The question whether indeterminism in quantum measurement outcomes is fundamental or is there a p... more 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.
Using a single NL-box, a winning strategy is given for the impossible colouring pseudo-telepathy ... more Using a single NL-box, a winning strategy is given for the impossible colouring pseudo-telepathy game for the set of vectors having Kochen-Specker property in four dimension. A sufficient condition to have a winning strategy for the impossible colouring pseudo-telepathy game for general d-dimension, with single use of NL-box, is then described. It is also shown that the magic square pseudo-telepathy game of any size can be won by using just two ebits of entanglement -for quantum strategy, and by a single NL-box -for non-local strategy.
ABSTRACT Entanglement in states of composite quantum systems is a manifestation of non-classical ... more ABSTRACT Entanglement in states of composite quantum systems is a manifestation of non-classical behavior of the systems. Can we quantitatively relate these two aspects, namely, entanglement and non-classicality? Non-classicality is manifested in different ways, among which non-locality is of prime importance. Instead of comparing the amounts of entanglement and non-locality in a state of a composite system, we intend to compare here--in a dual picture--quantum channels which can break entanglement and those which can bring every state to a local one. In the absence of any useful necessary-sufficient condition for identifying a state to be local, we check here whether, upon the channel action, all the states satisfy any local-realistic inequality. We find that if a unital qubit channel, after acting on one of the qubits of a two-qubit maximally entangled state, brings it to a Bell-CHSH inequality non-violating state, then the channel does the similar job for all two-qubit states. Unfortunately such a feature is not universally true in the case of non-unital qubit channels, even though there are exceptions e.g., the amplitude damping channel.
ABSTRACT In this note, we discuss a closed-form necessary and sufficient condition for any two-qu... more ABSTRACT In this note, we discuss a closed-form necessary and sufficient condition for any two-qubit state to show hidden nonlocality w.r.t the Bell-CHSH inequality. This is then used to numerically compute the relative volume of states showing hidden Bell-CHSH non-locality , among all two-qubit states with one-sided reduction maximally mixed.
The purpose of this short note is to utilize work on isotropic lines in [1], on Wigner distributi... more The purpose of this short note is to utilize work on isotropic lines in [1], on Wigner distributions for finite-state systems in [2], estimation of the state of a finite level quantum system based on Weyl operators in the L 2 -space over a finite field in [3] to display maximal abelian subsets of certain unitary bases for the matrix algebra M d of complex square matrices of order d > 3; and then, combine these special forms with constrained elementary measurements to obtain optimal ways to determine a d-level quantum state. This enables us to generalise illustrations and strengthen results related to quantum tomography in [4].
In this paper, we extend Simon's criterion for Gaussian states to the multi-mode Gaussian states ... more In this paper, we extend Simon's criterion for Gaussian states to the multi-mode Gaussian states using the Marchenko-Pastur theorem. We show that the Marchenko-Pastur theorem from random matrix theory as necessary and sufficient condition for separability.
The purpose of this paper is to study the equivalence relation on unitary bases defined by R. F. ... more The purpose of this paper is to study the equivalence relation on unitary bases defined by R. F. Werner [J. Phys. A: Math. Gen. 34 (2001) 7081], relate it to local operations on maximally entangled vectors bases, find an invariant for equivalence classes in terms of certain commuting systems, and, relate it to mutually unbiased bases and Hadamard matrices. Illustrations are given in the context of latin squares and projective representations as well. Applications to quantum tomography are indicated.
ABSTRACT The traditional scheme for realizing open-system quantum dynamics takes the initial stat... more ABSTRACT The traditional scheme for realizing open-system quantum dynamics takes the initial state of the system-bath composite as a simple product. Currently, however, the issue of system-bath initial correlations possibly affecting the reduced dynamics of the system has been attracting considerable interest. The influential work of Shabani and Lidar [PRL {\bf 102}, 100402 (2009)] famously related this issue to quantum discord, a concept which has in recent years occupied the centre-stage of quantum information theory and has led to several fundamental results. They suggested that reduced dynamics is completely positive if and only if the initial system-bath correlations have vanishing quantum discord. Here we show that there is, within the Shabani-Lidar framework, no scope for any distinguished role for quantum discord in respect of complete positivity of reduced dynamics. Since most applications of quantum theory to real systems rests on the traditional scheme, its robustness demonstrated here could be of far-reaching significance.
ABSTRACT We give the generic form of the entangled states of a system of two spin-1 (and two spin... more ABSTRACT We give the generic form of the entangled states of a system of two spin-1 (and two spin-) particles and the appropriate set of spin observables that together exhibit maximum nonlocality under Hardy's nonlocality test. We show the maximum nonlocality to be 0.090 17 just as in the case of two spin- particles. We conjecture that this result holds good for a system of two spin-j particles for all values of j.
We look for local unitary operators $W_1 \otimes W_2$ which would rotate all equally entangled tw... more We look for local unitary operators $W_1 \otimes W_2$ which would rotate all equally entangled two-qubit pure states by the same but arbitrary amount. It is shown that all two-qubit maximally entangled states can be rotated through the same but arbitrary amount by local unitary operators. But there is no local unitary operator which can rotate all equally entangled non-maximally
ABSTRACT In this paper, we study the decoherence and entanglement properties for the two-site Bos... more ABSTRACT In this paper, we study the decoherence and entanglement properties for the two-site Bose–Hubbard model in the presence of a non-linear damping. We apply the techniques of thermo field dynamics and then use Hartree-Fock approximation to solve the corresponding master equation. The expectation values of the approximated field operators appearing in the solution of master equation are computed self-consistently. We solve this master equation for a small time t so that we get the analytical solution, thereby we compute the decoherence and entanglement properties of the solution of the two-mode bosonic system. We have found that for a small initial time t, the entanglement of the system increases but at the same time the system decoheres exponentially.
We give a classical protocol to exactly simulate quantum correlations implied by a spin-s singlet... more We give a classical protocol to exactly simulate quantum correlations implied by a spin-s singlet state for the infinite sequence of spins satisfying (2s + 1) = 2 n , in the worst-case scenario, where n is a positive integer. The class of measurements we consider here are only those corresponding to spin observables. The required amount of communication is found to be log 2 d where d = 2s + 1 is the dimension of the spin-s Hilbert space.
Maximally entangled states-a resource for quantum information processing-can only be shared throu... more Maximally entangled states-a resource for quantum information processing-can only be shared through noiseless quantum channels, whereas in practice channels are noisy. Here we ask: Given a noisy quantum channel, what is the maximum attainable purity (measured by singlet fraction) of shared entanglement for single channel use and local trace preserving operations? We find an exact formula of the maximum singlet fraction attainable for a qubit channel and give an explicit protocol to achieve the optimal value. The protocol distinguishes between unital and nonunital channels and requires no local post-processing. In particular, the optimal singlet fraction is achieved by transmitting part of an appropriate pure entangled state, which is maximally entangled if and only if the channel is unital. A linear function of the optimal singlet fraction is also shown to be an upper bound on the distillable entanglement of the mixed state dual to the channel.
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.
We first consider teleportation of entangled states shared between Claire and Alice to Bob1 and B... more We first consider teleportation of entangled states shared between Claire and Alice to Bob1 and Bob2 when Alice and the two Bobs share a single copy of a GHZ state and where all the four parties are at distant locations. We extend this result to a more general state than GHZ-state and show that still a class of pure entangled states can be teleported, where the entanglement of this class ranges from 0 to e (≤1), depending on the entanglement (defined in the text) of the channel state. We then generalize this situation to the case of teleportation of entangled states shared between Claire1, Claire2, . . . , Claire(N − 1) and Alice to Bob1, Bob2, . . . , BobN when Alice and the N Bobs share a single copy of a GHZ-class state and where again all the 2N parties are at distant locations. Quantum teleportation, proposed by Bennett Brassard, Crepeau, Jozsa, Peres and Wootters (BBCJPW) [1], is a protocol by which the information of an arbitrary state of a quantum mechanical system can be transferred (teleported) exactly from one location (where say, Alice is operating) to a possibly distant location (operated say, by Bob) by using only local operations and classical communication, without sending the system itself (thus, at Bob's location, the exact † Present address: Note that in this way, Alice could make Bob and Claire share an arbitrary entangled state of two qubits, whether pure or mixed. But henceforth we shall consider entanglement teleportation of pure states only.
Quantum Teleportation, the transfer of the state of one quantum system to another without direct ... more Quantum Teleportation, the transfer of the state of one quantum system to another without direct interaction between both systems, is an important way to transmit information encoded in quantum states and to generate quantum correlations (entanglement) between remote quantum systems. So far, for photons only superpositions of two distinguishable states (one "qubit") could be teleported . We here show how to teleport a "qudit", i.e., a superposition of an arbitrary number d of distinguishable states present in the orbital angular momentum of a single photon using d beam splitters and d additional entangled photons. The same entanglement resource might also be employed to collectively teleport the state of d/2 photons at the cost of one additional entangled photon per qubit. This is superior to existing schemes for qubits which require an additional pair of entangled photons per qubit.
The question whether indeterminism in quantum measurement outcomes is fundamental or is there a p... more 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.
Using a single NL-box, a winning strategy is given for the impossible colouring pseudo-telepathy ... more Using a single NL-box, a winning strategy is given for the impossible colouring pseudo-telepathy game for the set of vectors having Kochen-Specker property in four dimension. A sufficient condition to have a winning strategy for the impossible colouring pseudo-telepathy game for general d-dimension, with single use of NL-box, is then described. It is also shown that the magic square pseudo-telepathy game of any size can be won by using just two ebits of entanglement -for quantum strategy, and by a single NL-box -for non-local strategy.
ABSTRACT Entanglement in states of composite quantum systems is a manifestation of non-classical ... more ABSTRACT Entanglement in states of composite quantum systems is a manifestation of non-classical behavior of the systems. Can we quantitatively relate these two aspects, namely, entanglement and non-classicality? Non-classicality is manifested in different ways, among which non-locality is of prime importance. Instead of comparing the amounts of entanglement and non-locality in a state of a composite system, we intend to compare here--in a dual picture--quantum channels which can break entanglement and those which can bring every state to a local one. In the absence of any useful necessary-sufficient condition for identifying a state to be local, we check here whether, upon the channel action, all the states satisfy any local-realistic inequality. We find that if a unital qubit channel, after acting on one of the qubits of a two-qubit maximally entangled state, brings it to a Bell-CHSH inequality non-violating state, then the channel does the similar job for all two-qubit states. Unfortunately such a feature is not universally true in the case of non-unital qubit channels, even though there are exceptions e.g., the amplitude damping channel.
ABSTRACT In this note, we discuss a closed-form necessary and sufficient condition for any two-qu... more ABSTRACT In this note, we discuss a closed-form necessary and sufficient condition for any two-qubit state to show hidden nonlocality w.r.t the Bell-CHSH inequality. This is then used to numerically compute the relative volume of states showing hidden Bell-CHSH non-locality , among all two-qubit states with one-sided reduction maximally mixed.
The purpose of this short note is to utilize work on isotropic lines in [1], on Wigner distributi... more The purpose of this short note is to utilize work on isotropic lines in [1], on Wigner distributions for finite-state systems in [2], estimation of the state of a finite level quantum system based on Weyl operators in the L 2 -space over a finite field in [3] to display maximal abelian subsets of certain unitary bases for the matrix algebra M d of complex square matrices of order d > 3; and then, combine these special forms with constrained elementary measurements to obtain optimal ways to determine a d-level quantum state. This enables us to generalise illustrations and strengthen results related to quantum tomography in [4].
In this paper, we extend Simon's criterion for Gaussian states to the multi-mode Gaussian states ... more In this paper, we extend Simon's criterion for Gaussian states to the multi-mode Gaussian states using the Marchenko-Pastur theorem. We show that the Marchenko-Pastur theorem from random matrix theory as necessary and sufficient condition for separability.
The purpose of this paper is to study the equivalence relation on unitary bases defined by R. F. ... more The purpose of this paper is to study the equivalence relation on unitary bases defined by R. F. Werner [J. Phys. A: Math. Gen. 34 (2001) 7081], relate it to local operations on maximally entangled vectors bases, find an invariant for equivalence classes in terms of certain commuting systems, and, relate it to mutually unbiased bases and Hadamard matrices. Illustrations are given in the context of latin squares and projective representations as well. Applications to quantum tomography are indicated.
ABSTRACT The traditional scheme for realizing open-system quantum dynamics takes the initial stat... more ABSTRACT The traditional scheme for realizing open-system quantum dynamics takes the initial state of the system-bath composite as a simple product. Currently, however, the issue of system-bath initial correlations possibly affecting the reduced dynamics of the system has been attracting considerable interest. The influential work of Shabani and Lidar [PRL {\bf 102}, 100402 (2009)] famously related this issue to quantum discord, a concept which has in recent years occupied the centre-stage of quantum information theory and has led to several fundamental results. They suggested that reduced dynamics is completely positive if and only if the initial system-bath correlations have vanishing quantum discord. Here we show that there is, within the Shabani-Lidar framework, no scope for any distinguished role for quantum discord in respect of complete positivity of reduced dynamics. Since most applications of quantum theory to real systems rests on the traditional scheme, its robustness demonstrated here could be of far-reaching significance.
ABSTRACT We give the generic form of the entangled states of a system of two spin-1 (and two spin... more ABSTRACT We give the generic form of the entangled states of a system of two spin-1 (and two spin-) particles and the appropriate set of spin observables that together exhibit maximum nonlocality under Hardy's nonlocality test. We show the maximum nonlocality to be 0.090 17 just as in the case of two spin- particles. We conjecture that this result holds good for a system of two spin-j particles for all values of j.
We look for local unitary operators $W_1 \otimes W_2$ which would rotate all equally entangled tw... more We look for local unitary operators $W_1 \otimes W_2$ which would rotate all equally entangled two-qubit pure states by the same but arbitrary amount. It is shown that all two-qubit maximally entangled states can be rotated through the same but arbitrary amount by local unitary operators. But there is no local unitary operator which can rotate all equally entangled non-maximally
ABSTRACT In this paper, we study the decoherence and entanglement properties for the two-site Bos... more ABSTRACT In this paper, we study the decoherence and entanglement properties for the two-site Bose–Hubbard model in the presence of a non-linear damping. We apply the techniques of thermo field dynamics and then use Hartree-Fock approximation to solve the corresponding master equation. The expectation values of the approximated field operators appearing in the solution of master equation are computed self-consistently. We solve this master equation for a small time t so that we get the analytical solution, thereby we compute the decoherence and entanglement properties of the solution of the two-mode bosonic system. We have found that for a small initial time t, the entanglement of the system increases but at the same time the system decoheres exponentially.
We give a classical protocol to exactly simulate quantum correlations implied by a spin-s singlet... more We give a classical protocol to exactly simulate quantum correlations implied by a spin-s singlet state for the infinite sequence of spins satisfying (2s + 1) = 2 n , in the worst-case scenario, where n is a positive integer. The class of measurements we consider here are only those corresponding to spin observables. The required amount of communication is found to be log 2 d where d = 2s + 1 is the dimension of the spin-s Hilbert space.
Maximally entangled states-a resource for quantum information processing-can only be shared throu... more Maximally entangled states-a resource for quantum information processing-can only be shared through noiseless quantum channels, whereas in practice channels are noisy. Here we ask: Given a noisy quantum channel, what is the maximum attainable purity (measured by singlet fraction) of shared entanglement for single channel use and local trace preserving operations? We find an exact formula of the maximum singlet fraction attainable for a qubit channel and give an explicit protocol to achieve the optimal value. The protocol distinguishes between unital and nonunital channels and requires no local post-processing. In particular, the optimal singlet fraction is achieved by transmitting part of an appropriate pure entangled state, which is maximally entangled if and only if the channel is unital. A linear function of the optimal singlet fraction is also shown to be an upper bound on the distillable entanglement of the mixed state dual to the channel.
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.
We first consider teleportation of entangled states shared between Claire and Alice to Bob1 and B... more We first consider teleportation of entangled states shared between Claire and Alice to Bob1 and Bob2 when Alice and the two Bobs share a single copy of a GHZ state and where all the four parties are at distant locations. We extend this result to a more general state than GHZ-state and show that still a class of pure entangled states can be teleported, where the entanglement of this class ranges from 0 to e (≤1), depending on the entanglement (defined in the text) of the channel state. We then generalize this situation to the case of teleportation of entangled states shared between Claire1, Claire2, . . . , Claire(N − 1) and Alice to Bob1, Bob2, . . . , BobN when Alice and the N Bobs share a single copy of a GHZ-class state and where again all the 2N parties are at distant locations. Quantum teleportation, proposed by Bennett Brassard, Crepeau, Jozsa, Peres and Wootters (BBCJPW) [1], is a protocol by which the information of an arbitrary state of a quantum mechanical system can be transferred (teleported) exactly from one location (where say, Alice is operating) to a possibly distant location (operated say, by Bob) by using only local operations and classical communication, without sending the system itself (thus, at Bob's location, the exact † Present address: Note that in this way, Alice could make Bob and Claire share an arbitrary entangled state of two qubits, whether pure or mixed. But henceforth we shall consider entanglement teleportation of pure states only.
Quantum Teleportation, the transfer of the state of one quantum system to another without direct ... more Quantum Teleportation, the transfer of the state of one quantum system to another without direct interaction between both systems, is an important way to transmit information encoded in quantum states and to generate quantum correlations (entanglement) between remote quantum systems. So far, for photons only superpositions of two distinguishable states (one "qubit") could be teleported . We here show how to teleport a "qudit", i.e., a superposition of an arbitrary number d of distinguishable states present in the orbital angular momentum of a single photon using d beam splitters and d additional entangled photons. The same entanglement resource might also be employed to collectively teleport the state of d/2 photons at the cost of one additional entangled photon per qubit. This is superior to existing schemes for qubits which require an additional pair of entangled photons per qubit.
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Papers by Sibasish Ghosh