Degree of Non-Markovianity of Quantum Evolution

Abstract

We propose a new characterization of non-Markovian quantum evolution based on the concept of non-Markovianity degree. It provides an analog of a Schmidt number in the entanglement theory and reveals the formal analogy between quantum evolution and the entanglement theory: Markovian evolution corresponds to a separable state and the non-Markovian one is further characterized by its degree. It enables one to introduce a non-Markovianity witness-an analog of an entanglement witness, and a family of measures-an analog of Schmidt coefficients, and finally to characterize maximally non-Markovian evolution being an analog of the maximally entangled state. Our approach allows us to classify the non-Markovianity measures introduced so far in a unified rigorous mathematical framework.

Non-Markovianity-assisted high-fidelity Deutsch–Jozsa algorithm in diamond

“…Non-Markovian effect of noise environment on RDJA These nontrivial phenomena deviate mainly from the quantum Born-Markovian process [28][29][30][31] and reflect the occurrence of nonMarkovian dynamics. To confirm this supposition and study how the memory effects of the environment affect the RDJA, we measured the non-Markovianity of the quantum system by employing the trace distance method, 29,31,44 which is given by…”

“…28 However, because of strong system-environment couplings, structured or finite reservoirs, low temperatures, or large initial system-environment correlations, the dynamics of an open quantum system may deviate substantially from the Born-Markov approximation and follow a non-Markovian process. [28][29][30][31][32] In such a process, the pronounced memory effect, which is the primary feature of a non-Markovian environment, can be used to revive the genuine quantum properties, [28][29][30][31][32][33][34] such as quantum coherence and correlations. Consequently, improving the performance of QIP by utilizing memory effects as important physical resources in the nonMarkovian environment is crucial.…”

Time-invariant discord in dynamically decoupled systems

“…Thus, similarly to DD techniques, non-Markovianity can also be used to restore monotonically decaying correlations [10]. An ongoing debate concerns itself with characterizing and quantifying non-Markovianity [11][12][13][14][15][16][17][18][19]. At present, no universal measure exists and indeed in some cases, connections between measures can not be established [20,21].…”

Collapse and revival of quantum coherence for a harmonic oscillator interacting with a classical fluctuating environment

“…For this reason a great deal of attention has been devoted to the study of the corresponding non-Markovian dynamics in different systems ranging from quantum optics to mechanical oscillators and harmonic lattices [46][47][48][49][50][51][52][53][54]. In addition, there is evidence that non-Markovian open quantum systems [55][56][57][58][59] can be useful for quantum technology [60][61][62].…”