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Andrzej Kossakowski

Publications and source records attributed to Andrzej Kossakowski.

At least 19 recordsLinked to original sources
arXiv2020

On the universal constraints for relaxation rates for quantum dynamical semigroup

A conjecture for the universal constraints for relaxation rates of a quantum dynamical semigroup is proposed. It is shown that it holds for several interesting classes of semigroups, e.g. unital semigroups and semigroups derived in the weak coupling limit from the proper microscopic model. Moreover, proposed conjecture is supported by numerical analysis. This conjecture has several important implications: it allows to provide universal constraints for spectra of quantum channels and provides necessary condition to decide whether a given channel is consistent with Markovian evolution.

quant-ph↗
arXiv2017

On generalized semi-Markov quantum evolution

We provide a large class of quantum evolution governed by the memory kernel master equation. This class defines quantum analog of so called semi-Markov classical stochastic evolution. In this Letter for the first time we provide a proper definition of quantum semi-Markov evolution and using the appropriate gauge freedom we propose a suitable generalization which contains majority of examples considered so far in the literature. The key concepts are quantum counterparts of classical waiting time distribution and survival probability -- quantum waiting time operator and quantum survival operator, respectively. In particular collision models and its generalizations considered recently are special examples of generalized semi-Markov evolution. This approach allows for an interesting generalization of trajectory description of the quantum dynamics in terms of POVM densities.

quant-ph↗
arXiv2016

Sufficient conditions for memory kernel master equation

We derive sufficient conditions for the memory kernel which guarantee legitimate (completely positive and trace-preserving) dynamical map. It turns out that these conditions provide a natural parameterizations of the dynamical map being a generalization of Markovian semigroup. It is shown that this class of maps cover almost all known examples -- from Markovian semigroup, semi-Markov evolution up to collision models and their generalization.

quant-ph↗
arXiv2013

A quantum particle in a box with moving walls

We analyze the non-relativistic problem of a quantum particle that bounces back and forth between two moving walls. We recast this problem into the equivalent one of a quantum particle in a fixed box whose dynamics is governed by an appropriate time-dependent Schroedinger operator.

math-ph↗
arXiv2013

Feshbach projection formalism for open quantum systems

We provide a new approach to open quantum systems which is based on the Feshbach projection method in an appropriate Hilbert space. Instead of looking for a master equation for the dynamical map acting in the space of density operators we provide the corresponding equation for the evolution in the Hilbert space of the system. Its solution enables one to construct a legitimate quantum evolution (completely positive and trace preserving). The big advantage of this approach is the ability of performing a consistent approximation which creates notorious problems in the standard Nakajima-Zwanzig approach. The new scheme is illustrated by well known spin-boson model beyond rotating wave approximation.

quant-ph↗
arXiv2012

Witnessing non-Markovianity of quantum evolution

We provide further characterization of non-Markovian quantum dynamics based on the concept of divisible dynamical maps. In analogy to entanglement witness we propose a non-Markovianity witness and introduce the corresponding measure of non-Markovianity. We also provide characterization of non-Markovianity in terms of entropic quantities, fidelity and Wigner-Yanase-Dyson skew information.

quant-ph↗
arXiv2012

Markovianity criteria for quantum evolution

We characterize a class of Markovian dynamics using the concept of divisible dynamical map. Moreover we provide a family of criteria which can distinguish Markovian and non-Markovian dynamics. These Markovianity criteria are based on a simple observation that Markovian dynamics implies monotonic behavior of several well known quantities like distinguishability of states, fidelity, relative entropy and genuine entanglement measures.

quant-ph↗
arXiv2011

On measures of non-Markovianity: divisibility vs. backflow of information

We analyze two recently proposed measures of non-Markovianity: one based on the concept of divisibility of the dynamical map and the other one based on distinguishability of quantum states. We provide a toy model to show that these two measures need not agree. In addition, we discuss possible generalizations and intricate relations between these measures.

quant-ph↗
arXiv2010

Bell diagonal states with maximal abelian symmetry

We provide a simple class of 2-qudit states for which one is able to formulate necessary and sufficient conditions for separability. As a byproduct we generalize well known construction provided by Horodecki et al. for d=3. It is hoped that these states with known separability/entanglement properties may be used to test various notions in entanglement theory.

quant-ph↗
arXiv2010

From Markovian semigroup to non-Markovian quantum evolution

We provided a class of legitimate memory kernels leading to completely positive trace preserving dynamical maps. Our construction is based on a simple normalization procedure. Interestingly, when applied to the celebrated Wigner-Weisskopf theory it gives the standard Markovian evolution governed by the local master equation.

quant-ph↗
arXiv2010

On the symmetry of the seminal Horodecki state

It is shown that the seminal Horodecki 2-qutrit state belongs to the class of states displaying symmetry governed by a commutative subgroup of the unitary group U(3). Taking a conjugate subgroup one obtains another classes of symmetric states and one finds equivalent representations of the Horodecki state.

quant-ph↗
arXiv2010

General form of quantum evolution

We propose a complete treatment of a local in time dynamics of open quantum systems. In this approach Markovian evolution turns out to be a special case of a general non-Markovian one. We provide a general representation of the local generator which generalizes well known Lindblad representation for the Markovian dynamics. It shows that the structure of non-Markovian generators is highly intricate and the problem of their classification is still open. Simple examples illustrate our approach.

quant-ph↗
arXiv2010

Long-time memory in non-Markovian evolutions

If the dynamics of an open quantum systems is non-Markovian, its {asymptotic} state strongly depends on the initial conditions, even if the dynamics possesses an {invariant} state. This is the very essence of memory effects. In particular, the {asymptotic} state can remember and partially preserve its initial entanglement. Interestingly, even if the non-Markovian evolution relaxes to an equilibrium state, this state needs not be invariant. Therefore, the non-invariance of equilibrium becomes a clear sign of non-Markovianity.

quant-ph↗
arXiv2010

Non-Markovian quantum dynamics: local versus non-local

We analyze non-Markovian evolution of open quantum systems. It is shown that any dynamical map representing evolution of such a system may be described either by non-local master equation with memory kernel or equivalently by equation which is local in time. These two descriptions are complementary: if one is simple the other is quite involved, or even singular, and vice versa. The price one pays for the local approach is that the corresponding generator keeps the memory about the starting point `t_0'. This is the very essence of non-Markovianity. Interestingly, this generator might be highly singular, nevertheless, the corresponding dynamics is perfectly regular. Remarkably, singularities of generator may lead to interesting physical phenomena like revival of coherence or sudden death and revival of entanglement.

quant-ph↗
arXiv2009

Geometry of quantum states: new construction of positive maps

We provide a new class of positive maps in matrix algebras. The construction is based on the family of balls living in the space of density matrices of n-level quantum system. This class generalizes the celebrated Choi map and provide a wide family of entanglement witnesses which define a basic tool for analyzing quantum entanglement.

quant-ph↗
arXiv2008

Spectral conditions for positive maps

We provide a partial classification of positive linear maps in matrix algebras which is based on a family of spectral conditions. This construction generalizes celebrated Choi example of a map which is positive but not completely positive. It is shown how the spectral conditions enable one to construct linear maps on tensor products of matrix algebras which are positive but only on a convex subset of separable elements. Such maps provide basic tools to study quantum entanglement in multipartite systems.

quant-ph↗