arXiv subjects

Manik Banik

Publications and source records attributed to Manik Banik.

At least 19 recordsLinked to original sources

arXiv2026

Almost-Quantum Correlations Violate Information Causality

Information causality (IC) posits that communicating m classical bits cannot give the receiver access to more than m bits of information about the sender's independent data. Although IC holds in quantum theory and excludes a broad class of supra-quantum correlations, its validity for the almost-quantum set has remained open. This semidefinite relaxation of the quantum set satisfies nontrivial communication complexity, no advantage for non-local computation, macroscopic locality, local orthogonality, and numerical evidence has suggested that it may also satisfy IC. Here we show that almost-quantum correlations violate IC, and do so without bound. Unlike earlier violations of IC, which rely on biased guesses, ours is driven by zero-error certificates: each is rare but never wrong, carries information linear in its probability, and vouches for many of the sender's bits at once. This establishes a sharp dichotomy: either IC is a valid physical principle that excludes these correlations, or any nonsignalling theory realizing them admits no mutual information obeying consistency, data processing and the chain rule. In the latter case, we discuss why the chain rule is the natural property to relinquish, and how this possibility relates to histories-based formulations and to locality defined relative to the state rather than presupposed in a fixed spacetime.

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arXiv2026

An Unbounded Separation of Almost-Quantum and Commuting-Operator Correlations in Zero-Error Communication

Almost-quantum correlations form the $\mathtt{1+AB}$ level of the Navascués--Pironio--Acín hierarchy. They strictly contain the quantum set, are characterized by a single semidefinite program, arise in Sorkin's quantum measure theory, and satisfy several principles proposed to single out quantum theory. We show that they are nevertheless unboundedly stronger than quantum correlations in a zero-error communication task. Alice and Bob receive labels $s,t\in[N]$, $N\ge3$; after one bit from Alice, Bob must decide whether $s=t$, never erring but allowed to abstain. For every model of quantum correlations, from finite-dimensional tensor products to commuting operators, the optimal worst-case probability of a conclusive answer is exactly $1/N$, the value attained with shared randomness, so the bound does not depend on the resolution of Tsirelson's problem. An explicit family of almost-quantum correlations attains $1/19$ for every $N$. For certificates of equality from binary-outcome boxes, we solve the underlying semidefinite programs in closed form. The almost-quantum optimum equals $N^2/(17N^2-80N+64)$ for $N\ge8$ and tends to $1/17$. The first level of the hierarchy, which coincides with the set singled out by macroscopic locality, attains $N/[8(N-2)]$, which tends to $1/8$; its optimal boxes lie outside the almost-quantum set for every $N\ge5$. For longer messages, entanglement saves at most one bit over shared randomness, whereas almost-quantum correlations reduce the one-way zero-error cost of deciding equality of $n$-bit strings from $n$ bits to at most $13$. The quantum bound also yields a linear witness of post-quantumness on a face of the nonsignalling polytope.

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arXiv2026

On the structure of low-rank PPT entangled states violating Peres conjecture

Bound-entangled states with positive partial transpose (PPT) can exhibit quantum steering and Bell nonlocality, disproving the long-standing Peres conjecture and its stronger steering counterpart. These counterexamples, obtained through explicit constructions or numerical searches, raise the question of whether they share a common structural origin. We address this question in the low-rank regime by asking whether known counterexamples can be obtained, up to invertible local filtering, from the complement of an unextendible product basis (UPB). We find that the answer depends crucially on the local dimension. In $3\otimes3$, the rank-four structure of PPT entangled states implies that both the steerable PPT state of Moroder \textit{et al.} and the Bell-nonlocal PPT state of Vértesi and Brunner can be obtained from UPB-complement states under invertible local filtering. For three qubits, in contrast, rank-four states that are PPT across every bipartition are separable across each cut. Moreover, comparison of the product-vector structure of the relevant kernels shows that the known three-qubit Bell-nonlocal PPT states cannot be obtained by invertible local filtering from the complement of any three-qubit UPB. Going beyond rank four, we further show that a known rank-eight three-qutrit state, supported on the complement of a UPB and PPT across every bipartition, is genuinely multipartite entangled. These results show that UPBs provide a unifying structural origin for important low-rank PPT entangled states in $3\otimes3$, but that nonlocal bound entanglement is not, in general, a UPB phenomenon.

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arXiv2026

All-vs-Nothing Operational Manifestation of Preparation Contextuality

Preparation contextuality is often manifested operationally through a quantitative advantage over preparation-noncontextual models in information-processing tasks, yet quantum theory typically falls short of perfect success. Here we introduce a parity-oblivious Hidden Matching task that instead yields an all-vs-nothing manifestation of preparation contextuality. Alice encodes an $n$-bit string so that her message reveals no information about any input parity other than the two-bit parities. Bob, given a perfect matching on the input positions, must output an edge of the matching together with the parity of its two bits. A quantum protocol using a single $\lceil\log_2 n\rceil$-qubit message satisfies the parity-obliviousness constraint and succeeds with certainty. We prove that no preparation-noncontextual model achieves perfect success for any even $n\ge6$. The result holds for arbitrary ontic state spaces and assumes neither outcome determinism nor measurement noncontextuality. For $n=6$ and $n=8$, the optimal noncontextual success probabilities are $4/5$ and $3/4$, respectively, while asymptotically the optimal noncontextual success probability is $1/2+Θ(1/\sqrt n)$. Our asymptotic upper bound follows from a Fourier-analytic sum rule derived via hypercontractivity on the Boolean hypercube. The resulting separation is qualitative rather than merely quantitative: quantum theory achieves perfect success, whereas preparation-noncontextual models cannot. We aslo show that at $n=8$ the noncontextual bound remains $3/4$ even when Bob is restricted to just suitable $4$ of the $105$ possible perfect matchings, bringing the effect within experimental reach.

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arXiv2026

On the Origin of Beyond-Classical Advantage in the Parity-Permutation Problem

We investigate the task of identifying the parity (odd vs even) of an unknown permutation applied to $n$ particles. Classically, using fewer than $n$ distinct labels per particle limits the success probability to random guessing, whereas quantum mechanics, exploiting entanglement in both preparation and measurement, accomplishes the task perfectly with as few as $\big\lceil \sqrt{n}\big\rceil$ levels per particle [\href{https://doi.org/10.1103/yhyv-xnwq}{PRL {\bf 135}, 260603 (2025)}]. We show that even without entangled preparation, quantum theory still offers a probabilistic advantage over classical strategies. Moreover, such product preparations yield perfect success in locally quantum theories, where elementary systems are quantum but their composition follows the minimal tensor product structure of generalized probabilistic theories (GPTs). We further identify GPT models that accomplish the task with certainty without requiring entanglement either at the preparation stage or at the measurement stage. Our central result establishes that the linear dimension of the elementary systems, rather than entanglement, is the fundamental resource governing the existence of probabilistic advantage in the permutation parity problem. In particular, below the required dimension threshold, no amount of entanglement can improve upon the random-guessing limit.

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arXiv2026

Exponential Advantage of Multipartite Entanglement over Quantum Communication with Applications to Bounded-Storage Cryptography

We establish an exponential communication advantage enabled by multipartite quantum entanglement. Building on the bipartite Hidden Matching problem, we introduce a communication task involving multiple spatially separated senders and a single receiver. We show that a shared Greenberger-Horne-Zeilinger state enables completion of this task using only logarithmically many bits of classical communication from each sender. In contrast, without preshared entanglement, any protocol achieving high success probability requires polynomial communication from at least one sender, even when \emph{quantum} communication is allowed. Thus, classical communication assisted by multipartite entanglement can be exponentially more powerful than quantum communication without preshared entanglement. As a cryptographic application, we construct a seeded two-source randomness extractor and establish an exponential separation between entangled and unentangled quantum side-information. Specifically, compromising the extractor with two unentangled quantum states storing information about the two sources, respectively, requires polynomial-size memory, whereas exponentially smaller quantum memory suffices in the presence of a small amount of shared entanglement.

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arXiv2026

Emergence and Recovery of (logical) Kochen-Specker Contextuality via Hamilton Extension

Logical Kochen-Specker (KS) contextuality is widely regarded as an intrinsic property of specially constructed measurement configurations. We show instead that it can emerge from KS-colorable vector sets through a constructive procedure we call the Hamilton extension. Defined for four-dimensional vector sets, the Hamilton extension associates each real vector with a measurement context while inducing additional measurement contexts among Hamilton-extended children of distinct parent vectors. These emergent contexts fundamentally alter the compatibility structure, transforming KS-colorable configurations into KS-uncolorable ones and recovering logical contextuality lost under apex-vertex augmentation. We establish a sharp and optimal threshold -- the Hamilton extension of every five-vector parent set remains KS-colorable, whereas suitably chosen six-vector parent sets already generate logical KS contradictions. Thus, six vectors constitute the smallest parent set capable of generating KS contradiction through this mechanism. Our results reveal a new structural route to contextuality, provide a systematic framework for constructing compact KS sets, and have implications for contextuality-based quantum information protocols and graph-theoretic approaches to nonclassicality.

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arXiv2026

Gottesman-Knill Limit on One-way Communication Complexity: Tracing the Quantum Advantage down to Magic Resources

Quantum systems are known to offer advantages over their classical counterpart in communication complexity protocols, where the aim is to minimize the amount of information exchange between distant parties to compute global functions of their distributed inputs. In this work, we establish that any one-way communication protocol implemented using a prime-dimensional quantum system -- restricted to stabilizer-state encodings and Clifford-operation decodings -- can be exactly simulated by transmitting a classical system of the same dimension, given access to shared randomness between the sender and receiver. In direct analogy with the Gottesman-Knill theorem, which attributes quantum computational speedup to non-stabilizer resources, commonly known as the magic resources, our result identifies the same non-stabilizer resources as the essential ingredient for the quantum advantage in one-way communication complexity. Furthermore, we present explicit tasks where even a 'minimal magic resource' suffices to achieve a provable quantum advantage, highlighting its efficient use in communication protocols.

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arXiv2026

Conclusive Identification Via Noisy Classical Channel: Superactivation and Quantum Advantage

We introduce conclusive identification task for classical channels: a receiver identifies transmitted inputs without error when possible, and responds inconclusively when outputs are ambiguous. For a symmetric not-fully-corrupted channel $N : X \to X$, the single-shot conclusive identification index $\mathrm{ci}_\circ(N)$ counts the maximum number of conclusively identifiable inputs. We show $\mathrm{ci}_\circ(N)$ exhibits a striking superactivation phenomenon: a channel with $\mathrm{ci}_\circ(N) = 0$ achieves $\mathrm{ci}_\circ(N \otimes \mathrm{id}^c_β) = |X|$ when assisted by a perfect classical channel of dimension $β< |X|$. The minimum classical assistance required equals the chromatic number $χ(\mathtt{S}_N)$ of the channel's support graph $\mathtt{S}_N$. We provide channel families where the superactivation gap $\mathrm{ci}_\circ(N \otimes \mathrm{id}^c_β) - \mathrm{ci}_\circ(\mathrm{id}^c_β)$ can be made arbitrarily large. A noiseless quantum channel of dimension equal to the orthogonal rank $ξ(\mathtt{S}_N)$ suffices, yielding a strict quantum advantage whenever $ξ(\mathtt{S}_N) < χ(\mathtt{S}_N)$. This advantage is demonstrated through three explicit constructions motivated by combinatorial and algebraic state-independent, and state-dependent proofs of Kochen-Specker contextuality. Via the co-normal product of graphs, we analyze the scaling of the quantum advantage ratio $χ_f(\mathtt{S}_N)/ξ(\mathtt{S}_N)$, and present a channel for which quantum assistance is exponentially more efficient than classical. Our results establish $\mathtt{S}_N$, rather than the confusability graph $\mathtt{G}_N$, as the natural combinatorial object for conclusive identification, revealing that channels deemed useless under Shannon's zero-error framework can exhibit rich superactivation and quantum advantage, with deep connections to quantum contextuality.

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arXiv2026

No Absolute Hierarchy of Quantum Complementarity

Bohr's principle of complementarity, prohibiting simultaneous access to certain physical properties within a single experimental arrangement, is considered to be a defining feature of quantum mechanics. It is commonly viewed as inducing an intrinsic hierarchy among incompatible observables: some sets of quantum properties are fundamentally more incompatible than others, as quantified by the maximal sharpness permitting their joint measurement. We show that this hierarchy ceases to be absolute in the multi-copy regime. Analyzing qubit spin observables, we prove a No-Comparison Theorem establishing that no global ordering of incompatible observable sets is preserved across all finite-copy configurations. In particular, two sets of observables can exhibit reversed complementarity ordering depending solely on whether the available resources are arranged as identical copies or as parallel-antiparallel pairs. Thus, the degree of quantum incompatibility is not an intrinsic property of observables alone but depends on the global configuration of the prepared quantum probes. Our results uncover a configuration-dependent structure of complementarity, reveal a subtle role of entanglement in shaping the structure of measurement limitations, and call for a reassessment of quantum information protocols under finite resources.

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arXiv2026

Quantum Incompatibility in Parallel vs Antiparallel Spins

We explore the joint measurability of incompatible qubit observables on ensembles of parallel and antiparallel spin-1/2 pairs. In parallel configuration, both spins are prepared in the same state, whereas in antiparallel case, each spin is paired with its flipped counterpart. We show that the antiparallel configuration uniquely enables exact simultaneous prediction of three mutually orthogonal spin components -- an advantage not achievable with parallel states. Extending beyond three observables, we examine joint measurability for larger sets of spin measurements and further generalize our analysis to state configurations beyond the parallel and antiparallel cases. As we show, our results reveal a deep connection to the 'mean King retrodiction task' proposed by Vaidman, Aharonov, and Albert, and have implications for a cryptographic protocol introduced by Jeffrey Bub. We further demonstrate how the enhanced compatibility in the antiparallel configuration can facilitate efficient estimation of unknown measurement devices. Finally, we discuss prospects for experimentally realizing the enhanced measurement compatibility in antiparallel configuration by analyzing the effect on finite sub-ensembles of states.

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arXiv2025

Thermodynamic Probes of Multipartite Entanglement in Strongly Interacting Quantum Systems

Quantifying multipartite entanglement in quantum many-body systems and hybrid quantum computing architectures is a fundamental yet challenging task. In recent years, thermodynamic quantities such as the maximum extractable work from an isolated system (the ergotropy) have allowed for entanglement measures that are operationally more accessible. However, these measures can be restrictive when applied to systems governed by Hamiltonians with strong collective or interparticle interactions. Motivated by advances in quantum simulators, we propose a framework that circumvents these restrictions by evaluating global and local ergotropy either through controlled quenching of interactions or by measuring suitable local observables only. We show that this formalism allows us to correctly estimate genuine multipartite entanglement in both stationary and time-evolved states of systems with strong interactions, including parametrized quantum states simulated on a quantum circuit with varying circuit depth and noise. We demonstrate its applicability to realistic physical models, namely, the Tavis-Cummings model, the three-level Dicke model, and the transverse-field Ising model, highlighting its potential as a versatile tool for characterizing entanglement in near-term quantum simulators.

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arXiv2025

Photonic Simulation of Beyond-Quantum Nonlocal Correlations (e.g. Popescu-Rohrlich Box) with Non-Signaling Quantum Resources

Bell nonlocality exemplifies the most profound departure of quantum theory from classical realism. Yet, the extent of nonlocality in quantum theory is intrinsically bounded, falling short of the correlations permitted by the relativistic causality (the no-signaling) principle. A paradigmatic example is the Popescu-Rohrlich correlation: two distant parties sharing arbitrary entanglement cannot achieve this correlation, though it can be simulated with classical communication between them. Here we show how such post-quantum correlations can instead be simulated using intrinsically non-signaling physical resources, and implement the proposed scheme using a quantum circuit on a four-qubit photonic platform. Unlike the conventional approaches, our method exploits dynamical correlations between distinct physical systems, with intrinsic randomness suppressing any signaling capacity. This enables the realization of post-quantum correlations both with and without entanglement. We also analyze how the simulation scheme extends to beyond quantum nonlocal correlations in multipartite systems. Our experimental demonstration using a photonic system establishes a versatile framework for exploring post-quantum correlations in both foundational settings and as a resource for computation and security applications.

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arXiv2025

No-Go Theorem for Generic Simulation of Qubit Channels with Finite Classical Resources

The mathematical framework of quantum theory, though fundamentally distinct from classical physics, raises the question of whether quantum processes can be efficiently simulated using classical resources. For instance, a sender (Alice) possessing the classical description of a qubit state can simulate the action of a qubit channel through finite classical communication with a receiver (Bob), enabling Bob to reproduce measurement statistics for any observable on the state. In this work, we contend that a more general simulation requires reproducing statistics of joint measurements, potentially involving entangled effects, on Alice's system and an additional system held by Bob, even when Bob's system state is unknown or entangled with a larger system. Within this broad framework, we prove that no finite amount of classical messaging, regardless of how many rounds are used or how large each message can be, can reproduce a perfect qubit channel, highlighting an inescapable barrier in quantum channel simulation with classical resources. We also establish that entangled effects crucially underlies this no-go result. However, for noisy qubit channels, such as those with depolarizing noise, we demonstrate that general simulation is achievable with finite communication. Notably, the required communication increases as the noise decreases, revealing an intricate relationship between the noise in the channel and the resources necessary for its classical simulation.

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arXiv2025

Ergodiscord: An Operational and Distinct Notion of Quantumness of Correlations

Nonclassicality in composite quantum systems depicts several puzzling manifestations, with Einstein-Podolsky-Rosen entanglement, Schrödinger steering, and Bell nonlocality being the most celebrated ones. In addition to those, an unentangled quantum state can also exhibit nonclassicality, as evidenced from notions such as quantum discord and work deficit. In this work, we present a general framework for exploring quantumness of correlations in multipartite quantum states. By exploiting the different signatures reflected on observable quantities depending on whether subsystems of a composite systems are probed jointly or independently, we introduce an operational quantifier of nonclassicality, termed {\em ergodiscord}. As we show, this newly proposed quantifier faithfully captures nonclassicality in any bipartite quantum state, while being fundamentally distinct from the original quantum discord. Moreover, ergodiscord uncovers an intriguing phenomenon called `nonlocal energy locking', where a useful form of energy (i.e. work) gets locked in correlations of nonclassical states. We also show that a mixed nonclassical state can lock more work than the maximally entangled state of the corresponding system, establishing an interesting super-additivity phenomenon of nonlocal energy locking. The present work may inspire novel designs of quantum energy storage devices by utilizing nonclassical correlations in composite quantum systems.

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arXiv2025

Nonlocality-Assisted Enhancement of Error-Free Communication in Noisy Classical Channels

The zero-error capacity of a noisy classical channel quantifies its ability to transmit information with absolute certainty, i.e., without any error. Unlike Shannon's standard channel capacity, which remains unaffected by pre-shared correlations, zero-error capacity can be enhanced through nonlocal correlations. In this work, we investigate zero-error communication utility of such correlations arising in the 2-2-m Bell scenario, where two parties have two inputs and m possible outcomes per input. For all m\geq2, we construct examples of noisy classical channels with zero zero-error capacity that, when assisted by extremal 2-2-m nonlocal correlations, can transmit one bit of information. While nonlocal correlations arising from quantum entangled states cannot achieve a positive zero-error capacity for these channels, they significantly enhance the probability of successfully transmitting a classical bit in a single use. Extending this analysis to the 2-m-2 Bell scenario, we identify channels with zero zero-error capacity that can nonetheless perfectly transmit log m bits of information when assisted by corresponding extremal nonlocal correlations. Our findings underscore the versatile utility of Bell nonlocal correlations in achieving zero-error communication.

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arXiv2025

Harnessing Causal Indefiniteness for Accessing Locally Inaccessible Data

Recent studies suggest that physical theories can exhibit indefinite causal structures, where the causal order of events is fundamentally undefined yet logically consistent. Beyond its foundational appeal, causal indefiniteness has also emerged as a novel information-theoretic resource, offering advantages in various information processing tasks. Here, we investigate its utility in the classical Data Retrieval (DR) task. In its simplest version, a referee encodes classical messages into bipartite quantum states and distributes the local parts to two distant parties, ensuring that neither can independently extract any information about the encoded message. To retrieve their assigned data, parties must collaborate, and we show that those embedded in an indefinite causal structure generally outperform those operating within a definite causal framework. For the bipartite case, we establish a duality between the DR task and the well known Guess Your Neighbour's Input game and derive a criterion analogous to the Peres-Horodecki separability test to identify quantum processes that yield nontrivial success in the DR task. We also report an intriguing super-activation phenomenon, where two quantum processes, each individually inefficient for the DR task, become useful when combined. Extending the analysis to tripartite case, we show that classical causally inseparable processes can outperform quantum bi-causal processes in the DR task. Our study, thus, reveals several unexplored aspects of causal indefiniteness, inviting deeper investigation.

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arXiv2025

Bipartite polygon models: entanglement classes and their nonlocal behaviour

Hardy's argument constitutes an elegantly logical test for identifying nonlocal features of multipartite correlations. In this paper, we investigate Hardy's nonlocal behavior within a broad class of operational theories, including the qubit state space as a specific case. Specifically, we begin by examining a wider range of operational models with state space descriptions in the form of regular polygons. First, we present a systematic method to characterize the possible forms of entangled states within bipartite compositions of these models. Then, through explicit examples, we identify the classes of entangled states that exhibit Hardy-type nonlocality. Remarkably, our findings highlight a closer analogy between odd polygon models and the qubit state space in terms of their bipartite Hardy nonlocal behavior compared to even-sided polygons. Furthermore, we demonstrate that the emergence of mixed-state Hardy nonlocality in any operational model is determined by a specific symmetry inherent in its dynamic description. Finally, our results uncover an unexplored class of almost-quantum correlations that can be associated with an explicit operational model.

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