arXiv subjects

Manik Banik

Publications and source records attributed to Manik Banik.

At least 37 records · Page 2Linked to original sources

arXiv2024

Scalable & Noise-Robust Communication Advantage of Multipartite Quantum Entanglement

Distributed computing, involving multiple servers collaborating on designated computations, faces a critical challenge in optimizing inter-server communication -- an issue central to the study of communication complexity. Quantum resources offer advantages over classical methods in addressing this challenge. In this work, we investigate a distributed computing scenario with multiple senders and a single receiver, establishing a scalable advantage of multipartite quantum entanglement in mitigating communication complexity. Specifically, we demonstrate that when the receiver and the senders share a multi-qubit Greenberger-Horne-Zeilinger (GHZ) state -- a quintessential form of genuine multipartite entanglement -- certain global functions of the distributed inputs can be computed with only one bit of classical communication from each sender. In contrast, without entanglement, two bits of communication are required from all but one sender. Consequently, quantum entanglement reduces communication overhead by (n-1) bits for n senders, allowing for arbitrary scaling with an increasing number of senders. We also show that the entanglement-based protocol exhibits significant robustness under white noise, thereby establishing the potential for experimental realization of this novel quantum advantage.

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arXiv2024

One-time Pad Encryption Model for Non-local Correlations

We present a cryptographic-inspired framework for modeling Bell nonlocal correlations. Drawing inspiration from the renowned De Broglie-Bohm theory, we conceptualize nonlocal boxes as realistic systems featuring instantaneous signaling at the hidden variable level. By introducing randomness into the distribution of the hidden variable the superluminal signaling model is made compatible with the operational no-signalling condition. As our design mimics the famous symmetric key encryption system called {\it One-time Pad} (OTP), we call this the OTP model for nonlocal boxes. We illustrate the efficacy of this model through various esoteric examples related to the non-classical nature of nonlocal boxes. In particular, the breakdown of communication complexity using nonlocal boxes can be better understood in this framework. Additionally, we delve into the Van Dam protocol, revealing its connection to homomorphic encryption studied in cryptography. Exploring potential avenues for encapsulating quantum-realizable nonlocal correlations within our framework, we highlight that the Information Causality principle imposes additional constraints at the hidden variable level. Present work thus orchestrates the results in classical cryptography to improve our understanding of nonlocal correlations and welcomes further research to this connection.

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arXiv2024

Asymptotic Birkhoff-Violation in Operational Theories: Thermodynamic Implications and Information Processing

In accordance with the entropy principle of thermodynamics, under spontaneous evolutions, physical systems always evolve towards states with equal or greater randomness. But, where does this randomness originate? Renowned Birkhoff-von Neumann theorem, often referred to as Birkhoff theorem, identifies source of this randomness to be the stochastic application of reversible operations on the system under study, thereby ensuring its epistemic origin. Analogue of this theorem is known to fail in the quantum case. Here, we extend this investigation beyond quantum mechanics to a broader class of operational theories described within the framework of general probabilistic theories (GPTs). In this generalized framework, we establish Birkhoff-violation as the prevalent trait; in fact the asymptotic variant of the theorem gets violated. We then demonstrate that Birkhoff-violation in GPTs can lead to consequences that are atypical to quantum theory. For instance, we report manifestation of Birkhoff-violation in a communication task, which otherwise is not observed in quantum world. We also show that, unlike the quantum case, in other operational theories the state transformation criteria can be distinct under mixtures of reversible transformations and doubly stochastic evolutions, leading to different resource theories of purity. Despite these exotic implications, we analyze how to define a coherent notion of entropy in this generalized framework, while upholding alignment with von Neumann's thought experiment.

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arXiv2024

Overcoming Traditional No-Go Theorems: Quantum Advantage in Multiple Access Channels

Extension of point-to-point communication model to the realm of multi-node configurations finds a plethora of applications in internet and telecommunication networks. Here, we establish a novel advantage of quantum communication in a commonly encountered network configuration known as the Multiple Access Channel (MAC). A MAC consists of multiple distant senders aiming to send their respective messages to a common receiver. Unlike the quantum superdense coding protocol, the advantage reported here is realized without invoking entanglement between the senders and the receiver. Notably, such an advantage is unattainable in traditional point-to-point communication involving one sender and one receiver, where the limitations imposed by the Holevo and Frankel Weiner no-go theorems come into play. Within the MAC setup, this distinctive advantage materializes through the receiver's unique ability to simultaneously decode the quantum systems received from multiple senders. Intriguingly, some of our MAC designs draw inspiration from various other constructs in quantum foundations, such as the Pusey-Barrett-Rudolph theorem and the concept of `nonlocality without entanglement', originally explored for entirely different purposes. Beyond its immediate applications in network communication, the presented quantum advantage hints at a profound connection with the concept of `quantum nonlocality without inputs' and holds the potential for semi-device-independent certification of entangled measurements.

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arXiv2024

Identifying the value of a random variable unambiguously: Quantum versus classical approaches

Quantum resources may provide advantage over their classical counterparts. Theoretically, in certain tasks, this advantage can be very high. In this work, we construct such a task based on a game, mediated by Referee and played between Alice and Bob. Referee sends Alice a value of a random variable. At the same time, Referee also sends Bob some partial information regarding that value. Here partial information can be defined in the following way. Bob gets the information of a random set which must contain the value of the variable, that is sent to Alice by the Referee, along with other value(s). Alice is not allowed to know what information is sent to Bob by the Referee. Again, Bob does not know which value of the random variable is sent to Alice. Now, the game can be won if and only if Bob can unambiguously identify the value of the variable, that is sent to Alice, with some nonzero probability, no matter what information Bob receives or which value is sent to Alice. However, to help Bob, Alice sends some limited amount of information to him, based on any strategy which is fixed by Alice and Bob before the game begins. We show that if Alice sends limited amount of classical information then the game cannot be won while the quantum analogue of the `limited amount of classical information' is sufficient for winning the game. Thus, it establishes quantum advantage. We further analyze several variants of the game and provide certain bounds on the success probabilities. Moreover, we establish connections between trine ensemble, mutually unbiased bases, and the encoding-decoding strategies of those variants. We also discuss the role of quantum coherence in the present context.

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arXiv2024

Quantum Nonlocality: Multi-copy Resource Inter-convertibility & Their Asymptotic Inequivalence

Quantum nonlocality, pioneered in Bell's seminal work and subsequently verified through a series of experiments, has drawn substantial attention due to its practical applications in various protocols. Evaluating and comparing the extent of nonlocality within distinct quantum correlations holds significant practical relevance. Within the resource theoretic framework this can be achieved by assessing the inter-conversion rate among different nonlocal correlations under free local operations and shared randomness. In this study we, however, present instances of quantum nonlocal correlations that are incomparable in the strongest sense. Specifically, when starting with an arbitrary many copies of one nonlocal correlation, it becomes impossible to obtain even a single copy of the other correlation, and this incomparability holds in both directions. Remarkably, these incomparable quantum correlations can be obtained even in the simplest Bell scenario, which involves two parties, each having two dichotomic measurements setups. Notably, there exist an uncountable number of such incomparable correlations. Our result challenges the notion of a 'unique gold coin', often referred to as the 'maximally resourceful state', within the framework of the resource theory of quantum nonlocality, which has nontrivial implications in the study of nonlocality distillation.

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arXiv2024

Classical analogue of quantum superdense coding and communication advantage of a single quantum system

We analyze utility of communication channels in absence of any short of quantum or classical correlation shared between the sender and the receiver. To this aim, we propose a class of two-party communication games, and show that the games cannot be won given a noiseless $1$-bit classical channel from the sender to the receiver. Interestingly, the goal can be perfectly achieved if the channel is assisted with classical shared randomness. This resembles an advantage similar to the quantum superdense coding phenomenon where pre-shared entanglement can enhance the communication utility of a perfect quantum communication line. Quite surprisingly, we show that a qubit communication without any assistance of classical shared randomness can achieve the goal, and hence establishes a novel quantum advantage in the simplest communication scenario. In pursuit of a deeper origin of this advantage, we show that an advantageous quantum strategy must invoke quantum interference both at the encoding step by the sender and at the decoding step by the receiver. We also study communication utility of a class of non-classical toy systems described by symmetric polygonal state spaces. We come up with communication tasks that can be achieved neither with $1$-bit of classical communication nor by communicating a polygon system, whereas $1$-qubit communication yields a perfect strategy, establishing quantum advantage over them. To this end, we show that the quantum advantages are robust against imperfect encodings-decodings, making the protocols implementable with presently available quantum technologies.

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arXiv2024

Experimental Verification of Many-Body Entanglement Using Thermodynamic Quantities

The phenomenon of quantum entanglement underlies several important protocols that enable emerging quantum technologies. Entangled states, however, are extremely delicate and often get perturbed by tiny fluctuations in their external environment. Certification of entanglement is therefore immensely crucial for the successful implementation of protocols involving this resource. In this work, we propose a set of entanglement criteria for multi-qubit systems that can be easily verified by measuring certain thermodynamic quantities. In particular, the criteria depend on the difference in optimal global and local works extractable from an isolated quantum system under global and local interactions, respectively. As a proof of principle, we demonstrate the proposed scheme on nuclear spin registers of up to 10 qubits using the Nuclear Magnetic Resonance architecture. We prepare noisy Bell-diagonal state and noisy Greenberger-Horne-Zeilinger class of states in star-topology systems and certify their entanglement through our thermodynamic criteria. Along the same line, we also propose an entanglement certification scheme in many-body systems when only partial or even no knowledge about the state is available.

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arXiv2023

When Mei-Gu Guan's 1960 Postmen Get Empowered with Bell's 1964 Nonlocal Correlations, or, Nonlocal Advantage in Vehicle Routing Problem

Vehicle routing problems, a comprehensive problem category originated from the seminal Chinese Postman Problem (first investigated by Chinese mathematician Mei-Gu Guan), entail strategic and tactical decision making for efficient scheduling and routing of vehicles. While Chinese postman problem is aimed at finding the minimum length cycle for a single postman, the broader challenges encompass scenarios with multiple postmen. Making cost-effective decisions in such cases depends on various factors, including vehicle sizes and types, vehicle usage time, road tax variations across routes, and more. In this work, we delve into a class of such problems wherein Bell nonlocal correlations provide advantages in optimizing the costs for non-communicating postmen, and thus establish a nascent utilization of quantum entanglement in traffic routing problem. Our investigation unveils promising applications for nonlocal correlations within combinatorial optimization and operational research problems, which otherwise have predominantly been explored within the quantum foundation and quantum information theory community.

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arXiv2023

Advantage of Hardy's Nonlocal Correlation in Reverse Zero-Error Channel Coding

Hardy's argument constitutes an elegant proof of quantum nonlocality. In this work, we report an exotic application of Hardy's nonlocal correlations in two-party communication setup. We come up with a task, wherein a positive payoff can be through an $1$ bit of communication from the sender to the receiver if and only if the communication channel is assisted with a no-signaling correlation exhibiting Hardy's nonlocality. This further prompts us to establish a counter-intuitive result in correlation assisted reverse zero-error channel coding scenario, where the aim is to simulate a higher input-output noisy classical channel by a lower input-output noiseless one in assistance with pre-shared correlations. We show that there exist such reverse zero-error channel simulation tasks where non-maximally entangled states are preferable over the assistance with a maximally entangled state, even when the former states carry an arbitrarily small amount of entanglement. Our work thus establishes that within the operational paradigm of local operations and limited classical communication the structure of entangled resources is even more complex to characterize.

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arXiv2023

Randomness-free Test of Non-classicality: a Proof of Concept

Quantum correlations and non-projective measurements underlie a plethora of information-theoretic tasks, otherwise impossible in the classical world. Existing schemes to certify such non-classical resources in a device-independent manner require seed randomness, which is often costly and vulnerable to loopholes, for choosing the local measurements performed on different parts of a multipartite quantum system. In this letter, we propose and experimentally implement a semi-device independent certification technique for both quantum correlations and non-projective measurements without seed randomness. Our test is semi-device independent in the sense that it requires only prior knowledge of the dimensions of the parts. We experimentally show a novel quantum advantage in correlated coin tossing by producing specific correlated coins from pairs of photons entangled in their transverse spatial modes. We establish the advantage by showing that the correlated coin obtained from the entangled photons cannot be obtained from two 2-level classical correlated coins. The quantum advantage requires performing qubit trine positive operator-valued measures (POVMs) on each part of the entangled pair, thus also certifying such POVMs in a semi-device-independent manner. This proof of concept firmly establishes a new cost-effective certification technique for both generating non-classical shared randomness and implementing non-classical measurements, which will be important for future multi-party quantum communications.

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arXiv2023

Distilling Nonlocality in Quantum Correlations

Nonlocality, as established by seminal Bell's theorem, is considered to be the most striking feature of correlations present in space like separated events. Its practical application in device independent protocols, such as secure key distribution, randomness certification, {\it etc.}, demands identification and amplification of such correlations observed in the quantum world. In this Letter we study the prospect of nonlocality distillation, wherein, by applying a natural set of free operations (called wirings) on many copies of weakly nonlocal systems, one aims to generate correlations of higher nonlocal strength. In the simplest Bell scenario, we identify a protocol, namely, logical OR-AND wiring, that can distil nonlocality to significantly high degree starting from arbitrarily weak quantum nonlocal correlations. As it turns out, our protocol has several interesting facets: (i) it demonstrates that set of distillable quantum correlations has non zero measure in the full eight-dimensional correlation space, (ii) it can distil quantum Hardy correlations by preserving its structure, (iii) it shows that (nonlocal) quantum correlations sufficiently close to the local deterministic points can be distilled by a significant amount. Finally, we also demonstrate efficacy of the considered distillation protocol in detecting postquantum correlations.

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arXiv2023

Quantum theory is exclusive: a distributed computing setup

The framework of distributed computing, consisting of several spatially separated input-output servers, has immense importance in distant data manipulation. One of the most challenging parts of this setting is to optimize the use of information transmission lines among distant servers. In this work, we have modeled such a physically motivated distributed computing setup for which quantum communication outperforms its classical counterpart, in terms of a limited usage of noiseless transmission lines. Moreover, a broader class of communication entities, that allow state-effect description more exotic than quantum and are described within the framework of generalized probabilistic theory, also fail to meet the strength of quantum theory. The computational strength of quantum communication has further been justified in terms of a stronger version of this task, namely the delayed-choice distributed computation. The proposed task thus provides a new approach to operationally single out quantum theory in the theory-space and hence promises a novel perspective towards the axiomatic derivation of Hilbert space quantum mechanics.

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arXiv2023

Principle of information causality rationalizes quantum composition

Principle of information causality, proposed as a generalization of no signaling principle, has efficiently been applied to outcast beyond quantum correlations as unphysical. In this letter we show that this principle when utilized properly can provide physical rationale towards structural derivation of multipartite quantum systems. In accordance with no signaling condition state and effect spaces of a composite system can allow different possible mathematical descriptions even when description for the individual systems are assumed to be quantum. While in one extreme, namely the maximal tensor product composition, the state space becomes quite exotic and permits composite states that are not allowed in quantum theory, the other extreme -- minimal tensor product composition -- contains only separable states and the resulting theory allows only Bell local correlation. As we show, none of these compositions does commensurate with information causality, and hence get invalidated to be the bona-fide description of nature. Information causality, therefore, promises information theoretic derivation of self-duality of state and effect cones for composite quantum systems.

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arXiv2022

Certifying beyond quantumness of locally quantum no-signalling theories through quantum input Bell test

Physical theories constrained with local quantum structure and satisfying the no-signalling principle can allow beyond-quantum global states. In a standard Bell experiment, correlations obtained from any such beyond-quantum bipartite state can always be reproduced by quantum states and measurements, suggesting local quantum structure and no-signalling to be the axioms to isolate quantum correlations. In this letter, however, we show that if the Bell experiment is generalized to allow local quantum inputs, then beyond-quantum correlations can be generated by every beyond-quantum state. This gives us a way to certify beyond-quantumness of locally quantum no-signalling theories and in turn suggests requirement of additional information principles along with local quantum structure and no-signalling principle to isolate quantum correlations. More importantly, our work establishes that the additional principle(s) must be sensitive to the quantum signature of local inputs. We also generalize our results to multipartite locally quantum no-signalling theories and further analyze some interesting implications.

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arXiv2022

Indefinite causal order enables perfect quantum communication with zero capacity channels

Quantum mechanics is compatible with scenarios where the relative order between two events can be indefinite. Here we show that two independent instances of a noisy process can behave as a perfect quantum communication channel when used in a coherent superposition of two alternative orders. This phenomenon occurs even if the original process has zero capacity to transmit quantum information. In contrast, perfect quantum communication does not occur when the message is sent directly from the sender to the receiver through a superposition of alternative paths, with an independent noise process acting on each path. The possibility of perfect quantum communication through independent noisy channels highlights a fundamental difference between the superposition of orders in time and the superposition of paths in space.

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arXiv2022

Timelike correlations and quantum tensor product structure

The state space structure for a composite quantum system is postulated among several mathematically consistent possibilities that are compatible with local quantum description. For instance, unentangled Gleason's theorem allows a state space that includes density operators as a proper subset among all possible composite states. However, bipartite correlations obtained in Bell type experiments from this broader state space are in-fact quantum simulable, and hence such spacelike correlations are no good to make distinction among different compositions. In this work we analyze communication utilities of these different composite models and show that they can lead to distinct utilities in a simple communication game involving two players. Our analysis, thus, establishes that beyond quantum composite structure can lead to beyond quantum correlations in timelike scenario and hence welcomes new principles to isolate the quantum correlations from the beyond quantum ones. We also prove a no-go that the classical information carrying capacity of different such compositions cannot be more than the corresponding quantum composite systems.

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arXiv2022

Thermodynamic Signatures of Genuinely Multipartite Entanglement

Theory of bipartite entanglement shares profound similarities with thermodynamics. In this letter we extend this connection to multipartite quantum systems where entanglement appears in different forms with genuine entanglement being the most exotic one. We propose thermodynamic quantities that capture signature of genuineness in multipartite entangled states. Instead of entropy, these quantities are defined in terms of energy -- particularly the difference between global and local extractable works (ergotropies) that can be stored in quantum batteries. Some of these quantities suffice as faithful measures of genuineness and to some extent distinguish different classes of genuinely entangled states. Along with scrutinizing properties of these measures we compare them with the other existing genuine measures, and argue that they can serve the purpose in a better sense. Furthermore, generality of our approach allows to define suitable functions of ergotropies capturing the signature of $k$-nonseparability that characterizes qualitatively different manifestations of entanglement in multipartite systems.

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