Abstract

In this article we derive the exact dynamics of a two qubit (spin 1/2) system interacting centrally with separate fermionic baths composed of qubits in thermal state. Further, each spin of a bath is coupled to every other spin of the same bath. The corresponding dynamical map is constructed. It is used to analyse the non-Markovian nature of the two qubit central spin dynamics. We further observe the evolution of quantum correlations like entanglement and discord under the influence of the environmental interaction. Moreover, we demonstrate the comparison between this exact two qubit dynamics and the locally acting fermionic central spin model. This work is a stepping stone towards the realization of non-Markovian heat engines and other quantum thermal devices.

Abstract

We devise a novel protocol to detect genuinely multipartite entangled states by harnessing quantum non-Markovian operations. We utilize a particular type of non-Markovianity known as the eternal non-Markovianity to construct a non-complete positive map to filter out the bi-separable states and detect genuine multipartite entanglement. We further propose a witness operator to detect gen- uinely multipartite entangled states experimentally based on this theory. Our study sheds light on a hitherto unexplored connection between entanglement theory and quantum non-Markovianity.

Abstract

here are certain dynamics which although are non-Markovian but never show information backflow. We show that if two such dynamical maps are considered in a scenario where the order of application of these two dynamical maps are not definite, then the effective channel can manifest information backflow. In particular, we use quantum SWITCH to activate such channels. In contrast, those channels can never be activated even if we use many copy of such channels in series or parallel action. We then investigate the actual cause and dynamics behind the quantum SWITCH experiment and find out that after the action of quantum SWITCH both the CP (Complete Positive)- divisiblity and P (Positive)- divisibility of the channel breaks down, triggering the information backflow. Our investigations shed new light on the fundamental cause of the advantages of quantum SWITCH

Abstract

We develop a theory of linear witnesses for detecting non-Markovianity, based on the geometric structure of the set of Choi states for all Markovian evolutions having Lindblad-type generators. We show that the set of all such Markovian Choi states form a convex and compact set under the small time interval approximation. Invoking geometric Hahn–Banach theorem, we construct linear witnesses to separate a given non-Markovian Choi state from the set of Markovian Choi states. We present examples of such witnesses for dephasing channel and Pauli channel in case of qubits. Furthermore, we have devised another method of detection NM of various qubit channels, by using projective measurements in the Bell basis. This can be done without the knowledge of what specific kind of channel we are dealing with. This gives us a huge operational advantage for NM detection. We further investigate the geometric structure of the Markovian Choi states to find that they do not form a polytope. This presents a platform to consider nonlinear improvement of non-Markovianity witnesses.

Abstract

We identify a set of dynamical maps of open quantum system, and refer to them as 'epsilon-Markovian' maps. It is constituted of maps which, in a higher dimensional system–environment Hilbert space, possibly violate Born approximation but only a 'little'. We characterize the 'epsilon-nonmarkovianity' of a general dynamical map by the minimum distance of that map from the set of epsilon-Markovian maps. We analytically derive an inequality which gives a bound on the epsilon-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 epsilon, this inequality gives a relation between the epsilon-nonmarkovianity of the reduced dynamical map on the system and the entanglement generated between the system and its immediate environment. We numerically investigate the behavior of the similar distant based measures of non-Markovianity for classes of amplitude damping and phase damping channels.

Abstract

n this work, we revisit the theory of open quantum systems from the perspective of fermionic baths. Specifically, we concentrate on the dynamics of a central spin half particle interacting with a spin bath. We have calculated the exact reduced dynamics of the central spin and constructed the Kraus operators in relation to that. Further, the exact Lindblad type canonical master equation corresponding to the reduced dynamics is constructed. We have also briefly touched upon the aspect of non-Markovianity from the backdrop of the reduced dynamics of the central spin. Quanta 2021; 10: 55–64

Abstract

Entanglement is a fascinating feature, typical and ubiquitous to the science of quantum information and computation. Over the last few decades, we have seen entanglement, or more precisely bipartite entanglement, playing an unparalleled role in various quantum information-theoretic tasks [1–3]. Multipartite entanglement comes with an even richer structure and a whole new set of features providing information processing advantages in quantum communication, simulation, or metrology. It is therefore essential to construct methods to identify genuinely multipartite entangled states [4–6]. However, detecting entanglement of an arbitrary quantum state is a problem of significant complexity [7, 8]. Thus, witnessing entanglement by using versatile experimentally feasible tools [9–18] is a challenging task. In the case of multipartite entanglement, the challenge enhances significantly and demands greater interest from the scientific community. In this paper, we propose a protocol to detect multipartite entanglement by utilizing the well-known phenomenon of non-Markovianity in open quantum systems [19, 20] and the theory of positive maps. The positive maps that are not completely positive can detect bipartite entanglement quite effectively, Partial Transposition [21] being a well-known example. Unfortunately, this technique cannot be directly extended to the case of multipartite entanglement, where diverse separability structures complicate the detection problem. Although semi-definite programming can be used to construct witnesses to certify genuine multipartite entangle

Abstract

We establish a convex resource theory of non-Markovianity inducing information backflow under the constraint of small time intervals within the temporal evolution. We identify the free operations and a generalized bona-fide measure of non-Markovian information backflow. The framework satisfies the basic properties of a consistent resource theory. The proposed resource quantifier is lower bounded by the optimization free Rivas–Huelga–Plenio (RHP) measure of non-Markovianity. We next define the robustness of non-Markovianity and show that it can directly linked with the RHP measure of non-Markovianity through a lower bound. This enables a physical interpretation of the RHP measure. We further relate robustness of non-Markovianity with the quantum capacity of dephasing channels.

Abstract

The problem of bound entanglement detection is a challenging aspect of quantum information theory for higher dimensional systems. Here, we propose an indecomposable positive map for two-qutrit systems, which is shown to generate a class of positive partial transposed (PPT) states. A corresponding witness operator is constructed and shown to be weakly optimal and locally implementable. Further, we perform a structural physical approximation of the indecomposable map to make it a completely positive one, and find a new PPT entangled state which is not detectable by certain other well-known entanglement detection criteria.

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 …