arXiv subjects

Satyaki Manna

Publications and source records attributed to Satyaki Manna.

13 recordsLinked to original sources

arXiv2026

Antidistinguishability of states in General Probabilistic Theories

We investigate antidistinguishability of states within the framework of general probabilistic theories (GPTs). We formulate antidistinguishability, strong and equal antidistinguishability as refined notions that imposed additional constraint on the measurement effects. We establish general results relating these notions of antidistinguishability and derive an upper bound on the cardinality of equally antidistinguishable sets in terms of the affine dimension of the state space. We then study antidistinguishability in polygonal theories, obtaining conditions for antidistinguishability of a set of states. In consequence, we show that the set of all pure states in a polygon model is antidistinguishable. Additionally, we identify broad families of strongly and equally antidistinguishable states. Finally, using Random Exclusion Codes, whose success probability is governed by the antidistinguishability of different sets of encoding states, we probe the nonclassicality of polygon theories. We find that certain polygon models can outperform the optimal quantum value, while their optimal performance converges to the quantum limit in the large-polygon limit.

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arXiv2026

Genuine certification of incompatible quantum instruments through sequential communication tasks

Quantum instruments constitute the general description of quantum dynamics, encompassing both quantum measurements and quantum channels as special cases. Consequently, the incompatibility of quantum instruments represents a fundamental manifestation of nonclassicality in quantum theory. Here, we establish the operational significance of this notion by demonstrating communication tasks with classical inputs and outputs that enable the semi-device-independent certification of incompatible quantum instruments. We introduce a class of three-party communication tasks involving a sender, a relayer, and a receiver, and derive the tight upper bounds of the figure of merits of these tasks achievable by all compatible instruments implemented by the relayer. Furthermore, we show that these bounds coincide with the optimal performance attainable in a classical communication subject to the same dimensional constraints. Violation of this bound certifies the incompatibility of the pair of quantum instruments implemented by the relayer. This identifies certification of incompatible instruments as a manifestation of quantum advantage in communication. This certification protocol is genuine as it is able to certify the incompatibility of a pair of instruments where the set of induced measurements and the set of induced channels are compatible and, therefore it does not depend on the incompability of measurements and channels induced by the instruments. Finally, we identify the simplest instance of our communication scenario that enable the certification of incompatible quantum instruments.

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arXiv2026

Usefulness of $d\otimes d$ dimensional pure entangled states for antidiscrimination of quantum measurements when $d$ is even

The usefulness of entanglement in quantum channel discrimination is a central topic in quantum information theory. A landmark result in this direction was established by Piani and Watrous [$Phys. Rev. Lett.102, 250501 (2009)$] who proved that all entangled states are useful for discrimination of quantum channels. We pose the same question in the context of antidiscrimination of quantum channels. We partially answer this by showing that for every pure entangled state of $\mathbbm{C}^d\otimes\mathbbm{C}^d$ (with even $d$), there exist three projective measurements which are antidiscriminable (but not discriminable) with that input state but those three measurements are not antidiscriminable with the product probe.

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arXiv2026

Nonlocality without entanglement in exclusion of quantum states

We study the task of quantum state exclusion, focusing on antidistinguishability and its generalization to $x$-antidistinguishability, under global measurements and local operations with classical communication (LOCC). We also introduce weak and strong notions of antidistinguiahbaility ($x$-antidistinguishability) depending on whether all states or all $x$-tuples are exhaustively eliminated. Our results reveal striking differences between state exclusion and the more familiar task of state discrimination. In particular, we show that LOCC antidistinguishability of multipartite product states is symmetric with respect to the initiating party but this symmetry breaks down for higher-order $x$-antidistinguishability. Most notably, we establish a manifestation of \emph{nonlocality without entanglement} in the context of state exclusion: we prove that three bipartite product states can be globally antidistinguishable while failing to be LOCC antidistinguishable, demonstrating that three is the minimal number of states required for this phenomenon. We further extend this separation to $2$-antidistinguishability and present example exhibiting the same type of nonlocality. At last, we provide an antidistinguishable tripartite product states that are not LOCC antidistinguishable across any bipartition, which ensures the phenomenon of \emph{genuine nonlocality without entanglement} in this framework.

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arXiv2026

Limitation of maximally entangled probes for single-shot distinguishability of unitaries

There have been many instances where the maximally entangled state as a probe acts better than the product and the non-maximally entangled states in the task of distinguishing quantum channels. We provide a proof that for single-shot discrimination of two unitary channels, entangled and product states are operationally equivalent. But we identify pairs of unitaries that are perfectly distinguishable using a non-maximally entangled state, but not with a maximally entangled one. This contrast becomes more pronounced when the number of unitaries exceeds two. In every dimension $\geqslant 3$, we show that there exists a class of unitaries that are indistinguishable under maximally entangled probes, yet perfectly distinguishable using product or non-maximally entangled inputs. Another interesting set of unitaries in every dimension $\geqslant 3$ has been presented where only non-maximally entangled state acts as the successful probe, while product states and maximally entangled states cannot.

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arXiv2026

Global versus Local Discrimination of Locally Implementable Multipartite Unitaries

We study single-shot distinguishability of locally implementable multipartite unitaries under Local Operations and Classical Communication (LOCC) and global operations. As unitary discrimination depends on both the choice of probing states and the measurements on the evolved states, we classify LOCC and global distinguishability into two categories: adaptive strategies, where probing states are chosen based on measurement outcomes from other subsystems, and restricted strategies, where probing states remain fixed. Our findings uncover three surprising features in the bipartite setting and establish new structural limits for unitary discrimination: (i) Certain pairs of unitaries are globally distinguishable with restricted strategies but indistinguishable under LOCC, even with adaptive strategies. (ii) There exist sets of four unitaries that are distinguishable via LOCC, yet remain globally indistinguishable with restricted strategies. (iii) Some sets of unitaries are globally indistinguishable under adaptive strategies, when probed with separable states, but become distinguishable via LOCC.

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arXiv2026

Entanglement assisted communication complexity measured by distinguishability

We investigate the quantum advantage that can arise in typical two-party communication scenarios, where the sender and the receiver are allowed to share prior correlations. Focusing on communication tasks constrained by the distinguishability of the sender's inputs, we demonstrate that entanglement-assisted communication with both classical and quantum message can outperform classical communication supplemented with shared randomness. We begin by developing a general framework for communication tasks with pre-shared correlations. Within this framework, we establish an equivalence among entanglement-assisted classical communication, entanglement-assisted quantum communication, and quantum communication, showing that no hierarchy exists between these three paradigms. We then investigate the scenario where the receiver has no input and prove that no advantage can arise in this case. However, an advantage in the entanglement-assisted setting emerges once additional constraints are imposed on the dimension of the communicated message. This further highlights the superiority of entanglement-assisted classical communication over standard quantum communication. Then we demonstrate several tasks where the entanglement-assisted protocol using one-bit communication proves to be advantageous over classical communication. Finally, by constructing an explicit class of communication tasks, we show that a non-maximally entangled states outperform the maximally entangled state as a pre-shared resource between the communicating parties.

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arXiv2026

Limits of Classical correlations and Quantum advantages under (Anti-)Distinguishability constraints in Multipartite Communication

We consider communication scenarios with multiple senders and a single receiver. Focusing on communication tasks where the distinguishability or antidistinguishability of the sender's input is bounded, we show that quantum strategies-without any shared entanglement-can outperform the classical ones. We introduce a systematic technique for deriving the facet inequalities that delineate the polytope of classical correlations in such scenarios. As a proof of principle, we recover the complete set of facet inequalities for some nontrivial scenarios involving two senders and a receiver with no input. Explicit quantum protocols are studied that violate these inequalities, demonstrating quantum advantage. We further investigate the task of antidistinguishing the joint input string held by the senders and derive upper bounds on the optimal classical success probability. Leveraging the Pusey-Barrett-Rudolph theorem, we prove that when each sender has a binary input, the quantum advantage grows with the number of senders. We also provide sufficient conditions for quantum advantage for arbitrary input sizes and illustrate them through several explicit examples.

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arXiv2026

Local Marking of Locally Implementable Unitary Operations

We investigate the task of local marking for locally implementable unitary operations. In this setting, multipartite quantum unitary channels, chosen randomly from a known set, are distributed among spatially separated parties without revealing their identities. The objective is to correctly identify (mark) the applied process using only local operations supplemented with classical communication (LOCC). While local distinguishability implies local marking, local marking does not guarantee either local or even global distinguishability of a set of unitaries. Thus the task of marking is not equivalent to the task of discrimination. We demonstrate a stronger manifestation of nonlocality without entanglement by constructing a set of globally distinguishable tripartite product unitaries that cannot be locally marked. In contrast to state marking, we find that marking a subset of product unitaries does not imply the ability to mark a larger subset. Finally, we explore the hierarchy of probes-entangled and product-in the context of local marking with respect to the standard discrimination scenario.

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arXiv2026

Single shot distinguishability of noisy quantum channels

Among the intriguing features of quantum theory, the problem of distinguishing quantum channels is of fundamental interest. In this paper, we focus on the single-shot discrimination of two noisy quantum channels using two distinct classes of probes: single-system (product) probes and entangled probes. Our aim is to identify optimal probing state for specific discrimination tasks and to analyze the necessity and role of entanglement in enhancing channel distinguishability. We show that maximally entangled probes are optimal for discriminating two qubit depolarizing channels, with any nonzero entanglement providing an advantage over single-system probes. In contrast, for dephasing channels in arbitrary dimensions, we prove that single-system probe can be optimal and that entanglement offers no improvement, even when the dephasing unitary is generalized. For qubit amplitude-damping channels, we identify distinct noise-dependent regimes in which either single-system probe outperforms maximally entangled probes and vice-versa. Moreover, we demonstrate that non-maximally entangled probes can act as the optimum probe if the noise parameters restricted to certain values in this task. We also present examples of noisy unitary channels for which discrimination is possible using non-maximally entangled probe, while both single-systems and maximally entangled probes fail. We introduce another class of noisy unitary channels for which perfect discrimination is achievable with a single system, while maximally entangled probes are insufficient. Finally, we show that two erasure channels can be optimally discriminated using any pure single-system probe, with no advantage gained from entanglement.

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arXiv2026

Single-shot antidistinguishability of unitary operations

The notion of antidistinguishability captures the possibility of ruling out certain alternatives in a quantum experiment without identifying the actual outcome. Although extensively studied for quantum states, the antidistinguishability of quantum channels remains largely unexplored. In this work, we investigate the single-shot antidistinguishability of unitary operations. We analyse two scenarios: antidistinguishability with single-system probes and with entangled probes. For sets of three unitaries, we first prove that all maximally entangled states are equivalent in their performance as probe. In the qubit case, we further establish that maximally entangled probes are always sufficient: if a set of three qubit unitaries is antidistinguishable with either a single-system or non-maximally entangled probe, then it is also antidistinguishable with a maximally entangled one. However, in higher dimension, this equivalence fails. In \textit{dimension 3}, there exists a set of unitaries that are antidistinguishable with non-maximally entangled probe or single-system probe but not with maximally entangled probe. We also establish that union of two antidistinguishable sets of three qubit unitaries also forms a set of antidistinguishable unitaries. Lastly, we provide methods to construct antidistinguishable unitaries from non-antidistinguishable ones.

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arXiv2025

Single-shot Distinguishability and Anti-distinguishability of Quantum Measurements

Among the surprising features of quantum measurements, the problem of distinguishing and antidistinguishing general quantum measurements is fundamentally appealing. Unlike classical systems, quantum theory offers entangled states and peculiar state update rule of the post-measurement state, which gives rise to four distinct scenarios: (i) probing single systems and without access to the Post-measurement States (PMS), (ii) probing entangled systems and without access to the PMS, (iii) probing single systems with access to the PMS, and (iv) probing entangled systems with access to the PMS. We study the probability of distinguishing (and antidistinguishing) quantum measurements sampled from a given set in the single-shot regime. For some scenarios, we provide the analytical expressions of distinguishability (and antidistinguishability) for qubit projective measurements. We show that the distinguishability of any pair of qubit projective measurements in scenario (iii) is always greater than its value in scenario (ii). Interestingly, certain pairs of non-projective qubit measurements achieve optimal distinguishability in scenario (ii) with a non-maximally entangled state. In general, for any set of measurements, distinguishability (and antidistinguishability) in scenario (i) never exceeds that in any other scenario, while it reaches its highest possible value in scenario (iv). We establish that there is no hierarchical relation between scenarios (ii) and (iii). In particular, we introduce different variants of the well-known `trine' qubit measurement to construct pairs (and triples) of qubit quantum measurements such that they are perfectly distinguishable (and antidistinguishable) in scenario (ii) but not in scenario (iii), and vice versa. Additionally, we present qubit measurements that are perfectly distinguishable (and antidistinguishable) in scenario (iv) but not in any other scenarios.

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arXiv2024

Unbounded quantum advantage in communication complexity measured by distinguishability

Communication complexity is a fundamental aspect of information science, concerned with the amount of communication required to solve a problem distributed among multiple parties. The standard quantification of one-way communication complexity relies on the minimal dimension of the communicated systems. In this paper, we measure the communication complexity of a task by the minimal distinguishability required to accomplish it, while leaving the dimension of the communicated systems unconstrained. Distinguishability is defined as the maximum probability of correctly guessing the sender's input from the message, quantifying the message's distinctiveness relative to the sender's input. This measure becomes especially relevant when maintaining the confidentiality of the sender's input is essential. After establishing the generic framework, we focus on three relevant families of communication complexity tasks -- the random access codes, equality problems defined by graphs and the pair-distinguishability tasks. We derive general lower bounds on the minimal classical distinguishability as a function of the success metric of these tasks. We demonstrate that quantum communication outperforms classical communication, presenting explicit protocols and utilizing semi-definite programming methods. In particular, we demonstrate unbounded quantum advantage for random access codes and Hadamard graph-based equality problems. Specifically, we show that the classical-to-quantum ratio of minimal distinguishability required to achieve the same success metric escalates polynomially and exponentially with the complexity of these tasks, reaching arbitrarily large values.

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