Abstract

Fully entangled fraction (FEF) is a significant figure of merit for density matrices. In bipartite d ⊗ d quantum systems, the threshold value FEF > 1/d, dictates prominent implications for tasks like teleportation and entanglement distillation. Like separability, the value of FEF is also related to the choice of global basis of the underlying Hilbert space. A state having its FEF ≤ 1/d, might give a value > 1/d in another global basis. A change in the global basis corresponds to a global unitary action on the quantum state. In the present work, we find that there are quantum states whose FEF remains less than 1/d, under the action of any global unitary i.e., any choice of global basis. Based on the fixed spectrum of density matrices, we provide necessary and sufficient criteria in two qubit systems which also prove to be sufficient in any d⊗d dimensions, to identify such states. Further, we prove that states having their FEF bounded by 1/d under any global unitary, form a convex and compact set. This entails the distinction of states whose FEF can be increased beyond 1/d, through unitary action. The demarcation is of paramount importance as it provides for the identification of states which can prove to be useful in teleportation and entanglement distillation after the action of global unitary operators, as underpinned by illustrations in our work.

Abstract

Linear n-local networks are compatible with quantum repeaters based entanglement distribution protocols. Different sources of imperfections such as error in entanglement generation, communication over noisy quantum channels and imperfections in measurements result in decay of quantumness across such networks. From practical perspectives it becomes imperative to analyze non classicality of quantum network correlations in presence of different types of noise. Present discussion provides a formal characterization of non n-local feature of quantum correlations in noisy network scenario. In this context, persistency of non n-locality has been introduced. Such a notion helps in analyzing decay of non n-local feature of network correlations with increasing length of the linear network in presence of one or more causes of imperfections.

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

It is well known that it is impossible to clone an arbitrary quantum state. However, this inability does not lead directly to no cloning of quantum coherence. Here, in this article, we show that it is impossible to clone the coherence of an arbitrary quantum state. In particular, with an ancillary system as machine state, we show that it is impossible to clone the coherence of states whose coherence is greater than the coherence of the known states on which the transformations are defined. Also, we characterize the class of states for which coherence cloning will be possible for a given choice of machine. Furthermore, we find the maximum range of states whose coherence can be cloned perfectly. The impossibility proof also holds when we do not include machine states. Lastly, we generalize the impossibility of cloning of coherence in terms of dimension of the quantum state and coherence measure taken into consideration.

Abstract

Quantum states that possess negative conditional von Neumann entropy provide quantum advantage in several information-theoretic protocols including superdense coding, state merging, distributed private randomness distillation and one-way entanglement distillation. While entanglement is an important resource, only a subset of entangled states have negative conditional von Neumann entropy. In this work, we characterize the class of density matrices having non-negative conditional von Neumann entropy as convex and compact. This allows us to prove the existence of a Hermitian operator (a witness) for the detection of states having negative conditional entropy for bipartite systems in arbitrary dimensions. We show two constructions of such witnesses. For one of the constructions, the expectation value of the witness in a state is an upper bound to the conditional entropy of the state. We pose the problem of obtaining a tight upper bound to the set of conditional entropies of states in which an operator gives the same expectation value. We solve this convex optimization problem numerically for a two qubit case and find that this enhances the usefulness of our witnesses. We also find that for a particular witness, the estimated tight upper bound matches the value of conditional entropy for Werner states. We explicate the utility of our work in the detection of useful states in several protocols.

Abstract

In Quantum secret sharing we can share both quantum and classical secrets with a quantum resource. In this article we study the problem of revocation of quantum secret shared by the dealer with two shareholders in a three party scenario. In the existing secret sharing protocols there are no means by which the dealer can retrieve back the secret once he/she finds all the share holders to be dishonest. Our protocol makes a significant advancement in solving this problem by designing strategy in bringing back the secret in the worst possible situation when all the shareholders/receivers are dishonest1. In our proposed strategy the dealer also possesses a quantum share of the secret which empowers the dealer to bring back the secret even after sharing is done. However the protocol along with the revocation process also ensures the normal reconstruction at the share holder’s location when they are honest. This advantage comes with the expense of extra one qubit on dealer’s side and consequently we require a four qubit resource to start with for 1-dealer and 2-share holder’s scenario. Here in this article we not only give the description of our protocol but also give an example where our protocol is working with the help of a four qubit entangled state. We also explicitly found out the range of parameter for the input state for which the protocol will be successful.

Abstract

Quantum states that possess negative conditional von Neumann entropy provide quantum advantage in several protocols including superdense coding, state merging, distributed private randomness distillation and one-way entanglement distillation. While entanglement is an important resource, only a subset of entangled states have negative conditional von Neumann entropy. Despite this utility, a proper resource theory for conditional von Neumann entropy has not been developed, unlike that of entanglement. We pave the way for such a resource theory by characterizing the class of density matrices having non-negative conditional von Neumann entropy as convex and compact. This allows us to prove the existence of a Hermitian operator (a witness) for the detection of states having negative conditional entropy for bipartite systems in arbitrary dimensions. We show constructions of this witness and explicate its utility in the detection of useful states in the above-mentioned protocols. We provide a local decomposition of the witness and probe its implications in the context of the uncertainty principle.

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

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

With progress in quantum technologies, the field of quantum networks has emerged as an important area of research. In the last few years, there has been substantial progress in understanding the correlations present in quantum networks. In this article, we study cloning as a prospective method to generate three party quantum networks which can be further used to create larger networks. We analyze various quantum network topologies that can be created using cloning transformations. This would be useful in the situations wherever the availability of entangled pairs is limited. In addition to that we focus on the problem of distinguishing networks created by cloning from those which are created by distributing independently generated entangled pairs. We find that there are several states which cannot be distinguished using the Finner inequalities in the standard way. For such states, we propose an extension to the existing Finner inequality for triangle networks by further increasing the number of observers from three to four or six depending on the network topology. This takes into account the additional correlations that exist in the case of cloned networks. In the last part of the article we have used tripartite mutual information to distinguish cloned networks from networks created by independent sources and have further used squashed entanglement as a measure to quantify the amount of dependence in the cloned networks