arXiv subjects

Pratapaditya Bej

Publications and source records attributed to Pratapaditya Bej.

11 recordsLinked to original sources

arXiv2024

Activation of entanglement in generalized entanglement swapping

We study entanglement activation in a generalized entanglement swapping process involving two Bell pairs and generalized measurements. The conventional understanding posits entangled measurements as both necessary and sufficient for establishing entanglement between distant parties. In this study, we reassess the role of measurement operators in entanglement generation within a generalized entanglement swapping process. We focus on maximally entangled two-qubit initial states and generalized measurements, investigating the necessity and sufficiency conditions for entangled measurement operators. By utilizing two Bell pairs, (1, 2) shared between Alice and Bob, and (3, 4) shared between Bob and Charlie, we demonstrate that while entangled measurements are sufficient, they are not indispensable for establishing entanglement between spatially separated observers. Through a sequential approach, if Bob performs an initial measurement which is not able to establish entanglement then followed by another measurement after post-processing the first measurement it is possible to establish entanglement. We identify specific criteria for different measurement operators that enable the potential for performing a second measurement to establish entanglement. Our findings highlight the feasibility of generating entanglement between distant parties through a combination of measurements, shedding light on entanglement distribution in quantum networks. Additionally, we showcase through illustrative examples how successive measurements enhance entanglement compared to single measurements, underscoring the practical benefits of our approach in enhancing entanglement. Moreover, our protocol extends beyond bipartite qubit states to higher-dimensional maximally entangled states, emphasizing its versatility and applicability.

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arXiv2024

Thermalization of isolated quantum many-body system and the role of entanglement

Thermalization of an isolated quantum system has been a nontrivial problem since the early days of quantum mechanics. In generic isolated quantum systems, nonequilibrium dynamics is expected to result in thermalization, indicating the emergence of statistical mechanics from quantum dynamics. However, what feature of a many-body quantum system facilitates quantum thermalization is still not well understood. Recent experimental advancements have shown that entanglement may act as a thermalizing agent, not universally but particularly. Here, we theoretically show that the thermal averages of an observable in an isolated many-body quantum system with a large number of degrees of freedom emerge from the entangled energy eigenstates of the system. In particular, we show that the expectation values of an observable in entangled energy eigenstates and its marginals are equivalent to the microcanonical and canonical averages of the observable.

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arXiv2024

A Secure Quantum Key Distribution Protocol Using Two-Particle Transmission

The evolution of Quantum Key Distribution (QKD) relies on innovative methods to enhance its security and efficiency. Unextendible Product Bases (UPBs) hold promise in quantum cryptography due to their inherent indistinguishability, yet they are underutilized in QKD protocols. This work introduces a protocol utilizing UPBs to establish quantum keys between distant parties. Specifically, we propose a protocol utilizing a $3\times 3$ tile UPB, where Alice sequentially transmits subsystem states to Bob through quantum channels. The protocol's security is underpinned by the no-cloning theorem, prohibiting the cloning of orthogonal states. We analyze potential attacks, including intercept-resend and detector blinding attacks when quantum channels are noiseless, and discuss the challenges posed by the indistinguishability of our protocol for eavesdroppers, thereby enhancing QKD security.

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arXiv2024

Quantum change point and entanglement distillation

In a quantum change point problem, a source emitting particles in a fixed quantum state (default) switches to a different state at some stage, and the objective is to identify when the change happened by measuring a sequence of particles emitted from such a source. Motivated by entanglement-sharing protocols in quantum information, we study this problem within the paradigm of local operations and classical communication (LOCC). Here, we consider a source that emits entangled pairs in a default state, but starts producing another entangled state (mutation) at a later stage. Then, a sequence of entangled pairs prepared from such a source and shared between distant observers cannot be used for quantum information processing tasks as the identity of each entangled pair remains unknown. We show that identifying the change point using LOCC leads to the distillation of free entangled pairs. In particular, if the default and the mutation are mutually orthogonal, there exists an efficient LOCC protocol that identifies the change point without fail and distills a sufficiently large number of pairs. However, if they are nonorthogonal, there is a probability of failure. In this case, we compute the number of entangled pairs that may be obtained on average. We also consider a relaxation of the two-state problem where the mutation is not known a priori, but instead belongs to a known set. Here we show that local distinguishability plays a crucial role: if the default and the possible mutations are locally distinguishable, the problem reduces to the two-state problem with orthogonal states, but if not, one may still identify the mutation, the change point, and distill entanglement, as we illustrate with a concrete example.

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arXiv2023

When Mei-Gu Guan's 1960 Postmen Get Empowered with Bell's 1964 Nonlocal Correlations, or, Nonlocal Advantage in Vehicle Routing Problem

Vehicle routing problems, a comprehensive problem category originated from the seminal Chinese Postman Problem (first investigated by Chinese mathematician Mei-Gu Guan), entail strategic and tactical decision making for efficient scheduling and routing of vehicles. While Chinese postman problem is aimed at finding the minimum length cycle for a single postman, the broader challenges encompass scenarios with multiple postmen. Making cost-effective decisions in such cases depends on various factors, including vehicle sizes and types, vehicle usage time, road tax variations across routes, and more. In this work, we delve into a class of such problems wherein Bell nonlocal correlations provide advantages in optimizing the costs for non-communicating postmen, and thus establish a nascent utilization of quantum entanglement in traffic routing problem. Our investigation unveils promising applications for nonlocal correlations within combinatorial optimization and operational research problems, which otherwise have predominantly been explored within the quantum foundation and quantum information theory community.

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arXiv2022

Creating quantum correlations in generalized entanglement swapping

We study how different types of quantum correlations can be established as the consequence of a generalized entanglement swapping protocol where starting from two Bell pairs (1, 2) and (3, 4), a general quantum measurement (denoted by a positive operator-valued measure or POVM) is performed on the pair (2, 3), which results in creating quantum correlation in (1, 4) shared between two spatially separated observers. Contingent upon using different kinds of POVMs, we show generation or destruction of different quantum correlations in the pairs (1, 4), (1, 2) and (3, 4). This thus reflects non-trivial transfer of quantum correlations from the pairs (1, 2) and (3, 4) to the pair (1, 4). As an offshoot, this study provides an operational tool to generate different types of single parameter families of quantum correlated states (for example, entangled but not EPR steerable, or EPR steerable but not Bell nonlocal, or Bell nonlocal) by choosing different quantum measurements in the basic entanglement swapping setup. We further extend our study by taking mixed initial states shared by the pairs (1,2) and (3,4). Finally, we study network nonlocality in our scenario. Here, we find out appropriate POVM measurement for which the generated correlation demonstrates/does not demonstrate network nonlocality for the whole range of the measurement parameter.

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arXiv2022

Optimal teleportation fidelity and its deviation in noisy scenarios

In this work, we study the combined effects of noisy resource state and noisy classical communication on teleportation fidelity and its deviation. Basically, we consider a teleportation protocol, where a general two-qubit state in canonical form is used as resource, which of course, can be a noisy entangled state. Thereafter, to teleport an unknown qubit, Alice measures her qubits in Bell basis and convey the measurement outcome to Bob via noisy classical channel(s). In particular, we derive the exact formulae of optimal teleportation fidelity and corresponding fidelity deviation where the resource state and the classical communication, both of them can be noisy. We further find conditions for non-classical fidelity and dispersion-free teleportation within the present protocol. In this way, we identify the noisy environments where it is possible to achieve the dispersion-free teleportation without compromising the non-classical fidelity. We also exhibit scenarios where the increase of entanglement in the resource state, may degrade the quality of teleportation. Finally, we discuss on minimum classical communication cost required to achieve non-classical fidelity in our protocol.

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arXiv2021

Braess Paradox in a quantum network

Dietrich Braess while working on traffic modelling, noticed that traffic flow in a network can be worsened by adding extra edges to an existing network. This seemingly counterintuitive phenomenon is known as the Braess paradox. We consider a quantum network, where edges represent shared entangled states between spatially separated parties(nodes). The goal is to entangle two previously uncorrelated nodes using entanglement swappings. The amount of entanglement between the distant nodes is quantified by the average concurrence of the states established, as a result of the entanglement swappings. We then introduce an additional edge of maximally entangled Bell states in the network. We show that the introduction of the additional maximally entangled states to this network leads to lower concurrence between the two previously un-correlated nodes. Thus we demonstrate the occurrence of a phenomenon in a quantum network that is analogous to the Braess' paradox in traffic networks.

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arXiv2021

Unextendible product bases, bound entangled states, and the range criterion

An unextendible product basis (UPB) is a set of orthogonal product states which span a subspace of a given Hilbert space while the complementary subspace contains no product state. These product bases are useful to produce bound entangled (BE) states. In this work we consider reducible and irreducible UPBs of maximum size, which can produce BE states of minimum rank. From a reducible UPB, it is possible to eliminate one or more states locally, keeping the post-measurement states orthogonal. On the other hand, for an irreducible UPB, the above is not possible. Particularly, the UPBs of the present size are important as they might be useful to produce BE states, having ranks of the widest variety, which satisfy the range criterion. Here we talk about such BE states. We also provide other types of BE states and analyze certain properties of the states. Some of the present BE states are associated with the tile structures. Furthermore, we provide different UPBs corresponding to the present BE states of minimum rank and discuss important properties of the UPBs.

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arXiv2020

Information-disturbance trade-off in generalized entanglement swapping

We study information-disturbance trade-off in generalized entanglement swapping protocols wherein starting from Bell pairs $\left(1,2\right)$ and $\left(3,4\right)$, one performs an arbitrary joint measurement on $\left(2,3\right)$, so that $\left(1,4\right)$ now becomes correlated. We obtain trade-off inequalities between information gain in correlations of $\left(1,4\right)$ and residual information in correlations of $\left(1,2\right)$ and $\left(3,4\right)$ respectively and argue that information contained in correlations (information) is conserved if each inequality is an equality. We show that information is conserved for a maximally entangled measurement but is not conserved for any other complete orthogonal measurement and Bell measurement mixed with white noise. However, rather surprisingly, we find that information is conserved for rank-two Bell diagonal measurements, although such measurements do not conserve entanglement. We also show that a separable measurement on $\left(2,3\right)$ can conserve information, even if, as in our example, the post-measurement states of all three pairs $\left(1,2\right)$, $\left(3,4\right)$, and $\left(1,4\right)$ become separable. This implies correlations from an entangled pair can be transferred to separable pairs in nontrivial ways so that no $information$ is lost in the process.

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arXiv2018

Geometry of quantum state space and entanglement

Recently, an explicit relation between a measure of entanglement and a geometric entity has been reported in Quantum Inf. Process. (2016) 15:1629-1638. It has been shown that if a qubit gets entangled with another ancillary qubit then negativity, up to a constant factor, is equal to square root of a specific Riemannian metric defined on the metric space corresponding to the state space of the qubit. In this article, we consider the different class of bi-partite entangled states and show explicit relation between two measures of entanglement and Riemannian metric.

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