Related papers: Requiring linearity leads to complete positivity
The dynamics of a closed quantum system, under a unitary time evolution $U$, is, obviously, linear. But, the reduced dynamics of an open quantum system $S$, interacting with an environment $E$, is not linear, in general. Dominy et al.…
Complete positivity is a ubiquitous assumption in the study of quantum systems interacting with the environment, despite repeated efforts to point out that the assumption is not empirically justified. It will be shown that Hamiltonian…
We correct a mistake in a result reported in [PRA 64, 062106 (2001)], where it is rightfully argued that initial correlations between a system and its environment may render the system reduced dynamics not completely positive. We prove how…
We expand the set of initial states of a system and its environment that are known to guarantee completely positive reduced dynamics for the system when the combined state evolves unitarily. We characterize the correlations in the initial…
We introduce a general framework for the construction of completely positive dynamical evolutions in the presence of system-environment initial correlations. The construction relies upon commutativity of the compatibility domain obtained by…
A system interacting with its environment will give rise to a quantum evolution. After tracing over the environment the net evolution of the system can be described by a linear Hermitian map. It has recently been shown that a necessary and…
The requirement of complete positivity is very often regarded as a fundamental consistency condition for the description of open quantum dynamics. We critically examine this requirement and discuss both its physical motivations and its…
We consider complete positivity of dynamics regarding subsystems of an open composite quantum system, which is subject of a completely positive dynamics. By "completely positive dynamics", we assume the dynamical maps called the completely…
We show that complete positivity is not only sufficient but also necessary for the validity of the quantum data-processing inequality. As a consequence, the reduced dynamics of a quantum system are completely positive, even in the presence…
Complete positivity of quantum dynamics is often viewed as a litmus test for physicality, yet it is well known that correlated initial states need not give rise to completely positive evolutions. This observation spurred numerous…
Starting form a microscopic system-environment model, we construct a quantum dynamical semigroup for the reduced evolution of the open system. The difference between the true system dynamics and its approximation by the semigroup has the…
Consider the set $\mathcal{S}=\lbrace\rho_{SE}\rbrace$ of possible initial states of the system-environment. The map which assigns to each $\rho_{S}\in \mathrm{Tr}_{E}\mathcal{S}$ a $\rho_{SE}\in \mathcal{S}$ is called the assignment map.…
Positivity or the stronger notion of complete positivity, and contextuality are central properties of quantum dynamics. In this work, we demonstrate that a physical unitary-universe dilation model could be employed to characterize the…
Finding the general set of system-environment states for which the reduced dynamics of the system is completely positive (CP) is the subject of some recent works. An advance in this context appeared in [X. Lu, Phys. Rev. A 93, 042332…
We study the concepts of complete positivity, positivity and non-Markovianity in a two-level open quantum system whose dynamics are governed by a time-local quantum master equation. We establish necessary and sufficient conditions on the…
While it is well known that complete positivity guarantees the fulfilment of the second law of thermodynamics, its possible violations have never been proposed as a check of the complete positivity of a given open quantum dynamics. We…
We show that the dynamics of any open quantum system that is initially correlated with its environment can be described by a set of (or less) completely positive maps, where d is the dimension of the system. Only one such map is required…
We consider a physical system in which the description of states and measurements follow the usual quantum mechanical rules. We also assume that the dynamics is linear, but may not be fully quantum (i.e unitary). We show that in such a…
Two recent arguments for linear dynamics in quantum theory are critically re-examined. Neither argument is found to be satisfactory as it stands, although an improved version of one of the arguments can in fact be given. This improved…
Maps that are not completely positive (CP) are often useful to describe the dynamics of open systems. An apparent violation of complete positivity can occur because there are prior correlations of the principal system with the environment,…