arXiv subjects

Sibasish Ghosh

Publications and source records attributed to Sibasish Ghosh.

At least 91 records · Page 5Linked to original sources

arXiv2010

Chain of Hardy-type local reality constraints for $n$ qubits

Non-locality without inequality is an elegant argument introduced by L. Hardy for two qubit systems, and later generalised to $n$ qubits, to establish contradiction of quantum theory with local realism. Interestingly, for $n=2$ this argument is actually a corollary of Bell-type inequalities, viz. the CH-Hardy inequality involving Bell correlations, but for $n$ greater than 2 it involves $n$-particle probabilities more general than Bell-correlations. In this paper, we first derive a chain of completely new local realistic inequalities involving joint probabilities for $n$ qubits, and then, associated to each such inequality, we provide a new Hardy-type local reality constraint without inequalities. Quantum mechanical maximal violations of the chain of inequalities and of the associated constraints are also studied by deriving appropriate Cirel'son type theorems. These results involving joint probabilities more general than Bell correlations are expected to provide a new systematic tool to investigate entanglement.

quant-ph↗

arXiv2010

Entanglement dynamics under local Lindblad evolution

The phenomenon of entanglement sudden death (ESD) in finite dimensional composite open systems is described here for both bi-partite as well as multipartite cases, where individual subsystems undergo Lindblad type heat bath evolution. ESD is found to be generic for non-zero temperature of the bath. At T=0, one-sided action of the heat bath on pure entangled states of two qubits does not show ESD.

quant-ph↗

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.

quant-ph↗

arXiv2008

Constant rotation of two-qubit equally entangled pure states by local quantum operations

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 entangled states by the same amount, unless it is unity. We have found the optimal sets of equally entangled non-maximally entangled states which can be rotated by the same but arbitrary amount via local unitary operators $W_1 \otimes W_2$, where at most one these two operators can be identity. In particular, when $W_1 = W_2 = (i/\sqrt{2})(σ_x + σ_y)$, we get the local quantum NOT operation. Interestingly, when we apply the one-sided local depolarizing map, we can rotate all equally entangled two-qubit pure states through the same amount. We extend our result for the case of three-qubit maximally entangled state.

quant-ph↗

arXiv2008

Robustness of entangled states that are positive under partial transposition

We study robustness of bipartite entangled states that are positive under partial transposition (PPT). It is shown that almost all PPT entangled states are unconditionally robust, in the sense, both inseparability and positivity are preserved under sufficiently small perturbations in its immediate neighborhood. Such unconditionally robust PPT entangled states lie inside an open PPT entangled ball. We construct examples of such balls whose radii are shown to be finite and can be explicitly calculated. This provides a lower bound on the volume of all PPT entangled states. Multipartite generalization of our constructions are also outlined.

quant-ph↗

arXiv2007

Simulation of two spin-$s$ singlet correlations for all $s$ involving spin measurements

In a recent paper [A. Ahanj et al., quant-ph/0603053], we gave a classical protocol to simulate quantum correlations corresponding to the spin $s$ singlet state for the infinite sequence of spins satisfying $2s+1 = 2^{n}$. In the present paper, we have generalized this result by giving a classical protocol to exactly simulate quantum correlations implied by the spin-$s$ singlet state corresponding to all integer as well as half-integer spin values $s$. The class of measurements we consider here are only those corresponding to spin observables, as has been done in the above-mentioned paper. The required amount of communication is found to be $\lceil {\rm log}_{2} (s + 1) \rceil$ in the worst case scenario, where $\lceil x \rceil$ is the least integer greater than or equal to $x$.

quant-ph↗

arXiv2007

Classical simulation of two spin-$S$ singlet state correlations involving spin measurements

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.

quant-ph↗

arXiv2007

Some families of density matrices for which separability is easily tested

We reconsider density matrices of graphs as defined in [quant-ph/0406165]. The density matrix of a graph is the combinatorial laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the "degree condition") to test separability of density matrices of graphs. The condition is directly related to the PPT-criterion. We prove that the degree condition is necessary for separability and we conjecture that it is also sufficient. We prove special cases of the conjecture involving nearest point graphs and perfect matchings. We observe that the degree condition appears to have value beyond density matrices of graphs. In fact, we point out that circulant density matrices and other matrices constructed from groups always satisfy the condition and indeed are separable with respect to any split. The paper isolates a number of problems and delineates further generalizations.

quant-ph↗

arXiv2006

The disentangling power of unitaries

We define the disentangling power of a unitary operator in a similar way as the entangling power defined by Zanardi, Zalka and Faoro [PRA, 62, 030301]. A general formula is derived and it is shown that both quantities are directly proportional. All results concerning the entangling power can simply be translated into similar statements for the disentangling power. In particular, the disentangling power is maximal for certain permutations derived from orthogonal latin squares. These permutations can therefore be interpreted as those that distort entanglement in a maximal way.

quant-ph↗

arXiv2006

The laplacian of a graph as a density matrix: a basic combinatorial approach to separability of mixed states

We study entanglement properties of mixed density matrices obtained from combinatorial Laplacians. This is done by introducing the notion of the density matrix of a graph. We characterize the graphs with pure density matrices and show that the density matrix of a graph can be always written as a uniform mixture of pure density matrices of graphs. We consider the von Neumann entropy of these matrices and we characterize the graphs for which the minimum and maximum values are attained. We then discuss the problem of separability by pointing out that separability of density matrices of graphs does not always depend on the labelling of the vertices. We consider graphs with a tensor product structure and simple cases for which combinatorial properties are linked to the entanglement of the state. We calculate the concurrence of all graph on four vertices representing entangled states. It turns out that for some of these graphs the value of the concurrence is exactly fractional.

quant-ph↗

arXiv2006

Winning strategies for pseudo-telepathy games using single non-local box

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.

quant-ph↗

arXiv2005

Entangling Power of Permutations

The notion of entangling power of unitary matrices was introduced by Zanardi, Zalka and Faoro [PRA, 62, 030301]. We study the entangling power of permutations, given in terms of a combinatorial formula. We show that the permutation matrices with zero entangling power are, up to local unitaries, the identity and the swap. We construct the permutations with the minimum nonzero entangling power for every dimension. With the use of orthogonal latin squares, we construct the permutations with the maximum entangling power for every dimension. Moreover, we show that the value obtained is maximum over all unitaries of the same dimension, with possible exception for 36. Our result enables us to construct generic examples of 4-qudits maximally entangled states for all dimensions except for 2 and 6. We numerically classify, according to their entangling power, the permutation matrices of dimension 4 and 9, and we give some estimates for higher dimensions.

quant-ph↗

arXiv2004

Estimation of pure qubits on circles

Gisin and Popescu [PRL, 83, 432 (1999)] have shown that more information about their direction can be obtained from a pair of anti-parallel spins compared to a pair of parallel spins, where the first member of the pair (which we call the pointer member) can point equally along any direction in the Bloch sphere. They argued that this was due to the difference in dimensionality spanned by these two alphabets of states. Here we consider similar alphabets, but with the first spin restricted to a fixed small circle of the Bloch sphere. In this case, the dimensionality spanned by the anti-parallel versus parallel alphabet is now equal. However, the anti-parallel alphabet is found to still contain more information in general. We generalize this to having N parallel spins and M anti-parallel spins. When the pointer member is restricted to a small circle these alphabets again span spaces of equal dimension, yet in general, more directional information can be found for sets with smaller |N-M| for any fixed total number of spins. We find that the optimal POVMs for extracting directional information in these cases can always be expressed in terms of the Fourier basis. Our results show that dimensionality alone cannot explain the greater information content in anti-parallel combinations of spins compared to parallel combinations. In addition, we describe an LOCC protocol which extract optimal directional information when the pointer member is restricted to a small circle and a pair of parallel spins are supplied.

quant-ph↗

arXiv2004

Non-full rank bound entangled states satisfying the range criterion

A systematic method for generating bound entangled states in any bipartite system, with ranks ranging from five to full rank, is presented. These states are constructed by mixing separable states with UPB (Unextendible Product Basis) - generated PPT bound entangled states. A subset of this class of PPT bound entangled states, having less than full rank, is shown to satisfy the range criterion [Phys. Lett. A, vol. 232 (1997) 333].

quant-ph↗

arXiv2004

Local cloning of Bell states and distillable entanglement

The necessary and sufficient amount of entanglement required for cloning of orthogonal Bell states by local operation and classical communication is derived, and using this result, we provide here some additional examples of reversible, as well as irreversible states.

quant-ph↗

arXiv2004

Locally Accessible Information and Distillation of Entanglement

A new type of complementary relation is found between locally accessible information and final average entanglement for given ensemble. It is also shown that in some well known distillation protocol, this complementary relation is optimally satisfied. We discuss the interesting trade-off between locally accessible information and distillable entanglement for some states.

quant-ph↗

arXiv2003

Probabilistic cloning and signalling

We give a proof of impossibility of probabilistic exact $1\to 2$ cloning of any three different states of a qubit. The simplicity of the proof is due to the use of a surprising result of remote state preparation [M.-Yong Ye, Y.-Sheng Zhang and G.-Can Guo, quant-ph/0307027 (2003)]. The result is extented to higher dimentional cases for special ensemble of states.

quant-ph↗

arXiv2003

Distinguishability of maximally entangled states

In $2 \otimes 2$, more than 2 orthogonal Bell states with single copy can never be discriminated with certainty if only local operations and classical communication (LOCC) are allowed. More than $d$ orthogonal maximally entangled states in $d \otimed d$, which are in cannonical form, used by Bennett et. al. [Phys. Rev. Lett. 70 (1993) 1895] can never be discriminated with certainty when a single copy of the states is provided. Interestingly we show that all orthogonal maximally entangled states, which are in cannonical form, can be discriminated with certainty if and only if two copies of each of the states are provided. The highly nontrivial problem of local discrimination of $d$ or less no. of pairwise orthogonal maximally entangled states in $d \otimes d$ (in single copy case), which are in cannonical form, is also discussed.

quant-ph↗