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arXiv:2005.04009 · Physical Review A

Constructive feedback of non-Markovianity on resources in random quantum states

Rivu Gupta, Shashank Gupta, Shiladitya Mal, Aditi Sen

Published Jan 25, 2022• 16 citations
arXivHTMLPDF

Abstract

We explore the impact of non-Markovian channels on the quantum correlations of Haar uniformly generated random two-qubit input states with different ranks: Either one of the qubits (single-sided channel) or both qubits independently (double-sided channel) are passed through a noisy channel. For dephasing and depolarizing channels with varying non-Markovian strength, entanglement and quantum discord of the output states collapse and revive with the increase of noise. By both analytical and numerical means, we find that in the case of the depolarizing double-sided channel, entanglement and quantum discord for random states show a higher number of revivals on average than for single-sided channels with a fixed non-Markovianity strength, irrespective of the rank of the states; we call such a counterintuitive event, constructive feedback of non-Markovianity. In contrast, the mean value of critical noise at which quantum correlations (QCs) first collapse decreases with the increase of non-Markovianity, independently of the rank of the random initial states. However, the average noise at which QCs of random states show the first revival decreases with the increase of the strength of non-Markovian noise, thereby indicating the role of non-Markovian channels in the regeneration of QCs even in the presence of a high amount of noise. Moreover, we observe that the tendency of a state to show regeneration increases with the increase of average QCs of the random input states along with non-Markovianity.

DOI
10.1103/physreva.105.012424

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We explore the impact of non-Markovian channels on the quantum correlations of Haar uniformly generated random two-qubit input states with different ranks: Either one of the qubits (single-sided channel) or both qubits independently (double-sided channel) are passed through a noisy channel. For dephasing and depolarizing channels with varying non-Markovian strength, entanglement and quantum discord of the output states collapse and revive with the increase of noise. By both analytical and numerical means, we find that in the case of the depolarizing double-sided channel, entanglement and quantum discord for random states show a higher number of revivals on average than for single-sided channels with a fixed non-Markovianity strength, irrespective of the rank of the states; we call such a counterintuitive event, constructive feedback of non-Markovianity. In contrast, the mean value of critical noise at which quantum correlations (QCs) first collapse decreases with the increase of non-Markovianity, independently of the rank of the random initial states. However, the average noise at which QCs of random states show the first revival decreases with the increase of the strength of non-Markovian noise, thereby indicating the role of non-Markovian channels in the regeneration of QCs even in the presence of a high amount of noise. Moreover, we observe that the tendency of a state to show regeneration increases with the increase of average QCs of the random input states along with non-Markovianity.
We study the dynamics of quantum dissension for three qubit states in various dissipative channels such as amplitude damping, dephasing and depolarizing. Our study is solely based on Markovian environments where quantum channels are without memory and each qubit is coupled to its own environment. We start with mixed GHZ, mixed W, mixture of separable states, a mixed biseparable state, as the initial states and mostly observe that the decay of quantum dissension is asymptotic in contrast to sudden death of quantum entanglement in similar environments. This is a clear indication of the fact that quantum correlation in general is more robust against the effect of noise. However, for a given class of initial mixed states we find a temporary leap in quantum dissension for a certain interval of time. More precisely, we observe the revival of quantum correlation to happen for certain time period. This signifies that the measure of quantum correlation such as quantum discord, quantum dissension, defined from the information theoretic perspective is different from the correlation defined from the entanglement-separability paradigm and can increase under the effect of the local noise. We also study the effects of these channels on the monogamy score of each of these initial states. Interestingly, we find that for certain class of states and channels, there is change from negative values to positive values of the monogamy score with classical randomness as well as with time. This gives us an important insight in obtaining states which are freely sharable (polygamous state) from the states which are not freely sharable (monogamous). This is indeed a remarkable feature, as we can create monogamous states from polygamous states Monogamous states are considered to have more signatures of quantum ness and can be used for security purpose.
We analyze the classical and quantum correlation properties of the standard and so-called quasiclassical depolarizing channel with correlated noise and non-Markovian dephasing channel, specifically we use the quantum discord, entanglement, and measurement-induced disturbance (MID) to measure the quantum correlations. For the depolarizing channel, we find that the memory effect has more influence on the MID and quantum discord than entanglement. For the dephasing channel, we show that the non-Markovian dephasing channel is more robust than Markovian dephasing channel against decoherence. We also find that at first MID and quantum discord take different values, and then after a specific time they will take almost the same value and both decay monotonically in the same way.
We address the effect of classical noise on the dynamics of quantum correlations, entanglement and quantum discord (QD), of two non-interacting qubits initially prepared in a Bell state. The effect of noise is modeled by randomizing the single-qubit transition amplitudes. We address both static and dynamic environmental noise corresponding to interaction with separate and common baths in either Markovian and non-Markovian regimes. In the Markov regime, a monotone decay of the quantum correlations is found, whereas for non-Markovian noise sudden death and revival phenomena may occur, depending on the characteristics of the noise. Entanglement and QD show the same qualitative behavior for all kind of noises considered. On the other hand, we find that separate and common environments may play opposite roles in preserving quantum correlations, depending on the noise regime considered.
Knowledge of the dynamical behavior of correlations with no classical counterpart, like entanglement, nonlocal correlations and quantum discord, in open quantum systems is of primary interest because of the possibility to exploit these correlations for quantum information tasks. Here we review some of the most recent results on the dynamics of correlations in bipartite systems embedded in non-Markovian environments that, with their memory effects, influence in a relevant way the system dynamics and appear to be more fundamental than the Markovian ones for practical purposes. Firstly, we review the phenomenon of entanglement revivals in a two-qubit system for both independent environments and a common environment. We then consider the dynamics of quantum discord in non-Markovian dephasing channel and briefly discuss the occurrence of revivals of quantum correlations in classical environments.
The principal resource in several quantum information-processing tasks is entanglement. Building practically useful versions of such tasks, one often needs to consider multipartite systems. And in such scenarios, it is impossible to eliminate the effects of the environment while distributing the resources. We show how information backflow from the environment due to non-Markovianity in the system dynamics affects the resources in multipartite systems, specifically multiparty entanglement. In particular, we find that the entanglement of multiqubit Greenberger-Horne-Zeilinger cat states saturates with time to a nonzero value for a non-Markovian dephasing noise. The multiqubit W states saturate to a higher value. Such nonzero time-saturated values are washed out if the non-Markovianity in the channel is removed. The multiqubit W states provide a richer set of features, including a nonzero value for an asymptotic number of qubits and an even-odd dichotomy in the entanglement with the number of qubits. Moving to a non-Markovian depolarizing channel, we find that both cat and W states exhibit a revival of entanglement after the collapse.
Abstract We study the dimensionless time evolution of the logarithmic negativity and geometric quantum discord of a qubit-qutrit XXX spin model under the both Markovian and non-Markovian noise channels. We find that at a special temperature interval the quantum entanglement based on the logarithmic negativity reveals entanglement sudden deaths together with revivals. The revival phenomenon is due to the non-Markovianity resulting from the feedback effect of the environment. At high temperatures, the scenario of death and revival disappears. The geometric quantum discord evolves alternatively versus time elapsing with damped amplitudes until the system reaches steady state. It is demonstrated that the dynamics of entanglement negativity undergoes substantial changes by varying temperature, and it is much more fragile against the temperature rather than the geometric quantum discord. The real complex heterodinuclear [Ni(dpt)(H 2 O)Cu(pba)] · 2H 2 O [with pba = 1,3-propylenebis(oxamato) and dpt = bis-(3-aminopropyl)amine] is an experimental representative of our considered bipartite qubit-qutrit system that may show remarkable entanglement deaths and revivals at relatively high temperatures and high magnetic field that is comparable with the strength of the exchange interaction J between Cu +2 and Ni +2 ions, i.e., k B T ≈ J and μ B B ≈ J .