arXiv subjects

Priyabrata Char

Publications and source records attributed to Priyabrata Char.

7 recordsLinked to original sources

arXiv2026

Pure State Transformations under Block Coherence

Block coherence provides a natural generalization of standard quantum coherence by treating superpositions across different subspaces as a resource. This work studies deterministic pure-state conversion under three free operations: physically block incoherent operations (PBIO), strictly block incoherent operations (SBIO), and block dephasing covariant incoherent operations (BDCO). For PBIO, we prove that, under a natural nondegeneracy condition on the active Kraus branches, any deterministic conversion from one pure state to another must be implemented by a block incoherent unitary. When the nondegeneracy requirement is removed, the condition becomes more general. It demands that the blockwise action of every active branch reproduce the target block structure with a common proportionality factor across all output blocks. For SBIO and BDCO, we show that deterministic pure-state transformation is completely characterized by the majorization relation between the input and output block probability vectors. The converse proof is constructive, yielding an explicit Kraus representation for every admissible BDCO transformation. In the rank-one limit, these conditions reduce to the known pure-state transformation criteria for physically incoherent operations (PIO), strictly incoherent operations (SIO), and dephasing covariant incoherent operations (DIO) in the standard resource theory of coherence. Using the majorization condition, a maximally block-coherent state with uniform block weights is also identified as a universal pure-state resource under BDCO and SBIO. We have also provided geometric numerical illustrations comparing the state transformation power of BDCO and DIO for a fixed input state, fixed output state and mutual convertibility scenarios.

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arXiv2026

Catalytic Enhancement of Coherence in Noisy Quantum Channels and Characterization of Strictly Incoherent Operations

In realistic quantum information processing tasks, quantum states are inevitably affected by environmental noise, leading to decoherence and degradation of useful quantum resources. The coherence fraction, which serves as an important figure of merit for several quantum protocols, may decrease significantly after the action of a noisy channel. Such degradation can result in unsatisfactory performance in real-world applications. In this work, we investigate whether catalysis can be used to pre-process the input state to enhance the coherence fraction of an output state from a quantum channel. Specifically, we study whether using a processed state $ρ_s'$ as the input to a quantum channel $Λ$, instead of the original state $ρ_s$, can yield an output state $Λ(ρ_s')$ whose coherence fraction exceeds that of $Λ(ρ_s)$. We analyze the conditions under which such an improvement is possible. We also provide a practical application of our setup for the phase discrimination task. Furthermore, we establish a necessary and sufficient condition for an incoherent state preserving CPTP(Completely Positive Trace Preserving) map $\mathcal{E}$ to be a particular type of Strictly Incoherent Operation (SIO). This characterization provides a new structural understanding of SIO and clarifies its role in coherence manipulation. Our results offer practical insights into coherence preservation and enhancement in noisy quantum processes and may be useful for optimizing quantum information protocols under realistic conditions. We also provide numerical examples to support our claims.

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arXiv2025

Dilution of Entanglement: Unveiling Quantum State Discrimination Advantages

The states in the three-qubit GHZ SLOCC class can exhibit diverse entanglement patterns, as they may have no entanglement in any reduced subsystems, or show entanglement across one, two, or all three bipartite cuts. Significant research has explored how such states can be used in entanglement-assisted discrimination tasks. In this paper, we analyze the relationship between probability of error and amount of bipartite and multiparty entanglement, examining how different levels of entanglement impact the accuracy of state discrimination. Also we have shown that the generic class of GHZ state provide some advantages in probabilistic distinguishibility. However, perfect discrimination typically requires maximally entangled states. The use of non-maximally entangled states as a resource for perfect discrimination remains an open problem in this area of research. In this manuscript, we propose a method to explore the perfect distinguishability of orthogonal product states using non-maximally entangled states, utilizing the GHZ SLOCC class structure. Moreover, these findings offer deeper insights into the relationship between entanglement classification and nonlocality, potentially shedding light on how different entanglement structures influence nonlocal behavior in quantum systems.

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arXiv2024

Structure of Resource Theory of Block Coherence

Emerging from the superposition principle, the resource theory of coherence plays a crucial role in many information-processing tasks. Recently, a generalization to this resource theory was investigated with respect to arbitrary positive operator valued measurement (POVM) based on Naimark's dilation theorem. Here, we introduce the notion of Block Incoherent Operations (BIO), Strictly Block Incoherent Operations (SBIO) and Physically Block Incoherent Operations (PBIO) and provide an analytical expression for Kraus operators of these operations to have a better understanding of the resource theory of block coherence which in turn gives a more clear picture of POVM based resource theory of coherence. A dilation theorem corresponding to SBIO has been introduced to enlighten the proper physical interpretation of this operation. These free operations will be helpful in finding out the conditions of state transformations and could be implemented in various protocols. For a transparent view of this resource theory, we have successfully introduced the concept of state transformation under SBIO.

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arXiv2024

Multipartite Monogamy of Entanglement for Three Qubit States

The distribution of entanglement in a multiparty system can be described through the principles of monogamy or polygamy. Monogamy is a fundamental characteristic of entanglement that restricts its distribution among several number of parties(more than two). In this work, our aim is to explore how quantum entanglement can be distributed in accordance with monogamy relations by utilizing both the genuine multipartite entanglement measures and bipartite entanglement measures. Specifically, we treat source entanglement as the genuine multipartite entanglement measure and use the entanglement of formation specifically for bipartite cases. For GHZ class states, we analytically demonstrate that the square of the source entanglement serves as an upper bound for the sum of the squares of the entanglement of formation of the reduced subsystems, with some exceptions for specific non-generic GHZ states. We also present numerical evidence supporting this result for W class states. Additionally, we explore the monogamy relation by using accessible entanglement as an upper bound.

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arXiv2021

Catalytic Transformations in Coherence Theory

In 2016, A. Winter et al.(Physical Review Letters 116 (12) (2016) 120404) provided an operational meaning to relative entropy of coherence and coherence of formation by introducing coherence distillation and dilation protocol in asymptotic setup. Though relative entropy of coherence introduced in 2014 by T. Baumgratz ( Physical Review Letters 113 (14) (2014) 140401) as a coherence measure but it's operational meaning in single copy setup was unknown so far. Here we have provided relative entropy of coherence (via IO (Incoherent Operations)) and coherence of formation (via IO) and quantum incoherent relative entropy (via LQICC(Local Quantum Incoherent Operations with Classical Communications)) a clear operational significance in single copy setup using the concept of catalyst. We have proved an existential correspondence between asymptotic and catalytic state transformation using IO, LICC(Local Incoherent Operations with Classical Communications) and LQICC. We have also discussed two very important protocols, assisted distillation and quantum incoherent state merging, in single copy setup using catalyst. Monotone property of relative entropy of coherence, coherence of formation and quantum incoherent relative entropy under the catalytic transformation are also discussed here.

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arXiv2020

Monogamy Relations for Multiqubit Systems

Recently a new class of monogamy relations (actually, exponentially many) was provided by Christopher Eltschka et al. in terms of squared concurrence. Their approach restricted to the distribution of bipartite entanglement shared between different subsystems of a global state. We have critically analyzed those monogamy relations in three as well as in four qubit pure states using squared negativity. We have been able to prove that in case of pure three qubit states those relations are always true in terms of squared negativity. However, if we consider the pure four qubit states, the results are not always true. Rather, we find opposite behaviour in some particular classes of four qubit pure states where some of the monogamy relations are violated. We have provided analytical and numerical evidences in support of our claim.

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