Indranil Chakrabarty

Quantum dissension: Generalizing quantum discord for three-qubit states

Abstract We introduce the notion of quantum dissension for a three-qubit system as a measure of quantum correlations. We use three classically equivalent expressions of three-variable mutual information. Their differences are zero classically but not so in quantum domain. It generalizes the notion of quantum discord to a multipartite system. There can be multiple definitions of the dissension depending on the nature of projective measurements done on the subsystems. As an illustration, we explore the consequences of these multiple definitions and compare them for three-qubit pure and mixed GHZ and W states. We find that unlike discord, dissension can be negative. This is because measurement on a subsystem may enhance the correlations in the rest of the system. Furthermore, when we consider a bipartite split of the system, the dissension reduces to discord. This approach can pave a way to generalize the notion of quantum correlations in the multiparticle setting.

Teleportation via a mixture of a two qubit subsystem of a N-qubit W and GHZ state

AbstractIn this work we study a state which is a random mixture of a two qubit subsystem of a N-qubit W state and GHZ state. We analyze several possibilities like separability criterion (Peres-Horodecki criterion [M. Horodecki, P. Horodecki, R. Horodecki, Phys. Lett. A 223, 1 (1996); A. Peres, Phys. Rev. Lett. 77, 1413 (1996)]), non violation of Bell’s inequality [J.F. Clauser, M.A. Horne, A. Shimony, R.A. Holt, Phys. Rev. Lett. 23, 80 (1969)] (M(ρ)<1) and teleportation fidelity [N. Gisin, Phys. Lett. A 210, 157 (1996); R. Horodecki, P. Horodecki, M. Horodecki, Phys. Lett. A 200, 340 (1995); S. Massar, S. Popescu, Phys. Rev. Lett. 74, 1259 (1995); S. Popescu, Phys. Rev. Lett. 72, 797 (1994); C.H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993)]

SHANNON ENTROPY: AXIOMATIC CHARACTERIZATION AND APPLICATION

(F_{max}>\frac{2}{3})

Retrieving and routing quantum information in a quantum network

for this state. We also obtain a relationship between N (number of qubits) and p (the classical probability of random mixture) for each of these possibilities. Finally we present a detailed analysis of all these possibilities for N=3,4,5 qubit systems. We also report that for N=3 and

Quantum cloning, Bell's inequality and teleportation

p\in(0.75,1]

Hybrid Quantum Cloning Machine

, this entangled state can be used as a teleportation channel without violating Bell’s inequality.

Complementarity between tripartite quantum correlation and bipartite Bell-inequality violation in three-qubit states

We have presented a new axiomatic derivation of Shannon entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function. We have then modified Shannon entropy to take account of observational uncertainty.The modified entropy reduces, in the limiting case, to the form of Shannon differential entropy. As an application, we have derived the expression for classical entropy of statistical mechanics from the quantized form of the entropy.

BOLTZMANN–SHANNON ENTROPY: GENERALIZATION AND APPLICATION

In extant quantum secret sharing protocols, once the secret is shared in a quantum network (qnet) it cannot be retrieved, even if the dealer wishes that his/her secret no longer be available in the network. For instance, if the dealer is part of the two qnets, say

Revisiting Impossible Quantum Operations Using Principles of No-Signaling and Nonincrease of Entanglement Under LOCC

{\mathcal {Q}}_1