arXiv subjects

Atanu Bhunia

Publications and source records attributed to Atanu Bhunia.

13 recordsLinked to original sources

arXiv2026

Hierarchy of hidden nonlocality: A genuine activation of Incompletability

Quantum nonlocality admits several operational manifestations, one of which emerges from sets of orthogonal quantum states that cannot be perfectly distinguished by local operations and classical communication (LOCC). Such sets are regarded as nonlocal because their perfect discrimination requires global measurements. In contrast, sets that are perfectly distinguishable by LOCC are generally considered locally accessible and operationally classical. In this work, we investigate the role of incompletability in local state discrimination and introduce the notion of \emph{activation of incompletability}. Specifically, we demonstrate the existence of orthogonal sets that are initially perfectly distinguishable by LOCC and free from local redundancy, but which can be transformed via LOCC into strictly incompletable sets. We prove that activation of incompletability necessarily implies activation of nonlocality, whereas the converse fails in general, thereby establishing a hierarchy between the two activation phenomena. Furthermore, within the framework of local incoherent operations and classical communication (LICC), we show that any set whose incompletability can be activated can nevertheless be extended to a complete orthonormal basis of the Hilbert space, although the resulting completed basis is no longer perfectly distinguishable by LOCC. Our results uncover a fundamental interplay among local distinguishability, incompletability, coherence, and nonlocality, and provide new insight into the structure of locally accessible quantum information.

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arXiv2026

Incompleteness is necessary for activation of nonlocality without entanglement

A set of orthogonal product states is said to exhibit "quantum nonlocality without entanglement" if it is locally indistinguishable, i.e. no sequence of local operations and classical communication (LOCC) can perfectly discriminate the states. Building on this foundational idea, recent studies have highlighted the phenomenon of "genuine activation of hidden nonlocality", where a set of initially distinguishable orthogonal states becomes locally indistinguishable through orthogonality-preserving LOCC transformations. In this letter, we establish that any complete orthogonal product basis that is initially locally distinguishable remains so under all orthogonality-preserving local projective measurements, thereby ruling out activation via orthogonality-preserving local projective measurements and classical communication. We further introduce and formalise the notions of "strongly local sets", namely locally distinguishable sets that remain non-activable under all bipartitions. Interestingly, the study of "local activability" of distinguishable sets is useful to characterise the boundary between LOCC distinguishability and its irreversible loss in multipartite systems. Our results provide a rigorous structural understanding of local-to-nonlocal transitions in quantum state discrimination.

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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

Classifying locally distinguishable sets: No activation across bipartitions

A set of orthogonal quantum states is said to be locally indistinguishable if they cannot be perfectly distinguished by local operations and classical communication (LOCC). Otherwise, the states are locally distinguishable. Interestingly, locally indistinguishable states can have productive applications in quantum information processing protocols. In this sense, locally indistinguishable states are useful. On the other hand, it is usual to consider that locally distinguishable states are useless. Nevertheless, recent works suggest that locally distinguishable states should be given due consideration as in certain situations these states can be converted to locally indistinguishable states under orthogonality-preserving LOCC (OP-LOCC). Such a counterintuitive phenomenon motivates us to ask when the aforesaid conversion is possible and when it is not. In this work, we provide different structures of locally distinguishable product and entangled states which do not allow the aforesaid conversion. We also provide certain structures of locally distinguishable states which allow the aforesaid conversion. In this way, we classify the locally distinguishable sets by introducing hierarchies among them. In a multipartite system, this study becomes more involved as there exist multipartite locally distinguishable sets which cannot be converted to locally indistinguishable sets by OP-LOCC across any bipartition. We say this as ``no activation across bi-partitions".

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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

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

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

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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arXiv2020

Nonlocality of tripartite orthogonal product states

Local distinguishability of orthogonal product states is an area of active research in quantum information theory. However, most of the relevant results about local distinguishability found in bipartite quantum systems and very few are known in multipartite systems. In this work, we construct a locally indistinguishable subset in ${\mathbb{C}}^{2d}\bigotimes{\mathbb{C}}^{2d}\bigotimes{\mathbb{C}}^{2d}$, $d\geq2$ that contains $18(d-1)$ orthogonal product states. Further, we generalize our method to arbitrary tripartite quantum systems ${\mathbb{C}}^{k}\bigotimes{\mathbb{C}}^{l}\bigotimes{\mathbb{C}}^{m}$. This result enables us to understand further the role of nonlocality without entanglement in multipartite quantum systems. Finally, we prove that a three-qubit GHZ state is sufficient as a resource to distinguish each of the above classes of states.

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