The nonincreasing feature of temporal quantum steering under a completely positive trace-preserving (CPTP) map, as proposed by Chen et al. [Phys. Rev. Lett. 116, 020503 (2016)], has been considered as a practical measure of non-Markovianity. In this paper we utilize an all-optical scheme to simulate a non-Markovian collision model and to examine how Gaussian steering can be used as a tool for quantifying the non-Markovianity of a structured continuous-variable (CV) Gaussian channel. By modifying the reflectivity of the beam splitters (BSs), we are able to tune the degree of non-Markovianity of the channel. After analyzing the non-Markovian degree of the dissipative channel within two steering scenarios, we discovered that the Gaussian-steering-based non-Markovian measure depends the specific scenario because of the asymmetry of Gaussian steering. We also compared the Gaussian-steering-based non-Markovianity to the one based on violation of divisibility of a CPTP map.
The nonincreasing feature of temporal quantum steering under a completely positive trace-preserving (CPTP) map, as proposed by Chen et al. [Phys. Rev. Lett. 116, 020503 (2016)], has been considered as a practical measure of non-Markovianity. In this paper we utilize an all-optical scheme to simulate a non-Markovian collision model and to examine how Gaussian steering can be used as a tool for quantifying the non-Markovianity of a structured continuous-variable (CV) Gaussian channel. By modifying the reflectivity of the beam splitters (BSs), we are able to tune the degree of non-Markovianity of the channel. After analyzing the non-Markovian degree of the dissipative channel within two steering scenarios, we discovered that the Gaussian-steering-based non-Markovian measure depends the specific scenario because of the asymmetry of Gaussian steering. We also compared the Gaussian-steering-based non-Markovianity to the one based on violation of divisibility of a CPTP map.
We put forward a measure based on Gaussian steering to quantify the non-Markovianity of continuous-variable (CV) Gaussian quantum channels. We employ the proposed measure to assess and compare the non-Markovianity of a quantum Brownian motion (QBM) channel, originating from the interaction with Ohmic and sub-Ohmic environments with spectral densities described by a Lorentz-Drude cutoff, both at high and low temperatures, showing that sub-Ohmic, high-temperature environments lead to highly non-Markovian evolution, with cyclic backflows of Gaussian steerability from the environment to the system. Our results add to the understanding of the interplay between quantum correlations and non-Markovianity for CV systems, and could be implemented at the experimental level to quantify non-Markovianity in some physical scenarios.
Abstract Based on the nonincreasing property of quantum coherence via skew information under incoherent completely positive and trace-preserving maps, we propose a non-Markovianity measure for open quantum processes. As applications, by applying the proposed measure to some typical noisy channels, we find that it is equivalent to the three previous measures of non-Markovianity for phase damping and amplitude damping channels, i.e. the measures based on the quantum trace distance, dynamical divisibility, and quantum mutual information. For the random unitary channel, it is equivalent to the non-Markovianity measure based on l 1 norm of coherence for a class of output states and it is incompletely equivalent to the measure based on dynamical divisibility. We also use the modified Tsallis relative entropy of coherence to detect the non-Markovianity of dynamics of quantum open systems, the results show that the modified Tsallis relative entropy of coherence are more comfortable than the original Tsallis relative entropy of coherence for small .
We introduce a non-Markovianity measure for continuous-variable open quantum systems based on the idea put forward in H.-P. Breuer et al. [Phys. Rev. Lett. 103, 210401 (2009);], that is, by quantifying the flow of information from the environment back to the open system. Instead of the trace distance we use here the fidelity to assess distinguishability of quantum states. We employ our measure to evaluate non-Markovianity of two paradigmatic Gaussian channels: the purely damping channel and the quantum Brownian motion channel with Ohmic environment. We consider different classes of Gaussian states and look for pairs of states maximizing the backflow of information. For coherent states we find simple analytical solutions, whereas for squeezed states we provide both exact numerical and approximate analytical solutions in the weak coupling limit.
Quantum steering-a strong correlation to be verified even when one party or its measuring device is fully untrusted-not only provides a profound insight into quantum physics but also offers a crucial basis for practical applications. For continuous-variable (CV) systems, Gaussian states among others have been extensively studied, however, mostly confined to Gaussian measurements. While the fulfilment of Gaussian criterion is sufficient to detect CV steering, whether it is also necessary for Gaussian states is a question of fundamental importance in many contexts. This critically questions the validity of characterizations established only under Gaussian measurements like the quantification of steering and the monogamy relations. Here, we introduce a formalism based on local uncertainty relations of non-Gaussian measurements, which is shown to manifest quantum steering of some Gaussian states that Gaussian criterion fails to detect. To this aim, we look into Gaussian states of practical relevance, i.e. two-mode squeezed states under a lossy and an amplifying Gaussian channel. Our finding significantly modifies the characteristics of Gaussian-state steering so far established such as monogamy relations and one-way steering under Gaussian measurements, thus opening a new direction for critical studies beyond Gaussian regime.
We investigate the non-Markovianity of continuous-variable Gaussian quantum channels through the evolution of an operational metrological quantifier, namely, the Gaussian interferometric power, which captures the minimal precision that can be achieved using bipartite Gaussian probes in a black-box phase estimation setup, where the phase shift generator is a priori unknown. We observe that the monotonicity of the Gaussian interferometric power under the action of local Gaussian quantum channels on the ancillary arm of the bipartite probes is a natural indicator of Markovian dynamics; consequently, its breakdown for specific maps can be used to construct a witness and an effective quantifier of non-Markovianity. In our work, we consider two paradigmatic Gaussian models, the damping master equation and the quantum Brownian motion, and identify analytically and numerically the parameter regimes that give rise to non-Markovian dynamics. We then quantify the degree of non-Markovianity of the channels in terms of Gaussian interferometric power, showing, in particular, that even nonentangled probes can be useful to witness non-Markovianity. This establishes an interesting link between the dynamics of bipartite continuous-variable open systems and their potential for optical interferometry. The results are an important supplement to the recent research on characterization of non-Markovianity in continuous-variable systems.
We introduce a method to construct non-Markovian variants of completely positive (CP) dynamical maps, particularly, qubit Pauli channels. We identify non-Markovianity with the breakdown in CP divisibility of the map, i.e., appearance of a not-completely positive intermediate map. In particular, we consider the case of non-Markovian dephasing in detail. The eigenvalues of the Choi matrix of the intermediate map crossover at a point which corresponds to a singularity in the canonical decoherence rate of the corresponding master equation and thus to a momentary noninvertibility of the map. Thereafter, the rate becomes negative, indicating non-Markovianity. We quantify the non-Markovianity by two methods, one based on CP divisibility [Hall et al., Phys. Rev. A 89, 042120 (2014)], which does not require optimization but requires normalization to handle the singularity, and another method, based on distinguishability [Breuer et al. Phys. Rev. Lett. 103, 210401 (2009)], which requires optimization but is insensitive to the singularity.