Ramij Rahaman

Quantum secret sharing based on local distinguishability

In this paper we analyze the (im)possibility of the exact distinguishability of orthogonal multipartite entangled states under {\em restricted local operation and classical communication}. Based on this local distinguishability analysis we propose a new scheme for quantum secret sharing (QSS). Our QSS scheme is quite general and cost efficient compared to other schemes. In our scheme no joint quantum operation is needed to reconstruct the secret. We also present an interesting

Complete proof of Gisin's theorem for three qubits

(2,n)

Multisetting Greenberger-Horne-Zeilinger theorem

-threshold QSS scheme, where any two cooperating players, one from each of two disjoint groups of players, can always reconstruct the secret. This QSS scheme is quite uncommon, as most

Local cloning of multipartite entangled states

(k,n)

Local randomness in Hardy's correlations: implications from the information causality principle

-threshold schemes have the restriction

Berry phase and fidelity susceptibility of the three-qubit Lipkin–Meshkov–Glick ground state

k\geq\lceil\frac{n}{2}\rceil

Comment on “Local Copying of d×d-dimensional Partially Entangled Pure States”

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Device- and semi–device-independent random numbers based on noninequality paradox

Gisins theorem assures that for any pure bipartite entangled state, there is violation of the inequality of Bell and of Clauser, Horne, Shimony, and Holt, revealing its contradiction with local realistic model. Whether a 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 Hardys nonlocality argument.

Quantum Cournot equilibrium for the Hotelling?Smithies model of product choice

We present a generalized Greenberger-Horne-Zeilinger (GHZ) theorem, which involves more than two local measurement settings for some parties, and cannot be reduced to one with less settings. Our results hold for an odd number of parties. We use a set of observables, which are incompatible but share a common eigenstate, here a GHZ state. Such observables are called concurrent. The idea is illustrated with an example of a three-qutrit system and then generalized to systems of higher dimensions, and more parties. The GHZ paradoxes can lead to, e.g., secret sharing protocols.

Local cloning of CAT states

No cloning theorem is a very fundamental issue in quantum mechanics. But the issue is much more involved if we consider quantum state shared among two or more than two parties and allow only local operation and classical communication. In the context of the fact that no known bipartite entangled state can be cloned by local operation and classical communication (LOCC) without assistance of extra entangled state, the cloning of unknown orthogonal entangled state becomes meaningful when there is some supply of free entanglement. With restriction on supply of free entanglement, various cases have been studied. In this paper, we try to give an overview of the subject and results that have been obtained across the literature along with a new result on probabilistic LOCC cloning of four Bell states.