arXiv subjects

Indrani Chattopadhyay

Publications and source records attributed to Indrani Chattopadhyay.

At least 19 recordsLinked to original sources

arXiv2026

Genuine Multipartite Nonlocality sharing under sequential measurement

The study of quantum nonlocality sharing has garnered significant attention, particularly for two-qubit and three-qubit entangled systems. In this paper, we extend the investigation to $n$-qubit Greenberger-Horne-Zeilinger (GHZ) systems, analyzing nonlocality sharing under unbiased unsharp measurements. Employing the Seevink and Svetlichny inequalities, we explore both unilateral and multilateral sequential measurement scenarios. In the unilateral scenario, we derive the range for which an observer's multiple copies can share genuine $n$-partite nonlocality with single copies of the remaining parties. In the multilateral scenario, we identify the maximum number of independent observers on $m$ sides who can share genuine $n$-partite nonlocality with other parties. A crucial aspect of our results is that all findings stem from a measurement strategy where each sequential observer utilizes unbiased unsharp measurements. As a specific case, for the four-qubit maximally entangled GHZ state, we demonstrate that at most two copies of an observer (e.g., Alice) can share nonlocality in the unilateral sequential measurement scenario. However, in the multilateral scenario, no additional sharing is possible compared to the unilateral case. This finding highlights the significance of unsharp measurements in optimizing the recycling of qubits for generating quantum nonlocality.

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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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arXiv2026

Entanglement concentration via measurement:- role of imaginarity

The role of complex numbers in quantum theory extends beyond mathematical convenience, having recently been formalized as a resource under the framework of the resource theory of imaginarity. Operationally, imaginarity translates into using fewer resources in optical setups. In this work, we investigate the operational advantage offered by complex-valued measurements in the entanglement of assistance protocol for three-qubit systems. We demonstrate that employing such measurement bases leads to a significant improvement in the concentration of bipartite entanglement with the aid of the third party. We further analyze a modified entanglement swapping protocol and show that a three-qubit complex measurement bases with certain symmetries outperform the standard GHZ-basis. This is also one example where a three-qubit non-maximally entangled basis surpasses a maximally entangled one in generating entanglement. Construction of the basis also addresses the open problems raised in [Phys. Rev. A. \textbf{108}, 022220 (2023)]. As an intriguing application, we show that using this approach in quantum network percolation on a honeycomb lattice reduces the required bond occupation probability by $22.7\%$ and, requirement of entanglement by $10.6\%$ in each bond.

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arXiv2026

Strong nonlocality with more imaginarity and less entanglement

Complex numbers are central to the formulation of quantum mechanics, yet their role as a genuine resource is only beginning to be understood. In this work, we demonstrate that quantum states with intrinsically complex amplitudes provide a fundamental advantage in state discrimination. We construct a set of five orthogonal three qubit pure states and show that the set is strongly nonlocal if and only if it includes imaginary components. Such a set becomes locally indistinguishable not only under local measurements but also against bipartite joint measurements. This enhanced robustness makes imaginarity a valuable resource for quantum cryptography since information encoded in these states remains secure against collaborative group attacks. Our results highlight a new operational role of complex numbers in quantum theory and establish imaginarity as a key enabler of cryptographic security. However, we reconstruct the set by replacing the only product state with a biseparable state whose shared entanglement between two parties nullifies the effect of imaginarity in exhibiting strong nonlocality. In fact, we show how entangling correlations between two distant parties can dilute the effect of imaginarity, and conversely, how imaginarity itself can mimic the role of entanglement. Nevertheless, the set spans a locally indistinguishable subspace, while its complement, in turn, produces distillable genuine entanglement. Notably, this is the smallest possible Unextendible Biseparable Basis (UBB) that resolves the open problem regarding the existence of a UBB of cardinality $d^2+d-1$ in $d^{\otimes 3}$. Our construction yields a highly powerful set, rich in resources from multiple perspectives of quantum information theory, including many-copy discrimination, unambiguous identification, entanglement creation from product state, and non-entangling perturbations.

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arXiv2025

Genuinely entangled subspaces beyond strongly nonlocal unextendible biseparable bases

Quantum information theory reveals a clear distinction between local and nonlocal correlations through the entanglement across spatially separated subsystems. The orthogonal complement of an unextendible biseparable basis (UBB) consists entirely of genuine multipartite entangled states, representing the most robust form of such nonlocal correlations. In this letter, we provide a sufficient condition for any subspace to be genuinely entangled, enabling the systematic construction of high-dimensional genuinely entangled subspaces (GESs) from UBBs. Our construction yields the largest known GES ever obtained from a UBB. In fact, every state in this subspace is 1-distillable across every bipartition which is one of the crucial result we obtained. Furthermore, we prove that every UBB is indistinguishable under LOCC protocols, underscoring a distinct manifestation of quantum nonlocality. The UBBs we construct exhibit strong nonlocality in this scenario, making cryptographic protocols secure not only against LOCC-based attacks but also against coordinated group attacks. We introduce a no-go condition that certifies such an extreme form of nonlocality. All previously known UBBs satisfy this condition, which may lead to the misconception that strong nonlocality is an inherent property of every UBB. However, we construct a UBB that violates the no-go condition and exhibits locality across certain bipartitions, challenging conventional notions of unextendibility and nonlocality in multipartite quantum systems.

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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

Entanglement of Assistance as a measure of multiparty entanglement

Quantifying multipartite entanglement poses a significant challenge in quantum information theory, prompting recent advancements in methodologies to assess it. We introduce the notion of \enquote{Volume of Assistance} (VoA), which computes the geometric mean of entanglement of assistance across all potential parties. We demonstrate the feasibility of VoA for three-qubit pure states and certain classes of pure tripartite qudit states. We have extended this measure to four-qubit states and general multipartite scenarios. We have done a comparative analysis to illustrate VoA's distinctiveness from established entanglement measures, notably showing it serves as an upper bound for the much celebrated generalized geometric measure (GGM). Remarkably, VoA excels in distinguishing a broad class of states that elude differentiation by the recently proposed Minimum Pairwise Concurrence (MPC) measure. Finally, VoA is applied to quantify genuine entanglement in the ground states of a three-qubit Heisenberg XY model, which highlights its practical utility in quantum information processing tasks.

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arXiv2024

Exploring strong locality : Quantum state discrimination regime and beyond

Based on the conviction of switching information from locally accessible to locally hidden environs, the concept of hidden nonlocality activation has recently been highlighted by Bandyopadhyay et al. in [Phys. Rev. A 104, L050201 (2021)]. They have demonstrated that a certain locally distinguishable set of pure quantum states can be transformed into a locally indistinguishable set with certainty through orthogonality preserving local measurements (OPLMs). This transformation makes the set locally inaccessible, despite being locally accessible before. This phenomenon is defined as the activation of hidden nonlocality. In this paper, we present two classes of locally distinguishable sets within $(2m+1) \otimes 2 \otimes (2m+1)$ systems. One class reveals nonlocality through local operations, whereas the other requires joint measurements for it. As the later class depends on nonlocal operations to exhibit nonlocality, it arguably has a lower degree of nonlocality, and accordingly, can be considered as more local compared to the first class. This analysis exhibits a stronger manifestation of locality by elucidating the nuanced interplay between these distinct local phenomena within the framework of quantum state discrimination. Furthermore, we also explore their significant applications in the context of data hiding. Additionally, we introduce the concept of \emph{``strong local"} set and compare it with various activatable sets, highlighting differences in terms of locality.

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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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arXiv2024

Strong quantum nonlocality: Unextendible biseparability beyond unextendible product basis

An unextendible biseparable basis (UBB) is a set of orthogonal pure biseparable states which span a subspace of a given Hilbert space while the complementary subspace contains only genuinely entangled states. These biseparable bases are useful to produce genuinely entangled subspace in multipartite system. Such a subspace could be more beneficial for information theoretic applications if we are able to extract distillable entanglement across every bipartition from each state of this subspace. In this manuscript, we have derived a rule for constructing such a class of UBB which exhibits the phenomenon of strong quantum nonlocality. This result positively answers the open problem raised by Agrawal et al. [Phys. Rev. A 99, 032335 (2019)]; that there exists a UBB which can demonstrate the phenomenon of strong quantum nonlocality in the perspective of local irreducibility paradigm.

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arXiv2023

Tight upper bound of genuine four party Svetlichny type nonlocality with and without local filtering

Identifying the nonlocality of a multiparty quantum state is an important task in quantum mechanics. Seevinck and Svetlichny [Phys. Rev. Lett. 89, 060401 (2002)], and independently, Collins and co-workers [Phys. Rev. Lett. 88, 170405 (2002)] have generalized the tripartite notion of Svetlichny nonlocality to n-parties. Here we have developed a tight upper bound for genuine four party Svetlichny type nonlocality. The constraints on the quantum states for the tightness of the bound are also presented. The method enables us to provide necessary and sufficient conditions for violating the four qubit Svetlichny type inequality for several quantum states. The relations between the genuine multipartite entanglement and the maximal quantum value of the Seevinck and Svetlichny operators for pure four qubit states are also discussed. Consequently, we have exhibited genuine four qubit hidden nonlocality under local filtering. Our result provides an effective and operational method for further study of multipartite quantum nonlocality.

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arXiv2023

More assistance of entanglement, less rounds of classical communication

Classical communication plays a crucial role to distinguish locally a class of quantum states. Despite considerable advances, we have very little knowledge about the number of measurement and communication rounds needed to implement a discrimination task by local quantum operations and classical communications (in short, LOCC). In this letter, we are able to show the relation between round numbers with the local discrimination of a set of pure bipartite orthogonal quantum states. To demonstrate the possible strong dependence on the round numbers, we consider a class of orthogonal product states in $d\otimes d$, which require at least $2d-2$ round of classical communications. Curiously the round number can be reduced to $d$ by the assistance of one-ebit of entanglement as resource and can be reduced further by assistance of more entanglement. We are also able to show that the number of LOCC rounds needed for a discrimination task may depend on the amount of entanglement assistances.

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arXiv2022

Entangled state distillation from single copy mixed states beyond LOCC

No pure entangled state can be distilled from a $2\otimes 2$ or $2\otimes 3$ mixed state by separable operations. In $3\otimes 3$, pure entanglement can be distilled by separable operation but not by LOCC. In this letter, we proved the conjecture [PRL. 103, 110502 (2009)] that it is possible to distill pure entanglement for $2\otimes 4$ system by LOCC and further improve these in higher dimensions to distill a pure entangled state of Schmidt rank $d$ from a $m\otimes n$ mixed state by separable operation when $m+n \geqslant 3d$. We found results for tripartite systems with target state $d$-level GHZ-type state. These results provide a class of systems where separable operation is strictly stronger than LOCC.

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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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arXiv2021

Nonlocality without entanglement: Party asymmetric case

A set of orthogonal product states of a composite Hilbert space is genuinely nonlocal if the states are locally indistinguishable across any bipartition. In this work, we construct a minimal set of party asymmetry genuine nonlocal set in arbitrary large dimensional composite quantum systems $C^d\otimes C^d\otimes C^d$. We provide a local discriminating protocol by using a three qubit GHZ state as a resource. On the contrary, we observe that single-copy of two qubit Bell states provide no advantage for this discrimination task. Recently, Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)], proposed the concept of strong nonlocality without entanglement and ask an open question whether there exist an incomplete strong nonlocal set or not. In [Phys. Rev. A 102, 042228 (2020)], an answer is provided by the authors. Here, we construct an incomplete party asymmetry strong nonlocal set which is more stronger than the set constructed in [Phys. Rev. A 102, 042228 (2020)] with respect to the consumption of entanglement as a resource for their respective discrimination tasks.

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arXiv2021

Arbitrary Measurement dependence in tripartite non-locality

The assumption of measurement independence is required for a local deterministic model to conduct a Bell test. The violation of a Bell inequality by such a model implies that this assumption must be relaxed. The degree to which the assumption needs to be relaxed to achieve violation of some bipartite Bell inequalities, has been investigated recently in [Phys. Rev. Lett. 105, 250404(2010), Phys. Rev. A 99, 012121(2019)]. In this work, we study the minimum degree of relaxation required to simulate violations of various well-known tripartite Bell inequalities and opens the possibility of relaxation in multipartite scenario. Local deterministic models are also provided to achieve the violations of these Bell inequalities.

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