Abstract

We propose the notion of quantum coherence for superpositions over states which are not necessarily mutually orthogonal. This anticipatedly leads to a resource theory of non-orthogonal coherence. We characterize free states and free operations in this theory, and connect the latter with free operations in the resource theory of quantum coherence for orthogonal bases. We show that the concept of non-orthogonal coherence naturally furnishes us with a wave-particle duality in quantum double-slit experiments where the channels beyond the slits are leaky between them. Furthermore, we demonstrate existence of a unique maximally coherent qubit state corresponding to any given purity. In addition, and in contradistinction with the case of orthogonal bases, there appears a non-trivial minimally coherent qubit state for a given purity. We also study the behavior of quantum coherence for some typical configurations of …

Abstract

We present a formalism for detection of non-Markovianity (NM) through uncertainty relations. We show that when there is an information back-flow to the system from its environment through CP-divisibility breaking, the Choi-states corresponding to the reduced system evolution contain at least one negative eigenvalue. The consequent break down of uncertainty relations for such states can be used to witness non-Markovian dynamics. We present some relevant examples of the phenomenon for qubit channels. We further prove that square of the variance of a suitable Hermitian operator can act as a non-linear witness of NM. We finally show that NM is necessary in order to decrease the uncertainty of the states undergoing unital dynamics for qubits. This provides another method of certifying NM.

Abstract

We establish a connection between non-Markovianity and negative entropy production rate for various classes of quantum operations. We analyse several aspects of unital and thermal operations in connection with resource theories of purity and thermodynamics. We fully characterize Lindblad operators corresponding to unital operations. We also characterize the Lindblad dynamics for a large class of thermal operations. We next generalize the definition of the entropy production rate for the non-equilibrium case to connect it with the rate of change of free energy of the system, and establish complementary relations between non-Markovianity and maximum loss of free energy. We naturally conclude that non-Markovianity in terms of divisibility breaking is a necessary resource for the backflow of other resources like purity or free energy under the corresponding allowed operations.

Abstract

We identify a set of dynamical maps of open quantum system, and refer to them as" -Markovian" maps. It is constituted of maps that possibly violate Markovianity but only a" little". We characterize the" -nonmarkovianity" of a general dynamical map by the minimum distance of that map from the set of -Markovian maps. We analytically derive an inequality which gives a bound on the -nonmarkovianity of the dynamical map, in terms of an entanglement-like resource generated between the system and its" immediate" environment. In the special case of a vanishing , this inequality gives a relation between the non-Markovianity of the reduced dynamical map on the system and the entanglement generated between the system and its immediate environment. We investigate the behavior of the measures for classes of amplitude damping and phase damping channels.

Abstract

A master equation has been constructed for a global system–bath interaction in the both absence and presence of non-Markovian noise. For the memoryless case, it has been exactly solved for a paradigmatic class of two qubit states in high- and zero-temperature thermal environment. For the non-Markovian model, it has been solved for zero-temperature bath. The evolution of quantum coherence and entanglement has been observed in the presence of the above-mentioned interactions. We show that the global part of the system–bath interaction compensates for the decoherence, resulting in slowdown of coherence and entanglement decay. For an appropriately defined limiting case, both coherence and entanglement show freezing behavior for the high-temperature bath. In case of zero-temperature bath, the mentioned interaction not only stabilizes the non-classical correlations, but also enhances them …