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We investigate the conditions under which the trace distance between two different states of a given open system increases in time due to the interaction with an environment, therefore signaling non-Markovianity. We find that the finite-time difference in trace distance is bounded by two sharply defined quantities that are strictly linked to the occurrence of system-environment correlations created throughout their interaction and affecting the subsequent evolution of the system. This allows us to shed light on the origin of non-Markovian behaviors in quantum dynamics. We best illustrate our findings by tackling two physically relevant examples: a non-Markovian dephasing mechanism that has been the focus of a recent experimental endeavor and the open-system dynamics experienced by a spin connected to a finite-size quantum spin chain. [ABSTRACT FROM AUTHOR]

We present a scheme to prepare quantum correlated states of two mechanical systems based on the pouring of preavailable all-optical entanglement into the state of two micromirrors belonging to remote and noninteracting optomechanical cavities. We show that, under realistic experimental conditions, the protocol allows for the preparation of a genuine quantum state of a composite mesoscopic system whose nonclassical features extend beyond the occurrence of entanglement. We finally discuss a way to access such mechanical correlations. [ABSTRACT FROM AUTHOR]

A post-Markovian master equation has been recently proposed as a tool to describe the evolution of a system coupled to a memory-keeping environment [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101 (R) (2005)]. For a single qubit affected by appropriately chosen environmental conditions, the corresponding dynamics is always legitimate and physical. Here we extend such a situation to the case of two qubits, only one of which experiences the environmental effects. We show how, despite the innocence of such an extension, the introduction of the second qubit should be done cum grano salis to avoid consequences such as the breaking of the positivity of the associated dynamical map. This hints at the necessity of using care when adopting phenomenologically derived models for evolutions occurring outside the Markovian framework. [ABSTRACT FROM AUTHOR]