Abstract

Linear n-local networks are compatible with quantum-repeater-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 the nonclassicality of quantum network correlations in the presence of different types of noise. The present discussion provides a formal characterization of non-n-local features of quantum correlations in a 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 features of network correlations with increasing length of the linear network in the presence of one or more causes of imperfections.

Abstract

We investigate whether it is possible to teleport the coherence of an unknown quantum state from Alice to Bob by communicating lesser number of classical bits in comparison to what is required in teleporting an unknown quantum state. We find that we cannot do perfect teleportation of coherence with one bit of classical communication for an arbitrary qubit. However, we find that if the qubit is chosen from equatorial and polar circles, then teleportation of coherence will be possible with transfer of one cbit of information if we have maximally entangled states as a shared resource. In the case of resource being a non maximally entangled state, we can teleport quantum coherence with a certain probability of success. In a general teleportation protocol for coherence, we derive a compact formula for the final state at Bob’s lab in terms of composition of the completely positive maps corresponding to the shared resource state and joint POVM performed by Alice on her qubit and the unknown state. With the help of this formula, we investigate the amount of coherence teleported when the resource shared state is the maximally entangled mixed state and Werner state for the unknown pure as well as mixed states state at Alice’s lab. In particular, we show that when the Werner state becomes separable then also the amount of teleported coherence is non-zero, implying the possibility of teleportation of coherence without entanglement. We have also shown that teleportation of coherence of an arbitrary state with real matrix elements is exactly possible with the help of maximally entangled state as a resource.

Abstract

We have established a novel method to detect non-Markovian indivisible quantum channels using structural physical approximation. We have shown that this method can be used to detect eternal non -Markovian operations. We have further established that harnessing eternal non-Markovianity, we can device a protocol to detect quantum entanglement.

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

The significance of negative quantum conditional entropy is underscored by its ubiquity in information processing tasks like dense coding, state merging and one-way entanglement distillation. Mere presence of entanglement is not sufficient for these tasks, a fact underpinned by the existence of entangled quantum states with non-negative conditional entropy. This stimulates one to go beyond the paradigm of entanglement theory and probe the hitherto unexplored area of operations influencing quantum conditional entropy. To this end, we introduce the class of A-unital channels. We characterize them and demonstrate that A-unital channels are to states having non-negative conditional entropy what separable channels are to separable states. We also show that A-unital channels form the largest class of channels that do not decrease the conditional entropy of any state, a relation analogous to unital channels and entropy. A comparative study between A-unital and other channels crucial to the resource theory of entanglement is done to further exemplify the distinction with entanglement theory. Non-local unitary operations can decrease conditional entropy to sub-zero levels. However, there exist states whose conditional entropy remains non-negative even under this action. Termed as states having absolute conditional entropy, they prove to be robust against non-local unitary action. In this work, the completely free operations for such states are also characterized. Finally, since von Neumann entropy is the mainspring of these discussions, the bounds on the conditional entropy of states having a given entropy are derived. The definition of A-unital channels naturally lends itself to a procedure for determining membership of channels in this class. Thus, we not only characterize completely free channels for quantum conditional entropy, but also show how resourceful channels can be detected.

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 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

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

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

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.