arXiv subjects

Guruprasad Kar

Publications and source records attributed to Guruprasad Kar.

At least 19 recordsLinked to original sources

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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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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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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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

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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arXiv2017

Quantum nonlocality does not demand all-out randomness in measurement choice

Nonlocality is the most characteristic feature of quantum mechanics. John Bell, in his seminal 1964 work, proved that local-realism imposes a bound on the correlations among the measurement statistics of distant observers. Surpassing this bound rules out local-realistic description of microscopic phenomena, establishing the presence of nonlocal correlation. To manifest nonlocality, it requires, in the simplest scenario, two measurements performed randomly by each of two distant observers. In this work, we propose a novel framework where three measurements, two on Alice's side and one on Bob's side, suffice to reveal quantum nonlocality and hence does not require all-out randomness in measurement choice. Our method relies on a very naive operational task in quantum information theory, namely, the minimal error state discrimination. As a practical implication this method constitutes an economical entanglement detection scheme, which uses a less number of entangled states compared to all such existing schemes. Moreover, the method applies to class of generalized probability theories containing quantum theory as a special example.

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arXiv2017

Necessary Condition for Local Distinguishability of Maximally Entangled States: Beyond Orthogonality Preservation

The (im)possibility of local distinguishability of orthogonal multipartite quantum states still remains an intriguing question. Beyond $\mathbb{C}^{3}\otimes\mathbb{C}^{3}$, the problem remains unsolved even for maximally entangled states (MES). So far, the only known condition for the local distinguishability of states is the well-known orthogonality preservation (OP). Using an upper bound on the locally accessible information for bipartite states, we derive a very simple necessary condition for any set of pairwise orthogonal MES in $\mathbb{C}^{d}\otimes \mathbb{C}^{d}$ to be perfectly locally distinguishable. This condition is seen to be stronger than the OP condition. This is particularly so for any set of $d$ number of pairwise orthogonal MES in $\mathbb{C}^{d}\otimes \mathbb{C}^{d}$. When testing this condition for the local distinguishability of all sets of four generalized Bell states in $\mathbb{C}^{4}\otimes \mathbb{C}^{4}$, we find that it is not only necessary but also sufficient to determine their local distinguishability. This demonstrates that the aforementioned upper-bound may play a significant role in the general scenario of local distinguishability of bipartite states.

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arXiv2015

GHZ correlation provides secure Anonymous Veto Protocol

Anonymous Veto (AV) and Dining cryptographers (DC) are two basic primitives for the cryptographic problems where the main aim is to hide the identity of the senders of the messages. These can be achieved by classical methods where the security is based either on computational hardness or on shared private keys. In this regard, we present a secure quantum protocol for both DC and AV by exploiting the GHZ correlations. We first solve a generalized version of the DC problem with the help of multiparty GHZ state. This allow us to provide a secure quantum protocol for the AV. Securities for both the protocols rely on some novel and fundamental features of GHZ correlations related to quantum nonlocality.

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arXiv2015

Reciprocal ontological models show indeterminism of the order of quantum theory

The question whether indeterminism in quantum measurement outcomes is fundamental or is there a possibility of constructing a finer theory underlying quantum mechanics that allows no such indeterminism, has been debated for a long time. We show that within the class of ontological models due to Harrigan and Spekkens, those satisfying preparation-measurement reciprocity must allow indeterminism of the order of quantum theory. Our result implies that one can design quantum random number generator, for which it is impossible, even in principle, to construct a reciprocal deterministic model.

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arXiv2014

Several foundational and information theoretic implications of Bell's theorem

In 1935, Albert Einstein and two colleagues, Boris Podolsky and Nathan Rosen (EPR) developed a thought experiment to demonstrate what they felt was a lack of completeness in quantum mechanics. EPR also postulated the existence of more fundamental theory where physical reality of any system would be completely describe by the variables/states of that fundamental theory. This variable is commonly called hidden variable and the theory is called hidden variable theory (HVT). In 1964, John Bell proposed an empirically verifiable criterion to test for the existence of these HVTs. He derived an inequality, which must be satisfied by any theory that fulfill the conditions of locality and reality} He also showed that quantum mechanics, as it violates this inequality, is incompatible with any local-realistic theory. Later it has been shown that Bell's inequality can be derived from different set of assumptions and it also find applications in useful information theoretic protocols. In this review we will discuss various foundational as well as information theoretic implications of Bell's inequality. We will also discuss about some restricted nonlocal feature of quantum nonlocality and elaborate the role of Uncertainty principle and Complementarity principle in explaining this feature.

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arXiv2013

Degree of Complementarity Determines the Nonlocality in Quantum Mechanics

Complementarity principle is one of the central concepts in quantum mechanics which restricts joint measurement for certain observables. Of course, later development shows that joint measurement could be possible for such observables with the introduction of a certain degree of unsharpness or fuzziness in the measurement. In this paper, we show that the optimal degree of unsharpness, which guarantees the joint measurement of all possible pairs of dichotomic observables, determines the degree of nonlocality in quantum mechanics as well as in more general no-signaling theories.

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arXiv2011

LOCC distinguishability of unilaterally transformable quantum states

We consider the question of perfect local distinguishability of mutually orthogonal bipartite quantum states, with the property that every state can be specified by a unitary operator acting on the local Hilbert space of Bob. We show that if the states can be exactly discriminated by one-way LOCC where Alice goes first, then the unitary operators can also be perfectly distinguished by an orthogonal measurement on Bob's Hilbert space. We give examples of sets of N<=d maximally entangled states in $d \otimes d $ for d=4,5,6 that are not perfectly distinguishable by one-way LOCC. Interestingly for d=5,6 our examples consist of four and five states respectively. We conjecture that these states cannot be perfectly discriminated by two-way LOCC.

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arXiv2011

Hardy's non-locality and generalized non-local theory

Hardy's non-locality theorem for multiple two-level systems is explored in the context of generalized nonlocal theory. We find nonlocal but non-signaling probabilities, providing Hardy's nonlocal argument, which are higher than those in Quantum Mechanics. Maximum probability of success of Hardy's argument is obtained for three two-level systems in quantum as well as in a more generalized theory. Interestingly, the maximum in the nonlocal generalized theory for both the cases turns out to be same.

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arXiv2011

A complementary relation between classical bits and randomness in local part in simulating singlet state

Recently Leggett's proposal of non-local model generates new interest in simulating the statistics of singlet state. Singlet state statistics can be simulated by 1 bit of classical communication without using any further nonlocal correlation. But, interestingly, singlet state statistics can also be simulated with no classical cost if a non-local box is used. In the first case, the output is completely unbiased whereas in second case outputs are completely random. We suggest a new (possibly) signaling correlation resource which successfully simulates singlet statistics and this result suggests a new complementary relation between required classical bits and randomness in local output when the classical communication is limited by 1 cbit. This result reproduces the above two models of simulation as extreme cases. This also explains why Leggett's non-local model and the model presented by Branciard et.al. should fail to reproduce the statistics of a singlet.

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arXiv2009

Complete proof of Gisin's theorem for three qubits

Gisin's theorem assures that for any pure bipartite entangled state, there is violation of Bell-CHSH inequality revealing its contradiction with local realistic model. Whether, similar result holds for three-qubit pure entangled states, remained unresolved. We show analytically that all three-qubit pure entangled states violate a Bell-type inequality, derived on the basis of local realism, by exploiting the Hardy's non-locality argument.

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arXiv2008

Causality, Joint measurement and Tsirelson's bound

Tsirelson showed that $2\sqrt{2}$ is the maximum value that CHSH expression can take for quantum-correlations [B. S.Tsirelson, Lett. Math. Phys, 4 (1980) 93]. This bound simply follows from the algebra of observables. Recently by exploiting the physical structure of quantum mechanics like unitarity and linearity, Buhrman and Massar [H. Buhrman and S.Massar, Phys. Rev. A, 72 (2005) 052103] have established that violation of Tsirelson's bound in quantum mechanics will imply signalling. We prove the same with the help of realistic joint measurement in quantum mechanics and a Bell's inequality which has been derived under the assumption of existence of joint measurement and no signalling condition.

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arXiv2007

Local cloning of genuine entangled states of three qubit

We discuss (im)possibility of the exact cloning of orthogonal but genuinely entangled three qubit states aided with entangled ancila under local operation and classical communication. Whereas any two orthogonal GHZ states taken from the canonical GHZ basis, can be cloned with the help of a known GHZ state, surprisingly we find that no two W states can be cloned by using any known three qubit (possibly entangled) state as blank copy.

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arXiv2006

No-Flipping as a consequence of No-Signalling and Non-increase of Entanglement under LOCC

Non existence of Universal NOT gate for arbitrary quantum mechanical states is a fundamental constraint on the allowed operations performed on physical systems. The largest set of states that can be flipped by using a single NOT gate is the set of states lying on a great circle of the Bloch-sphere. In this paper, we show the impossibility of universal exact-flipping operation, first by using the fact that no faster than light communication is possible and then by using the principle of "non-increase of entanglement under LOCC". Interestingly, exact flipping of the states of any great circle does not violate these two principles, as expected.

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