arXiv subjects

Manik Banik

Publications and source records attributed to Manik Banik.

At least 55 records · Page 3Linked to original sources

arXiv2022

Exploring super-additivity of coherent information of noisy quantum channels through Genetic algorithms

Machine learning techniques are increasingly being used in fundamental research to solve various challenging problems. Here we explore one such technique to address an important problem in quantum communication scenario. While transferring quantum information through a noisy quantum channel, the utility of the channel is characterized by its quantum capacity. Quantum channels, however, display an intriguing property called super-additivity of coherent information. This makes the calculation of quantum capacity a hard computational problem involving optimization over an exponentially increasing search space. In this work, we first utilize a neural network ansatz to represent quantum states and then apply an evolutionary optimization scheme to address this problem. We find regions in the three-parameter space of qubit Pauli channels where coherent information exhibits this super-additivity feature. We characterised the quantum codes that achieves high coherent information, finding several non-trivial quantum codes that outperforms the repetition codes for some Pauli channels. For some Pauli channels, these codes displays very high super-additivity of the order of 0.01, much higher than the observed values in other well studied quantum channels. We further compared the learning performance of the Neural Network ansatz with the raw ansatz to find that in the three-shot case, the neural network ansatz outperforms the raw representation in finding quantum codes of high coherent information. We also compared the learning performance of the evolutionary algorithm with a simple Particle Swarm Optimisation scheme and show empirical results indicating comparable performance, suggesting that the Neural Network ansatz coupled with the evolutionary scheme is indeed a promising approach to finding non-trivial quantum codes of high coherent information.

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arXiv2022

Self-testing quantum states via nonmaximal violation in Hardy's test of nonlocality

Self-testing protocols enable certification of quantum devices without demanding full knowledge about their inner workings. A typical approach in designing such protocols is based on observing nonlocal correlations which exhibit maximum violation in a Bell test. We show that in Bell experiment known as Hardy's test of nonlocality not only the maximally nonlocal correlation self-tests a quantum state, rather a non-maximal nonlocal behavior can serve the same purpose. We, in fact, completely characterize all such behaviors leading to self-test of every pure two qubit entangled state except the maximally entangled ones. Apart from originating a novel self-testing protocol, our method provides a powerful tool towards characterizing the complex boundary of the set of quantum correlations.

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arXiv2022

Composition of multipartite quantum systems: perspective from time-like paradigm

Figuring out the physical rationale behind natural selection of quantum theory is one of the most acclaimed quests in quantum foundational research. This pursuit has inspired several axiomatic initiatives to derive mathematical formulation of the theory by identifying general structure of state and effect space of individual systems as well as specifying their composition rules. This generic framework can allow several consistent composition rules for a multipartite system even when state and effect cones of individual subsystems are assumed to be quantum. Nevertheless, for any bipartite system, none of these compositions allows beyond quantum space-like correlations. In this letter we show that such bipartite compositions can admit stronger than quantum correlations in the time-like domain and, hence, indicates pragmatically distinct roles carried out by state and effect cones. We discuss consequences of such correlations in a communication task, which accordingly opens up a possibility of testing the actual composition between elementary quanta.

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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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arXiv2021

Multiparty orthogonal product states with minimal genuine nonlocality

Nonlocality without entanglement and its subsequent generalizations offer deep information-theoretic insights and subsequently find several useful applications. Concept of genuinely nonlocal set of product states emerges as a natural multipartite generalization of this phenomenon. Existence of such sets eventually motivates the problem concerning their entanglement-assisted discrimination. Here, we construct examples of genuinely nonlocal product states for arbitrary number of parties. Strength of genuine nonlocality of these sets can be considered minimal as their perfect discrimination is possible with entangled resources residing in Hilbert spaces having the smallest possible dimensions. Our constructions lead to fully separable measurements that are impossible to implement even if all but one party come together. Furthermore, they also provide the opportunity to compare different multipartite states that otherwise are incomparable under single copy local manipulation.

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arXiv2021

Quantum Advantage for Shared Randomness Generation

Sharing correlated random variables is a resource for a number of information theoretic tasks such as privacy amplification, simultaneous message passing, secret sharing and many more. In this article, we show that to establish such a resource called shared randomness, quantum systems provide an advantage over their classical counterpart. Precisely, we show that appropriate albeit fixed measurements on a shared two-qubit state can generate correlations which cannot be obtained from any possible state on two classical bits. In a resource theoretic set-up, this feature of quantum systems can be interpreted as an advantage in winning a two players co-operative game, which we call the `non-monopolize social subsidy' game. It turns out that the quantum states leading to the desired advantage must possess non-classicality in the form of quantum discord. On the other hand, while distributing such sources of shared randomness between two parties via noisy channels, quantum channels with zero capacity as well as with classical capacity strictly less than unity perform more efficiently than the perfect classical channel. Protocols presented here are noise-robust and hence should be realizable with state-of-the-art quantum devices.

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arXiv2021

From no causal loop to absoluteness of cause: discarding the quantum NOT logic

The principle of `absoluteness of cause' (AC) assumes the cause-effect relation to be observer independent and is a distinct assertion than prohibiting occurrence of any causal loop. Here, we study implication of this novel principle to derive a fundamental no-go result in quantum world. AC principle restrains the `time order' of two spacelike separated events/processes to be a potential cause of another event in their common future, and in turn negates existence of a quantum device that transforms an arbitrary pure state to its orthogonal one. The present {\it no-go} result is quite general as its domain of applicability stretches out from the standard linear quantum theory to any of its generalizations allowing deterministic or stochastic nonlinear evolution. We also analyze different possibilities of violating the AC principle in generalized probability theory framework. A strong form of violation enables instantaneous signaling, whereas a weak form of violation forbids the theory to be locally tomographic. On the other hand, impossibility of an intermediate violation suffices to discard the universal quantum NOT logic.

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arXiv2021

Bell Nonlocality and the Reality of Quantum Wavefunction

Status of quantum wavefunction is one of the most debated issues in quantum foundations -- whether it corresponds directly to the reality or just represents knowledge or information about some aspect of reality. In this letter we propose a {\it $ψ$-ontology} theorem that excludes a class of ontological explanations where quantum wavefunction is treated as mere information. Our result, unlike the acclaimed Pusey-Barrett-Rudolph's theorem, does not presume the absence of holistic ontological properties for product quantum preparations. At the core of our derivation we utilize the seminal no-go result by John S. Bell that rules out any local realistic world view for quantum theory. We show that the observed phenomenon of quantum nonlocality cannot be incorporated in a class of $ψ$-epistemic models. Using the well known Clauser-Horne-Shimony-Holt inequality we obtain a threshold bound on the degree of epistemicity above which the ontological models are not compatible with quantum statistics.

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arXiv2021

Device-independent bounds from Cabello's nonlocality argument

Hardy-type arguments manifest Bell nonlocality in one of the simplest possible ways. Except for demonstrating nonclassical signature of entangled states in question, they can also serve for device-independent self-testing of states, as shown, e.g., in Phys. Rev. Lett. 109, 180401 (2012). Here we develop and broaden these results to an extended version of Hardy's argument, often referred to as Cabello's nonlocality argument. We show that, as in the simpler case of Hardy's nonlocality argument, the maximum quantum value for Cabello's nonlocality is achieved by a pure two-qubit state and projective measurements that are unique up to local isometries. We also examine the properties of a more realistic case when small errors in the ideal constraints are accepted within the probabilities obtained and prove that also in this case the two-qubit state and measurements are sufficient for obtaining the maximum quantum violation of the classical bound.

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arXiv2021

Better transmission with lower capacity: lossy compression over quantum channels

Shannon's channel coding theorem describes the maximum possible rate of reliable information transfer through a classical noisy communication channel. It, together with the source coding theorem, characterizes lossless channel communication in the classical regime. Lossy compression scenarios require the additional description provided by rate-distortion theory, which characterizes the trade-off between compression rate and the distortion of the compressed signal. Even in this context, the capacity characterizes the usefulness of a channel -- a channel with more capacity will always outperform a channel with less capacity. We show that this is no longer true when sending classical information over a quantum channel. In particular, we find a pair of quantum channels where the channel with the lower capacity causes less distortion than the higher capacity channel when both are used at a fixed rate.

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arXiv2021

Mutually Unbiased Balanced Functions & Generalized Random Access Codes

Quantum resources and protocols are known to outperform their classical counterparts in variety of communication and information processing tasks. Random Access Codes (RACs) are one such cryptographically significant family of bipartite communication tasks, wherein, the sender encodes a data set (typically a string of input bits) onto a physical system of bounded dimension and transmits it to the receiver, who then attempts to guess a randomly chosen part of the sender's data set (typically one of the sender's input bits). In this work, we introduce a generalization of this task wherein the receiver, in addition to the individual input bits, aims to retrieve randomly chosen functions of sender's input string. Specifically, we employ sets of mutually unbiased balanced functions (MUBS), such that perfect knowledge of any one of the constituent functions yields no knowledge about the others. We investigate and bound the performance of (i.) classical, (ii.) quantum prepare and measure, and (iii.) entanglement assisted classical communication (EACC) protocols for the resultant generalized RACs (GRACs). Finally, we detail the case of GRACs with three input bits, find maximal success probabilities for classical, quantum and EACC protocols, along with the effect of noisy quantum channels on the performance of quantum protocols. Moreover, with the help of this case study, we reveal several characteristic properties of the GRACs which deviate from the standard RACs.

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arXiv2021

Multi-copy adaptive local discrimination: Strongest possible two-qubit nonlocal bases

Ensembles of composite quantum states can exhibit nonlocal behaviour in the sense that their optimal discrimination may require global operations. Such an ensemble containing N pairwise orthogonal pure states, however, can always be perfectly distinguished under adaptive local scheme if (N-1) copies of the state are available. In this letter, we provide examples of orthonormal bases in two-qubit Hilbert space whose adaptive discrimination require 3 copies of the state. For this composite system we analyze multi-copy adaptive local distinguishability of orthogonal ensembles in full generality which in turn assigns varying nonlocal strength to different such ensembles. We also come up with ensembles whose discrimination under adaptive separable scheme require less number of copies than adaptive local schemes. Our construction finds important application in multipartite secret sharing tasks and indicates towards an intriguing super-additivity phenomenon for locally accessible information.

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arXiv2021

On the state space structure of tripartite quantum systems

State space structure of tripartite quantum systems is analyzed. In particular, it has been shown that the set of states separable across all the three bipartitions [say $\mathcal{B}^{int}(ABC)$] is a strict subset of the set of states having positive partial transposition (PPT) across the three bipartite cuts [say $\mathcal{P}^{int}(ABC)$] for all the tripartite Hilbert spaces $\mathbb{C}_A^{d_1}\otimes\mathbb{C}_B^{d_2}\otimes\mathbb{C}_C^{d_3}$ with $\min\{d_1,d_2,d_3\}\ge2$. The claim is proved by constructing state belonging to the set $\mathcal{P}^{int}(ABC)$ but not belonging to $\mathcal{B}^{int}(ABC)$. For $(\mathbb{C}^{d})^{\otimes3}$ with $d\ge3$, the construction follows from specific type of multipartite unextendible product bases. However, such a construction is not possible for $(\mathbb{C}^{2})^{\otimes3}$ since for any $n$ the bipartite system $\mathbb{C}^2\otimes\mathbb{C}^n$ cannot have any unextendible product bases [Phys. Rev. Lett. 82, 5385 (1999)]. For the $3$-qubit system we, therefore, come up with a different construction.

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arXiv2020

Random-Receiver Quantum Communication

We introduce the task of random-receiver quantum communication, in which a sender transmits a quantum message to a receiver chosen from a list of n spatially separated parties. The choice of receiver is unknown to the sender, but is known by the n parties, who coordinate their actions by exchanging classical messages. In normal conditions, random-receiver quantum communication requires a noiseless quantum communication channel from the sender to each of the n receivers. In contrast, we show that random-receiver quantum communication can take place through entanglement-breaking channels if the order of such channels is controlled by a quantum bit that is accessible through quantum measurements. Notably, this phenomenon cannot be mimicked by allowing free quantum communication between the sender and any subset of k<n parties.

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arXiv2020

Advantage of Quantum Theory Over Non-classical Models of Communication

Quantum correlations provide dramatic advantage over the corresponding classical resources in several communication tasks. However a broad class of probabilistic theories exists that attributes greater success than quantum theory in many of these tasks by allowing supra-quantum correlations in `space-like' and/or `time-like' paradigms. In this letter we propose a communication task involving three spatially separated parties where one party (verifier) aims to verify whether the bit strings possessed by the other two parties (terminals) are equal or not. We call this task {\it authentication with limited communication}, the restrictions on communication being: (i) the terminals cannot communicate with each other, but (ii) each of them can communicate with the verifier through single use of channels with limited capacity. Manifestly, classical resources are not sufficient for perfect success of this task. Moreover, it is also not possible to perform this task with certainty in several non-classical theories although they might possess stronger `space-like' and/or `time-like' correlations. Surprisingly quantum resources can achieve the perfect winning strategy. The proposed task thus stands apart from all previously known communication tasks as it exhibits quantum advantage over other non-classical strategies.

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arXiv2020

Operational Characterization of Multipartite Nonlocal Correlations

Nonlocality, one of the most puzzling features of multipartite quantum correlation, has been identified as a useful resource for device-independent quantum information processing. Motivated by the resource theory of quantum entanglement recently an operational framework have been proposed by Gallego et al. [\href{https://doi.org/10.1103/PhysRevLett.109.070401}{Phys. Rev. Lett. 109, 070401 (2012)}] and Bancal et al. [\href{https://doi.org/10.1103/PhysRevA.88.014102}{Phys. Rev. A 88, 014102 (2013)}] that characterizes the nonlocal resource present in multipartite quantum correlations. While the bipartite no-signaling correlations allows a dichotomous classification -- local vs. nonlocal, in multipartite scenario the authors have shown existence of several types of nonlocality that are inequivalent under the proposed operational framework. In this work we present a finer characterization of multipartite no-signaling correlations based on the same operational framework. We also clarify a statement in Gallego et al.'s work that could be misinterpreted and make the conclusions of that work more precise here.

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arXiv2019

The principle of information symmetry constrains the state-space in any physical theory

Symmetry shares an entwined history with the structure of physical theory. We propose a consequence of symmetry towards the axiomatic derivation of Hilbert space quantum theory. We introduce the notion of information symmetry (IS) and show that it constraints the state-space structure in any physical theory. To this end, we study the minimal error binary state discrimination problem in the framework of generalized probabilistic theories. A theory is said to satisfy IS if the probability of incorrectly identifying each of two randomly prepared states is same for both the states. It is found that this simple principle rules out several classes of theories while being perfectly compatible with quantum theory.

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arXiv2019

Two-Qubit Pure Entanglement as Optimal Social Welfare Resource in Bayesian Game

Entanglement is of paramount importance in quantum information theory. Its supremacy over classical correlations has been demonstrated in numerous information theoretic protocols. Here we study possible adequacy of quantum entanglement in Bayesian game theory, particularly in social welfare solution (SWS), a strategy which the players follow to maximize the sum of their payoffs. Given a multi-partite quantum state as an advice, players can come up with several correlated strategies by performing local measurements on their parts of the quantum state. A quantum strategy is called quantum-SWS if it is advantageous over a classical equilibrium (CE) strategy in the sense that none of the players has to sacrifice their CE-payoff rather some have incentive and at the same time it maximizes the sum of all players' payoffs over all possible quantum advantageous strategies. Quantum state yielding such a quantum-SWS is called a quantum social welfare advice (SWA). We show that any two-qubit pure entangled state, even if it is arbitrarily close to a product state, can serve as quantum-SWA in some Bayesian game. Our result, thus, gives cognizance to the fact that every two-qubit pure entanglement is the best resource for some operational task.

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