Quantum non-Markovianity: characterization, quantification and detection

Rivas, Ana María Rivas; Huelga, Susana F.; Plenio, Martin B.

doi:10.1088/0034-4885/77/9/094001

Cited by 935 publications

(1,268 citation statements)

References 288 publications

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“…Although the concept of non-Markovianity is well established in the classical realm [22], its quantum extension is often riddled with inconsistency and subtle variations. This has led to a substantial amount of literature attempting to quantitatively characterize non-Markovianity based primarily on the nonmonotonic time evolution of some quantum information measure (for reviews, see [23][24][25]). Such nonmonotonic behavior arises from the nondivisibility of the completely positive and trace preserving (CPTP) maps [6] that describe the dynamics of the open quantum system, which is perhaps the most established marker of non-Markovianity [24][25][26] (cf.…”

Section: Introductionmentioning

confidence: 99%

Characterizing non-Markovianity via quantum interferometric power

2015

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Non-Markovian evolution in open quantum systems is often characterized in terms of the backflow of information from environment to system and is thus an important facet in investigating the performance and robustness of quantum information protocols. In this work, we explore non-Markovianity through the breakdown of monotonicity of a metrological figure of merit, called the quantum interferometric power, which is based on the minimal quantum Fisher information obtained by local unitary evolution of one part of the system, and can be interpreted as a quantifier of quantum correlations beyond entanglement. We investigate our proposed non-Markovianity indicator in two relevant examples. First, we consider the action of a single-party dephasing channel on a maximally entangled two-qubit state, by applying the Jamiołkowski-Choi isomorphism. We observe that the proposed measure is consistent with established non-Markovianity quantifiers defined using other approaches based on dynamical divisibility, distinguishability, and breakdown of monotonicity for the quantum mutual information. Further, we consider the dynamics of two-qubit Werner states, under the action of a local, single-party amplitude damping channel, and observe that the nonmonotonic evolution of the quantum interferometric power is more robust than the corresponding one for entanglement in capturing the backflow of quantum information associated with the non-Markovian process. Implications for the role of non-Markovianity in quantum metrology and possible extensions to continuous variable systems are discussed.

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Section: Introductionmentioning

confidence: 99%

Characterizing non-Markovianity via quantum interferometric power

2015

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“…Various concepts of non-Markovianity were introduced recently to define the border between Markovian and non-Markovian quantum evolution, although the very definition of non-Markovianity is still a debated issue. Many different measures of non-Markovianity have been proposed in the literature to quantify memory effects in open systems, based on, for examples, the divisibility of dynamical map [5][6][7][8], the distinguishability of states [9][10][11][12], quantum entanglement [13][14][15][16][17], quantum Fisher information [18][19][20][21], mutual information [22][23][24][25], geometrical characterization [8,26] and the decay rate of the master equation itself [27,28]. Predominately, almost all these measures of non-Markovianity are introduced in terms of mathematical quantities.…”

Section: Introductionmentioning

confidence: 99%

Non-Markovianity measure using two-time correlation functions

Ali

et al. 2015

Phys. Rev. A

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We investigate non-Markovianity measure using two-time correlation functions for open quantum systems. We define non-Markovianity measure as the difference between the exact two-time correlation function and the one obtained in the Markov limit. Such non-Markovianity measure can easily be measured in experiments. We found that the non-Markovianity dynamics in different time scale crucially depends on the system-environment coupling strength and other physical parameters such as the initial temperature of the environment and the initial state of the system. In particular, we obtain the short-time and long-time behaviors of non-Markovianity for different spectral densities. We also find that the thermal fluctuation always reduce the non-Markovian memory effect. Also, the non-Markovianity measure shows non-trivial initial state dependence in different time scales.

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“…Different measures have been proposed to quantify the nonMarkovianity [31][32][33]. Breuer's non-Markovianity measure [35,63,64] is based on the trace distance of pairs of initial states…”

Section: Witness Of Non-markovianitymentioning

confidence: 99%

Analysis of the non-Markovianity for electron transfer reactions in an oligothiophene-fullerene heterojunction

2017

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a b s t r a c tThe non-Markovianity of the electron transfer in an oligothiophene-fullerene heterojunction described by a spin-boson model is analyzed using the time dependent decoherence canonical rates and the volume of accessible states in the Bloch sphere. The dynamical map of the reduced electronic system is computed by the hierarchical equations of motion methodology (HEOM) providing an exact dynamics. Transitory witness of non-Markovianity is linked to the bath dynamics analyzed from the HEOM auxiliary matrices. The signature of the collective bath mode detected from HEOM in each electronic state is compared with predictions of the effective mode extracted from the spectral density. We show that including this main reaction coordinate in a one-dimensional vibronic system coupled to a residual bath satisfactorily describes the electron transfer by a simple Markovian Redfield equation. Non-Markovianity is computed for three inter fragment distances and compared with a priori criterion based on the system and bath characteristic timescales.

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Quantum non-Markovianity: characterization, quantification and detection

Cited by 935 publications

References 288 publications

Characterizing non-Markovianity via quantum interferometric power

Characterizing non-Markovianity via quantum interferometric power

Non-Markovianity measure using two-time correlation functions

Analysis of the non-Markovianity for electron transfer reactions in an oligothiophene-fullerene heterojunction

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