Abstract

It is known that beyond 2 ⊗ 2 and 2 ⊗ 3 dimensional quantum systems, Peres-Hordecki criterion is no longer sufficient as an entanglement detection criterion as there are entangled states with both positive and negative partial transpose (PPT and NPT). Further, it is also true that all PPT entangled states are bound entangled states. However, in the class of NPT states, there can exist bound entangled states as well as free entangled states. All free/useful/distillable entanglement is a part of the class of NPT entangled states. In this article, we ask the question that given an NPT entangled state in 3 ⊗ 3 dimensional system as a resource, how much entanglement can we broadcast so that resource still remains NPT. We have chosen 3 ⊗ 3 system as a first step to understand broadcasting of NPT states in higher dimensional systems. In particular, we find out the range of broadcasting of NPT entanglement for Two parameter Class of States (TPCS) and Isotropic States (IS). Interestingly, as a derivative of this process we are also able to locate the existence of absolute PPT states (ABPPT) in 3 ⊗ 3 dimensional system. Here we implement the strategy of broadcasting through approximate cloning operations.

Abstract

Since the eminent work of J. S. Bell, spatial correlations in quantum mechanics have gained much progress. Nevertheless, up to now, there is no agreement on the nature of temporal correlations. In this paper, based on the entangled-history theory, we prove that temporal correlations are just quantum channels. Moreover, by using the state tomography technology, the quantum channel can be uniquely determined. What is more, through the entanglement of formation, temporal correlations can be quantified. Cases when the temporal correlation is strongest and weakest are investigated, too.

Abstract

In this work, we extensively study the problem of broadcasting of entanglement as state dependent versus state independent cloners. We start by re-conceptualizing the idea of state dependent quantum cloning machine (SD-QCM), and in that process, we introduce different types of SD-QCMs, namely, orthogonal and non-orthogonal cloners. We derive the conditions for which the fidelity of these cloners will become independent of the input state. We note that such a construction allows us to maximize the cloning fidelity at the cost of having partial information of the input state. In the discussion on broadcasting of entanglement, we start with a general two qubit state as our resource and later we consider a specific example of Bell diagonal state. We apply both state dependent and state independent cloners (orthogonal and non-orthogonal), locally and non locally, on input resource state and obtain a range for broadcasting of entanglement in terms of the input state parameters. Our results highlight several instances where the state dependent cloners outperform their state independent counterparts in broadcasting entanglement. Our study provides a comparative perspective on the broadcasting of entanglement via cloning in two qubit scenario, when we have some knowledge of the resource ensemble versus a situation when we have no such information.

Abstract

In this work, we exhaustively investigate 1 → 2 local and nonlocal broadcasting of entanglement as well as correlations beyond entanglement (geometric discord) using asymmetric Pauli cloners with most general two qubit state as the resource. We exemplify asymmetric broadcasting of entanglement using 'Maximally Entangled Mixed States'. We demonstrate the variation of broadcasting range with the amount of entanglement present in the resource state as well as with the asymmetry in the cloner. We show that it is impossible to optimally broadcast geometric discord with the help of these asymmetric Pauli cloning machines. We also study the problem of 1 → 3 broadcasting of entanglement using non-maximally entangled state (NME) as the resource. For this task, we introduce a method we call successive broadcasting which involves application of 1 → 2 optimal cloning machines multiple times. We compare and contrast the performance of this method with the application of direct 1 → 3 optimal cloning machines. We show that 1 → 3 optimal cloner does a better job at broadcasting than the successive application of 1 → 2 cloners and the successive method can be beneficial in the absence of 1 → 3 cloners. We also bring out the fundamental difference between the tasks of cloning and broadcasting in the final part of the manuscript. We create examples to show that there exist local unitaries which can be employed to give a better range for broadcasting. Such unitary operations are not only economical, but also surpass the best possible range obtained using existing cloning machines enabling broadcasting of lesser entangled states. This result opens up a new direction in exploration of methods to facilitate broadcasting which may outperform the standard strategies implemented through cloning transformations

Abstract

Bell non-locality and steering are essential features of quantum mechanics which mark significant departures from classical notion. They basically refer to the presence of quantum correlations between separated systems which violate a non-local inequality, the violation being not possible if we restrict ourselves only to classical correlations. In view of the importance of such unique correlations one may be interested to generate more non-local states starting from a few, a protocol which is termed as broadcasting. However in the present submission we show that if one restricts to broadcasting through quantum cloning, then such non-local states cannot be broadcasted. Our study is done in the purview of the Bell-CHSH inequality and a steering inequality pertaining to three measurement settings. We also find suitable restrictions on the Werner and Bell diagonal states which will make them unsteerable under any number of measurement settings, after broadcasting.

Abstract

We propose a new measure of relative incompatibility for a quantum system with respect to two noncommuting observables, and call it quantumness of relative incompatibility. In case of a classical state, order of observation is inconsequential, hence probability distribution of outcomes of any observable remains undisturbed. We define relative entropy of the two marginal probability distributions as a measure of quantumness in the state, which is revealed only in presence of two non-commuting observables. Like all other measures, we show that the proposed measure satisfies some basic axioms. Also, we find that this measure depicts complementarity with quantum coherence. The relation is more vivid when we choose one of the observables in such a way that its eigen basis matches with the basis in which the coherence is measured. Our result indicates that the quantumness in a single system is still an interesting question to explore and there can be an inherent feature of the state which manifests beyond the idea of quantum coherence.

Abstract

Quantum mechanical properties like entanglement, discord and coherence act as fundamental resources in various quantum information processing tasks. Consequently, generating more resources from a few, typically termed as broadcasting is a task of utmost significance. One such strategy of broadcasting is through the application of cloning machines. In this article, broadcasting of quantum resources beyond 2 ⊗ 2 systems is investigated. In particular, in 2 ⊗ 3 dimension, a class of states not useful for broadcasting of entanglement is characterized for a choice of optimal universal Heisenberg cloning machine. The broadcasting ranges for maximally entangled mixed states (MEMS) and two parameter class of states (TPCS) are obtained to exemplify our protocol. A significant derivative of the protocol is the generation of entangled states with positive partial transpose in 3 ⊗ 3 dimension and states which are absolutely separable in 2 ⊗ 2 dimension. Moving beyond entanglement, in 2 ⊗ d dimension, the impossibility to optimally broadcast quantum correlations beyond entanglement (QCsbE) (discord) and quantum coherence(l1-norm) is established. However, some significant illustrations are provided to highlight that non-optimalbroadcasting of QCsbE and coherence are still possible

Abstract

In this brief report, we prove that the robustness of coherence (ROC), in contrast with many popular quantitative measures of quantum coherence derived from the resource-theoretic framework of coherence, may be a subadditive for a specific class of multipartite quantum states. We investigate how the subadditivity is affected by admixture with other classes of states for which ROC is superadditive. We show that pairs of quantum states may have different orderings with respect to relative entropy of coherence, l1-norm of coherence and ROC and numerically study the difference in ordering for the chosen pairwise coherence measures.

Abstract

Conditional von Neumann entropy is an intriguing concept in quantum information theory. In the present work, we examine the effect of global unitary operations on the conditional entropy of the system. We start with the set containing states with non-negative conditional entropy and find that some states preserve the non-negativity under unitary operations on the composite system. We call this class of states as Absolute Conditional von Neumann entropy Non Negative class (ACVENN). We are able to characterize such states for 2 ⊗ 2 dimensional systems. On a different perspective the characterization accentuates the detection of states whose conditional entropy becomes negative after the global unitary action. Interestingly, we show that this ACVENN class of states forms a set which is convex and compact. This feature enables the existence of hermitian witness operators. With these we can distinguish the unknown states which will have negative conditional entropy after the global unitary operation. We also show that this has immediate application in super dense coding and state merging as negativity of conditional entropy plays a key role in both these information processing tasks. Some illustrations followed by analysis are also provided to probe the connection of such states with absolutely separable (AS) states and absolutely local (AL) states.

Abstract

Steerability is a characteristic non-local trait of quantum states lying in between entanglement and Bell non-locality. A given quantum state is considered to be steerable if it violates a suitably chosen steering inequality. A quantum state which otherwise satisfies a certain inequality can violate the inequality under a global change of basis, i.e., if the state is transformed by a non-local unitary operation. Intriguingly, there are states which preserve their non-violation (pertaining to the said inequality) under any global unitary operation. The present work explores the effect of global unitary operations on the steering ability of a quantum state which lives in two qubits. We characterize such states in terms of a necessary and sufficient condition on their spectrum. Such states are also characterized in terms of some analytic characteristics of the set to which they belong. Looking back at steerability the present work also provides a relation between steerability and quantum teleportation together with the derivation of a result related to the optimal violation of steering inequality. An analytic estimation of the size of such non-violating states in terms of purity is also obtained. Interestingly, the estimation in terms of purity also gives a necessary and sufficient condition in terms of Bloch parameters of the state. Illustrations from some signature class of quantum states further underscore our observations.