arXiv subjects

Tathagata Gupta

Publications and source records attributed to Tathagata Gupta.

10 recordsLinked to original sources

arXiv2026

Local state antimarking : Nonlocality without entanglement

A set of quantum states is said to be antidistinguishable if, upon being given a randomly chosen state, it is possible to identify a state that the system was definitively not prepared in. In this work, we begin with a study of quantum nonlocality within the framework of local state antidistinguishability (LSAD), and find that any ensemble of mutually orthogonal multipartite pure states is locally antidistinguishable. We then extend this paradigm by introducing the task of local state antimarking (LSAM), where a non-repetitive sequence from a known set of multipartite states is randomly selected and distributed to spatially separated parties who must identify at least one sequence that was not supplied using LOCC only. We present an ensemble of product states that is not globally antidistinguishable, but choosing states from it, without replacement, produces such sequences of states which are globally antidistinguishable but not locally-revealing a form of nonlocality without entanglement. Finally, we compare LSAD and LSAM with conclusive local state discrimination and conclusive local state marking. We demonstrate that no strict hierarchy exists between these paradigms: there exist product-state ensembles that permit one task while strictly forbidding the other, and vice versa.

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arXiv2026

Local strategies are pretty good at computing Boolean properties of quantum sequences

Quantum memory is a scarce and costly resource, yet little is known about which learning tasks remain feasible under severe memory constraints. We study the problem of computing global properties of quantum sequences when quantum systems must be measured individually, without storing or jointly processing them. In our setting, a bit string $x \in \{0,1\}^n$ is encoded into an $n$-qubit product state $|\psi_{x_1}\rangle \otimes \cdots \otimes |\psi_{x_n}\rangle$, and the goal is to infer $f(x) \in \{0,1\}$ from measurements of this quantum encoding. We consider a simple local strategy, which we call the greedy strategy, that applies the same optimal single-system measurement independently to each subsystem and then infers $f(x)$ from the outcomes. Our main result gives a complete characterization of when the greedy strategy is optimal: it achieves the same maximum success probability as an unrestricted global measurement if and only if the target Boolean function is affine (in all but finitely many cases). We establish a universal performance guarantee for general Boolean functions, showing that the success probability of the greedy strategy is always at least the square of the optimal global success probability, in direct analogy with the Barnum-Knill bound for the pretty good measurement. These results demonstrate that even under extreme memory constraints, simple local measurement strategies can remain provably competitive for learning global properties of quantum sequences.

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arXiv2026

Quantum state exclusion with many copies

Quantum state exclusion is the task of identifying at least one state from a known set that was not used in the preparation of a quantum system. A set of quantum states is said to admit state exclusion if there exists a measurement whose outcomes can be put in one-to-one correspondence with the states in the set, such that each outcome rules out its corresponding state with certainty (while possibly also ruling out other states), and each outcome occurs with nonzero probability for at least one state in the set. State exclusion, however, is not always possible in the single-copy setting. In this paper, we investigate whether access to multiple identical copies of the system enables state exclusion. We prove that for any set of three or more pure states, state exclusion becomes possible with a finite number of copies. Moreover, we show that the number of copies required may be arbitrarily large: in particular, for every natural number $N$, we construct sets of states for which state exclusion remains impossible with $N$ or fewer copies.

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arXiv2025

Quantum nonlocality without entanglement and state discrimination measures

An ensemble of product states is said to exhibit "quantum nonlocality without entanglement" if it cannot be optimally discriminated using local operations and classical communication (LOCC). We show that this property can depend on the chosen discrimination measure. Specifically, we construct a family of ensembles, each consisting of six linearly independent, equally probable bipartite product states, for which LOCC fails to achieve optimal minimum-error discrimination but succeeds in achieving optimal unambiguous discrimination. We further extend our construction to multipartite systems and provide strong numerical evidence that a similar separation between local and global optima is present for minimum-error discrimination, but not for unambiguous discrimination.

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arXiv2024

Optimal discrimination of quantum sequences

A key concept of quantum information theory is that accessing information encoded in a quantum system requires us to discriminate between several possible states the system could be in. A natural generalization of this problem, namely, quantum sequence discrimination, appears in various quantum information processing tasks, the objective being to determine the state of a finite sequence of quantum states. Since such a sequence is a composite quantum system, the fundamental question is whether an optimal measurement is local, i.e., comprising measurements on the individual members, or collective, i.e. requiring joint measurement(s). In some known instances of this problem, the optimal measurement is local, whereas in others, it is collective. But, so far, a definite prescription based solely on the problem description has been lacking. In this paper, we prove that if the members of a given sequence are drawn secretly and independently from an ensemble or even from different ensembles, the optimum success probability is achievable by fixed local measurements on the individual members of the sequence, and no collective measurement is necessary. This holds for both minimum-error and unambiguous state discrimination paradigms.

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arXiv2024

Unambiguous discrimination of sequences of quantum states

We consider the problem of determining the state of an unknown quantum sequence without error. The elements of the given sequence are drawn with equal probability from a known set of linearly independent pure quantum states with the property that their mutual inner products are all real and equal. This problem can be posed as an instance of unambiguous state discrimination where the states correspond to that of all possible sequences having the same length as the given one. We calculate the optimum probability by solving the optimality conditions of a semidefinite program. The optimum value is achievable by measuring individual members of the sequence, and no collective measurement is necessary.

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arXiv2023

Local Inaccessibility of Random Classical Information and Their Implications in the Change Point Problem

Discrimination of quantum states under local operations and classical communication (LOCC) is an intriguing question in the context of local retrieval of classical information, encoded in the multipartite quantum systems. All the local quantum state discrimination premises, considered so far, mimic a basic communication set-up, where the spatially separated decoding devices are independent of any additional input. Here, exploring a generalized communication scenario, we introduce a framework for input-dependent local quantum state discrimination, which we call local random authentication (LRA). We report that impossibility of LRA certifies the presence of entangled states in the ensemble, a feature absent from erstwhile nonlocality arguments based on local state discrimination. Additionally, we explore the salient features of this state discrimination prototype for arbitrary set of orthogonal quantum states and compare them with the traditional notion of local quantum state discrimination. Finally, our results reveal a fundamental information-theoretic implications in the local estimation of quantum change point problems.

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arXiv2022

Local Quantum State Marking

We propose the task of local state marking (LSM), where some multipartite quantum states chosen randomly from a known set of states are distributed among spatially separated parties without revealing the identities of the individual states. The collaborative aim of the parties is to correctly mark the identities of states under the restriction that they can perform only local quantum operations (LO) on their respective subsystems and can communicate with each other classically (CC) -- popularly known as the operational paradigm of LOCC. While mutually orthogonal states can always be marked exactly under global operations, this is in general not the case under LOCC. We show that the LSM task is distinct from the vastly explored task of local state distinguishability (LSD) -- perfect LSD always implies perfect LSM, whereas we establish that the converse does not hold in general. We also explore entanglement assisted marking of states that are otherwise locally unmarkable and report intriguing entanglement assisted catalytic LSM phenomenon.

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arXiv2022

Genuine Activation of Quantum Nonlocality: Stronger Than Local Indistinguishability

The structure of quantum theory assures the discrimination of any possible orthogonal set of states. However, the scenario becomes highly nontrivial in the limited measurement setting and leads to different classes of impossibility, viz., indistinguishability, unmarkability, irreducibility etc. These phenomena, often referred to as other nonlocal aspects of quantum theory, have utmost importance in the domain of secret sharing etc. It, therefore, becomes a pertinent question to distill/activate such behaviours from a set, apparently devoid of these nonlocal features and free from local redundancy. While the activation of local indisitinguishability in the sets of entangled states has recently been reported, other stronger notion of quantum nonlocality has yet not been inspected in the parlance of activation. Here, we explored all such stronger versions of nonlocality and affirmatively answered to activate each of them. We also find a locally distinguishable set of multipartite entangled states which can be converted with certainty to a nontrivial set of locally irreducible genuinely entangled states.

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arXiv2022

Activating Strongest Possible Nonlocality from Local Sets: An Elimination Paradigm

Apart from the Bell nonlocality, which deals with the correlations generated from the local input-output statistics, quantum theory exhibits another kind of nonlocality that involves the indistiguishability of the locally preparable set of multipartite states. While Bell-type nonlocality cannot be distilled from a given local correlation, it is already reported that the latter kind of nonlocality can be activated from a "local", i.e., locally distinguishable set of states. Although, recently it is shown that a stronger notion of such a nonlocality, which deals with elimination instead of discrimination, can be activated from locally preparable bipartite states of dimension 7 $\times$ 8, the present work observes that the same notion can be demonstrated even in lower dimensional multipartite systems. Importantly,the strongest possible version of such an activation is further depicted here, where none of the transformed product states can be eliminated, even if all but one of the parties come together.

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