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Abstract

In this article we present a benchmark for resource characterization in the process of controlled quantum state reconstruction and secret sharing for general three-qubit states. This is achieved by providing a closed expression for the reconstruction fidelity, which relies on the genuine tripartite correlation and the bipartite channel between the dealer and the reconstructor characterized by the respective correlation parameters. We formulate the idea of quantum advantage in approximate state reconstruction as surpassing the classical limit set at 2 3 . This article introduces new interoperability between teleportation and state reconstruction. This is detailed through a case-by-case analysis of relevant correlation matrices. We reformulate the idea of quantum secret sharing by setting up additional constraints on the teleportation capacity of the bipartite channels between dealer and shareholders by ensuring that, individually, the shareholders cannot reconstruct the secret. We believe that this will give us an ideal picture of how quantum secret sharing should be.

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

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

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

The most simplest form of quantum network is an one dimensional quantum network with a single player in each node. In remote entanglement distribution each of the players carry out measurement at the intermediate nodes to produce an entangled state between initial and final node which are remotely separated. It is imperative to say that the flow of information as well as the percolation of entanglement in a network between the source and target node is an important area of study. This will help us to understand the limits of the resource states as well as the measurements that are carried out in the process of remote entanglement distribution. In this article we investigate how the concurrence of the final entangled state obtained is connected with the concurrences of the initial entangled states present in a 1-D chain. We extend the works done for the pure entangled states for mixed entangled states like Werner states, Bell diagonal states and for general mixed states. We did not limit ourselves to a situation where the measurements are happening perfectly. We also investigate how these relations change when we consider imperfect swapping. We obtain the limits on the number of swappings as well as the success probability measurements to ensure the final state to be entangled state after swapping. In addition to these we also investigate on how much quantum information can be sent from the initial node to the final node (by computing the teleportation fidelity) when the measurement is perfect and imperfect with the same set of examples. Here also we obtain the limits on the number of swapping and the success probability of measurement

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 will help us to create larger networks. We analyze various quantum network topologies that can be created using cloning transformations. This would be useful in 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 that are created by distributing independently generated entangled pairs. We find that there are several states that 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 use tripartite mutual information to distinguish cloned networks from networks created by independent sources and further use squashed entanglement as a measure to quantify the amount of dependence in the cloned networks.

Abstract

Absolute separable (AS) quantum states are those states from which it is impossible to create entanglement, even under global unitary operations. It is known from the resource theory of non- absolute separability that the set of absolute separable states forms a convex and compact set, and global unitaries are free operations. We show that the action of a quantum switch controlled by an ancilla qubit over the global unitaries can break this robustness of AS states and produce ordinary separable states. First, we consider bipartite qubit systems and find the effect of quantum switch starting from the states sitting on the boundary of the set of absolute separable states. As particular examples, we illustrate what happens to modified Werner states and Bell diagonal (BD) states. For the Bell diagonal states, we provide the structure for the set of AS BD states and show how the structure changes under the influence of a switch. Further, we consider numerical generalization of the global unitary operations and show that it is always possible to take AS states out of the convex set under switching operations. We also generalized our results in higher dimensions.

Abstract

Counter-intuitive to classical notions, quantum conditional entropy can be negative, playing a pivotal role in information-processing tasks. This article delves deeply into quantum channels, em- phasizing negative conditional entropy breaking channels (NCEB) and introducing negative condi- tional entropy annihilating channels (NCEA). We characterize these channels from both topological and information-theoretic perspectives, examining their properties when combined serially and in parallel. Our exploration extends to complimentary channels associated with NCEB, leading to the introduction of information-leaking channels. Utilizing the parameters of the standard depolarizing channel, we provide tangible examples and further characterization. We demonstrate the relation- ship of NCEB and NCEA with newly introduced channels like coherent information breaking (CIB) and mutual information breaking (MIB), along with standard channels like zero capacity channels. Preservation of quantum resources is an integral constituent of quantum information theory. Rec- ognizing this, we lay prescriptions to detect channels that do not break the negativity of conditional entropy, ensuring the conservation of this quantum resource

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.