Abstract

We show that the average of the maximum teleportation fidelities between all pairs of nodes in a large quantum repeater network is a measure of the resourcefulness of the network as a whole. It can be used to rank networks of arbitrary topologies, with and without loops. For demonstration purposes, we use simple Werner state-based models to characterize some fundamental topologies (the star, the chain, some trees, and also the ring and the complete graph) with this measure in three (semi)realistic scenarios. Most of our results are analytic and apply to arbitrary network sizes. We identify the parameter ranges where these networks can achieve quantum advantages and show the large-N behaviors.

Abstract

Quantum digital signatures ensure unforgeable message authenticity and integrity using quantum principles, offering unconditional security against both classical and quantum attacks. They are crucial for secure communication in high-stakes environments, ensuring trust and long-term protection in the quantum era. Nowadays, the majority of arbitrated quantum signature (AQS) protocols encrypt data qubit by qubit using the quantum one-time pad (QOTP). Despite providing robust data encryption, QOTP is not a good fit for AQS because of its susceptibility to many types of attacks. In this work, we present an efficient AQS protocol to encrypt quantum message ensembles using a distinct encryption technique, the chained controlled unitary operations. In contrast with existing protocols, our approach successfully prevents disavowal and forgery attacks. We hope this contributes to advancing future investigations into the development of AQS protocols .

Abstract

The possibility of a quantum system to exhibit properties that are akin to both the classically held notions of being a particle and a wave, is one of the most intriguing aspects of the quantum description of nature. These aspects have been instrumental in understanding paradigmatic natural phenomena as well as to provide non-classical applications. A conceptual foundation for the wave nature of a quantum state has recently been presented, through the notion of quantum coherence. We introduce here a parallel notion for the particle nature of a quantum state of an arbitrary physical system. We provide elements of a resource theory of particleness, and give a quantification of the same. Finally, we provide evidence for a complementarity between the particleness thus introduced, and the coherence of an arbitrary quantum state.

Abstract

The fully entangled fraction (FEF) measures the proximity of a quantum state to maximally entangled states. FEF , in systems, is a significant benchmark for various quantum information processing protocols including teleportation. Quantum conditional entropy (QCE) on the other hand is a measure of correlation in quantum systems. Conditional entropies for quantum systems can be negative, marking a departure from conventional classical systems. The negativity of quantum conditional entropies plays a decisive role in tasks like state merging and dense coding. In the present work, we investigate the relation of these two important yardsticks. Our probe is mainly done in the ambit of states with maximally mixed marginals, with a few illustrations from other classes of quantum states. We start our study in two-qubit systems, where for the Werner states, we obtain lower bounds to its FEF when the conditional Rényi entropy is negative. We then obtain relations between FEF and QCE for two-qubit Weyl states. Moving on to two qudit states, we find a necessary and sufficient condition based on FEF, for the isotropic state to have negative conditional entropy. In two qudit systems, the relation between FEF and QCE is probed for the rank-deficient and generalized Bell diagonal states. FEF is intricately linked with k-copy nonlocality and k- copy steerability. The relations between FEF and QCE facilitates to find conditions for k- copy nonlocality and k- copy steerability based on QCE. We obtain such conditions for certain classes of states in two qubits and two qudits. Applications of the relations obtained are provided in the context of work extraction, faithful entanglement and entropic uncertainty relations.

Abstract

A tripartite state is said to be a potential resource for secret sharing if in addition to being useful for the secret reconstruction, it imposes restrictions on the teleportation fidelity of the bipartite channels associated with three qubit states (dealer–reconstructor and dealer–assistant channels). It is important to ask the question: for a given class of states satisfying some constraint, which secret sharing resources will have the maximum possible reconstruction fidelity? Here we address this question for a pure three-qubit GHZ class of states (sometimes referred as Acin states). We are able to characterize the set of states with maximum possible reconstruction fidelity (called as Maximal Secret Reconstructible state [MSR]). Here, the constraint in characterizing the states is a fixed value of the maximum of the teleportation fidelity of both the bipartite (dealer–receivers) channels. In that spirit our result paves the way in setting the practical information transfer limit in a possible resource theoretic extension of secret sharing. Similarly for a value giving the maximum of Bell-CHSH value of both bipartite channels (dealer–reconstructor and dealer–assistant), we are able to find the maximum achievable reconstruction fidelity. Interestingly, we find that all secret shareable states satisfy Bell’s inequality in both the channels (dealer–reconstructor and dealer–assistant partitions). This brings out a new mutual exclusivity between secret shareable state and Bell’s inequality violation.

Abstract

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Abstract

Bell non-locality and steering are archetypal characteristics of quantum mechanics that mark a significant departure from conventional classical notions. They basically refer to the presence of quantum correlations between separated systems which violate a non-local inequality, the violation otherwise is 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 states exhibiting non-locality starting from a few, a protocol which is termed as broadcasting. However, in the present submission, we show using universal Buzek–Hillary (BH) quantum cloning machine that, if one restricts to broadcasting through local quantum cloning, then such non-locality cannot be broadcasted. Our study is done in the purview of the Bell-CHSH inequality and the CJWR [E G Cavalcanti et al, Phys. Rev. A 80, 032112 (2009)] steering inequality. It is observed that when the number of measurement settings is greater than 6, some of the output states are steerable after the application of local optimal BH cloners. We found that, under some restrictions, if the Werner and Bell diagonal states are subjected to such procedures, then the resultant state is rendered unsteerable. We extended this study to three qubit systems and found that genuine tripartite non-locality cannot be broadcasted using universal BH local quantum cloners, when the Svetlichny’s inequality was considered. For two qubit systems, we considered simulated general local unitaries over Werner and Bell-diagonal states and found that for none of these states, broadcasting on non-locality and 3-steerability is possible.

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

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

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.