Guruprasad Kar - Academia.edu (original) (raw)

Papers by Guruprasad Kar

Hidden Variable Theory (HVT) is a programme to replace quantum mechanics by a relatively more com... more Hidden Variable Theory (HVT) is a programme to replace quantum mechanics by a relatively more complete theory which is expected to respect our general notion of reality. Bell and Kochen-Specker, for the first time, shattered that dream for some classes of Hidden Variable Theory. Very recently there are some results which claim to have rejected the whole class of HVT where quantum state is not a part of the reality of the physical system. We discuss this development along with some new result regarding a connection between GHJW theorem and nonlocality in all HVT theories. Along with these we also discuss a recently suggested two-party game which, for the first time, presents some operational criteria to separate entangled states from separable states.

The simultaneous verification of wave and particle property in some recently suggested experiment... more The simultaneous verification of wave and particle property in some recently suggested experiments has been reviewed in the light of Hilbert space formalism. In this respect, the recent analysis of biprism experiment [

More than two multipartite orthogonal states cannot always be discriminated (with certainty) if o... more More than two multipartite orthogonal states cannot always be discriminated (with certainty) if only local operations and classical communication (LOCC) are allowed. Using an existing inequality among the measures of entanglement, we show that any three Bell states cannot be discriminated by LOCC. Exploiting the inequality, we calculate the distillable entanglement of a certain class of (4\otimes 4) mixed states

The principle of 'absoluteness of cause' (AC) assumes the cause-effect relation to be observer in... more 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 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.

arXiv: Quantum Physics, Dec 21, 2000

Non existence of Universal NOT gate for arbitrary quantum mechanical states is a fundamental cons... more 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, in both the cases, there is no violation of the two principles if and only if the set of states to be flipped, form a great circle. PACS number(s): 03.67.Mn, 03.67.Hk

Quantum Information and Computation, 2010

Hardy's non-locality theorem for multiple two-level systems is explored in the context of gen... more Hardy's non-locality theorem for multiple two-level systems is explored in the context of generalized non-local theory. We find non-local but non-signaling probabilities satisfying Hardy's argument for two two-level and three two-level systems. Maximum probability of success of Hardy's argument is obtained for three two-level systems in quantum theory as well as in a more generalized theory. Interestingly, the maximum in the generalized non-local theory for both the two two-level systems and three two-level systems turns out to be the same.

Physical Review Letters, 2021

Ensembles of composite quantum states can exhibit nonlocal behaviour in the sense that their opti... more 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.

arXiv: Quantum Physics, 2015

Anonymous Veto (AV) and Dining cryptographers (DC) are two basic primitives for the cryptographic... more 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.

New Journal of Physics, 2021

Quantum mechanics is compatible with scenarios where the relative order between two events can be... more 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.

Physical Review A, 2017

The (im)possibility of local distinguishability of orthogonal multipartite quantum states still r... more The (im)possibility of local distinguishability of orthogonal multipartite quantum states still remains an intriguing question. Beyond C 3 ⊗ 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 C d ⊗ 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 C d ⊗ C d. When testing this condition for the local distinguishability of all sets of four generalized Bell states in C 4 ⊗ 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.

International Journal of Quantum Information, 2016

In 1935, Albert Einstein and two colleagues, Boris Podolsky and Nathan Rosen (EPR) developed a th... more 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 (QM). EPR also postulated the existence of more fundamental theory where physical reality of any system would be completely described 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 QM, as it violates this inequality, is incompatible with any local-realistic theory. Later it has been shown that Bell’s inequality (BI) can be derived from different set of assumptions and it also find applications in useful information theoretic protocols. In this review...

Mathematics, 2016

It has been recently shown that measurement incompatibility and fine grained uncertainty-a partic... more It has been recently shown that measurement incompatibility and fine grained uncertainty-a particular form of preparation uncertainty relation-are deeply related to the nonlocal feature of quantum mechanics. In particular, the degree of measurement incompatibility in a no-signaling theory determines the bound on the violation of Bell-CHSH inequality, and a similar role is also played by (fine-grained) uncertainty along with steering, a subtle non-local phenomenon. We review these connections, along with comments on the difference in the roles played by measurement incompatibility and uncertainty. We also discuss why the toy model of Spekkens (Phys. Rev. A 75, 032110 (2007)) shows no nonlocal feature even though steering is present in this theory.

Anonymous Veto (AV) and Dining cryptographers (DC) are two basic primitives for the cryptographic... more Anonymous Veto (AV) and Dining cryptographers (DC) are two basic primitives for the cryptographic problems that can hide the identity of the sender(s) of classical information. They can be achieved by classical methods and the security is based on computational hardness or requires pairwise shared private keys. In this regard, we present a secure quantum protocol for both DC and AV problems by exploiting the GHZ correlation. 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 problem. Security of both the protocols rely on some novel and fundamental features of the GHZ correlation known as GHZ paradox.

Here we will discuss a winning strategy of impossible colouring pseudo-telepathy game for the set... more Here we will discuss a winning strategy of impossible colouring pseudo-telepathy game for the set of vectors having Kochen-Specker property in four dimension with single use of NLbox. Then we discuss some sufficient condition for the winning strategy of impossible colouring pseudo-telepathy game for general d-dimension with single use of NL-box.

Gisin's theorem assures that for any pure bipartite entangled state, there is violation of Bell-C... more 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.

John Bell taught us that quantum mechanics can not be reproduced by non-contextual and local Hidd... more John Bell taught us that quantum mechanics can not be reproduced by non-contextual and local Hidden variable theory. The impossibility of replacing quantum mechanics by non-contextual Hidden Variable Theory can be turned to a impossible coloring pseudo-telepathy game to be played by two distant players. The game can not be won without communication in the classical world. But if the

Foundations of Physics, 2014

The ontological model framework for an operational theory has generated much interest in recent y... more The ontological model framework for an operational theory has generated much interest in recent years. The debate concerning reality of quantum states has been made more precise in this framework. With the introduction of generalized notion of contextuality in this framework, it has been shown that completely mixed state of a qubit is preparation contextual. Interestingly, this new idea of preparation contextuality has been used to demonstrate nonlocality of some ψ-epistemic models without any use of Bell's inequality. In particular, nonlocality of a non maximally ψ-epistemic model has been demonstrated from preparation contextuality of a maximally mixed qubit and Schrödinger's steerability of the maximally entangled state of two qubits [Phys. Rev. Lett 110, 120401 (2013)]. In this paper, we, show that any mixed state is preparation contextual. We, then, show that nonlocality of any

An algorithm based on quantum phase estimation, which discriminates quantum states nondestructive... more An algorithm based on quantum phase estimation, which discriminates quantum states nondestructively within a set of arbitrary orthogonal states, is described and experimentally verified by a NMR quantum information processor. The procedure is scalable and can be applied to any set of orthogonal states. Scalability is demonstrated through Matlab simulation. * This paper is dedicated to the memory of Jharana Rani Samal.

Hidden Variable Theory (HVT) is a programme to replace quantum mechanics by a relatively more com... more Hidden Variable Theory (HVT) is a programme to replace quantum mechanics by a relatively more complete theory which is expected to respect our general notion of reality. Bell and Kochen-Specker, for the first time, shattered that dream for some classes of Hidden Variable Theory. Very recently there are some results which claim to have rejected the whole class of HVT where quantum state is not a part of the reality of the physical system. We discuss this development along with some new result regarding a connection between GHJW theorem and nonlocality in all HVT theories. Along with these we also discuss a recently suggested two-party game which, for the first time, presents some operational criteria to separate entangled states from separable states.

The simultaneous verification of wave and particle property in some recently suggested experiment... more The simultaneous verification of wave and particle property in some recently suggested experiments has been reviewed in the light of Hilbert space formalism. In this respect, the recent analysis of biprism experiment [

More than two multipartite orthogonal states cannot always be discriminated (with certainty) if o... more More than two multipartite orthogonal states cannot always be discriminated (with certainty) if only local operations and classical communication (LOCC) are allowed. Using an existing inequality among the measures of entanglement, we show that any three Bell states cannot be discriminated by LOCC. Exploiting the inequality, we calculate the distillable entanglement of a certain class of (4\otimes 4) mixed states

The principle of 'absoluteness of cause' (AC) assumes the cause-effect relation to be observer in... more 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 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.

arXiv: Quantum Physics, Dec 21, 2000

Non existence of Universal NOT gate for arbitrary quantum mechanical states is a fundamental cons... more 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, in both the cases, there is no violation of the two principles if and only if the set of states to be flipped, form a great circle. PACS number(s): 03.67.Mn, 03.67.Hk

Quantum Information and Computation, 2010

Hardy's non-locality theorem for multiple two-level systems is explored in the context of gen... more Hardy's non-locality theorem for multiple two-level systems is explored in the context of generalized non-local theory. We find non-local but non-signaling probabilities satisfying Hardy's argument for two two-level and three two-level systems. Maximum probability of success of Hardy's argument is obtained for three two-level systems in quantum theory as well as in a more generalized theory. Interestingly, the maximum in the generalized non-local theory for both the two two-level systems and three two-level systems turns out to be the same.

Physical Review Letters, 2021

Ensembles of composite quantum states can exhibit nonlocal behaviour in the sense that their opti... more 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.

arXiv: Quantum Physics, 2015

Anonymous Veto (AV) and Dining cryptographers (DC) are two basic primitives for the cryptographic... more 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.

New Journal of Physics, 2021

Quantum mechanics is compatible with scenarios where the relative order between two events can be... more 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.

Physical Review A, 2017

The (im)possibility of local distinguishability of orthogonal multipartite quantum states still r... more The (im)possibility of local distinguishability of orthogonal multipartite quantum states still remains an intriguing question. Beyond C 3 ⊗ 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 C d ⊗ 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 C d ⊗ C d. When testing this condition for the local distinguishability of all sets of four generalized Bell states in C 4 ⊗ 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.

International Journal of Quantum Information, 2016

In 1935, Albert Einstein and two colleagues, Boris Podolsky and Nathan Rosen (EPR) developed a th... more 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 (QM). EPR also postulated the existence of more fundamental theory where physical reality of any system would be completely described 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 QM, as it violates this inequality, is incompatible with any local-realistic theory. Later it has been shown that Bell’s inequality (BI) can be derived from different set of assumptions and it also find applications in useful information theoretic protocols. In this review...

Mathematics, 2016

It has been recently shown that measurement incompatibility and fine grained uncertainty-a partic... more It has been recently shown that measurement incompatibility and fine grained uncertainty-a particular form of preparation uncertainty relation-are deeply related to the nonlocal feature of quantum mechanics. In particular, the degree of measurement incompatibility in a no-signaling theory determines the bound on the violation of Bell-CHSH inequality, and a similar role is also played by (fine-grained) uncertainty along with steering, a subtle non-local phenomenon. We review these connections, along with comments on the difference in the roles played by measurement incompatibility and uncertainty. We also discuss why the toy model of Spekkens (Phys. Rev. A 75, 032110 (2007)) shows no nonlocal feature even though steering is present in this theory.

Anonymous Veto (AV) and Dining cryptographers (DC) are two basic primitives for the cryptographic... more Anonymous Veto (AV) and Dining cryptographers (DC) are two basic primitives for the cryptographic problems that can hide the identity of the sender(s) of classical information. They can be achieved by classical methods and the security is based on computational hardness or requires pairwise shared private keys. In this regard, we present a secure quantum protocol for both DC and AV problems by exploiting the GHZ correlation. 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 problem. Security of both the protocols rely on some novel and fundamental features of the GHZ correlation known as GHZ paradox.

Here we will discuss a winning strategy of impossible colouring pseudo-telepathy game for the set... more Here we will discuss a winning strategy of impossible colouring pseudo-telepathy game for the set of vectors having Kochen-Specker property in four dimension with single use of NLbox. Then we discuss some sufficient condition for the winning strategy of impossible colouring pseudo-telepathy game for general d-dimension with single use of NL-box.

Gisin's theorem assures that for any pure bipartite entangled state, there is violation of Bell-C... more 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.

John Bell taught us that quantum mechanics can not be reproduced by non-contextual and local Hidd... more John Bell taught us that quantum mechanics can not be reproduced by non-contextual and local Hidden variable theory. The impossibility of replacing quantum mechanics by non-contextual Hidden Variable Theory can be turned to a impossible coloring pseudo-telepathy game to be played by two distant players. The game can not be won without communication in the classical world. But if the

Foundations of Physics, 2014

The ontological model framework for an operational theory has generated much interest in recent y... more The ontological model framework for an operational theory has generated much interest in recent years. The debate concerning reality of quantum states has been made more precise in this framework. With the introduction of generalized notion of contextuality in this framework, it has been shown that completely mixed state of a qubit is preparation contextual. Interestingly, this new idea of preparation contextuality has been used to demonstrate nonlocality of some ψ-epistemic models without any use of Bell's inequality. In particular, nonlocality of a non maximally ψ-epistemic model has been demonstrated from preparation contextuality of a maximally mixed qubit and Schrödinger's steerability of the maximally entangled state of two qubits [Phys. Rev. Lett 110, 120401 (2013)]. In this paper, we, show that any mixed state is preparation contextual. We, then, show that nonlocality of any

An algorithm based on quantum phase estimation, which discriminates quantum states nondestructive... more An algorithm based on quantum phase estimation, which discriminates quantum states nondestructively within a set of arbitrary orthogonal states, is described and experimentally verified by a NMR quantum information processor. The procedure is scalable and can be applied to any set of orthogonal states. Scalability is demonstrated through Matlab simulation. * This paper is dedicated to the memory of Jharana Rani Samal.