time

Paulson,

Banerjee,

Srikanth

2021

Preprint

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“…Both the qualitative and quantitative analysis of quantum non-Markovianity is of fundamental importance in the theory of open quantum dynamics. Over the past decade, there has been numerous proposals for quantifing non-Markovianity based on CP divisibility [36,44] and non-Markovianity witness [10,36,39,40,[44][45][46][47][48][49][50][51][52][53][54][55][56]. One of the prominent non-Markovianity measures based on the composition of the dynamical map was introduced in [36], the so called RHP measure.…”

Section: Dynamics Of Non-markovianitymentioning

confidence: 99%

Revisiting the Quantum Open System Dynamics of Central Spin Model

Bhattacharya

Banerjee

2021

Quanta

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In this work, we revisit the theory of open quantum systems from the perspective of fermionic baths. Specifically, we concentrate on the dynamics of a central spin half particle interacting with a spin bath. We have calculated the exact reduced dynamics of the central spin and constructed the Kraus operators in relation to that. Further, the exact Lindblad type canonical master equation corresponding to the reduced dynamics is constructed. We have also briefly touched upon the aspect of non-Markovianity from the backdrop of the reduced dynamics of the central spin.Quanta 2021; 10: 55–64.

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“…The modified Ornstein-Uhlenback noise (OUN) and power law noise (PLN) have similar structure whose Kraus operators [63] are same as E j s in Eq. ( 22) with Λ(t) given by…”

Section: Modified Ornstein-uhlenback and Power Law Noisesmentioning

confidence: 99%

Attainable and usable coherence in X states over Markovian and non-Markovian channels

Mishra,

Thapliyal,

Pathak

2021

Preprint

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The relations between the resource theoretic measures of quantum coherence are rigorously investigated for various Markovian and non-Markovian channels for the two-qubit X states with specific attention to the maximum and minimum attainable coherence and usefulness of these states in performing quantum teleportation in noisy environment. The investigation has revealed that under both dephasing and dissipative type noises the maximally entangled mixed states and Werner states lose their form and usefulness. However, maximally non-local mixed states (MNMSs) lose their identity in dissipative noise only. Thus, MNMSs are established to be useful in teleporting a qubit with fidelity greater than the classical limit in the presence of dephasing noise. MNMSs also remain useful for device independent quantum key distribution in this case as they still violate Bell's inequality. In the presence of noise, coherence measured by relative entropy of coherence is found to fall faster than the same measured using l1 norm of coherence. Further, information back-flow from the environment to the system is observed over non-Markovian channels which leads to revival in coherence. Additionally, sequential interaction of two qubits with the same environment is found to result in correlated noise on both qubits, and coherence is observed to be frozen in this case under dephasing channel. Under the effect of Markovian and non-Markovian dephasing channels studied here, we observed that MNMSs have maximum relative coherence, i.e., they have the maximum amount of l1 norm of coherence among the states with the same amount of relative entropy of coherence. However, this feature is not visible in any X state evolving over dissipative channels.

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

Cited by 45 publications

References 49 publications

The effect of quantum memory on quantum speed limit time

The effect of quantum memory on quantum speed limit time

Revisiting the Quantum Open System Dynamics of Central Spin Model

Attainable and usable coherence in X states over Markovian and non-Markovian channels

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