76 research outputs found
Two theorems of Jhon Bell and Communication Complexity
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 players share entangled state (quantum correlation) the game can be won
deterministically using no communication. This again shows that though quantum
correlation can not be used for communication, two parties can not simulate
quantum correlation without classical communication. The motivation of the
article is to present the earlier works on Hidden Variable Theory and recently
developed pseudo-telepathy problem in a simpler way, which may be helpful for
the beginners in this area.Comment: 11 pages, Invited lecture at the workshop on Quantum
Information,computation and Communication (QICC-2005), IIT
Kharagpur,India,February 200
GHZ correlation provides secure Anonymous Veto Protocol
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.Comment: 5 pages, In this version we provide detail security proof of our
quantum protocol
Several foundational and information theoretic implications of Bell's theorem
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. EPR also postulated the existence of more
fundamental theory where physical reality of any system would be completely
describe 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 quantum mechanics, as it violates this inequality, is
incompatible with any local-realistic theory. Later it has been shown that
Bell's inequality can be derived from different set of assumptions and it also
find applications in useful information theoretic protocols. In this review we
will discuss various foundational as well as information theoretic implications
of Bell's inequality. We will also discuss about some restricted nonlocal
feature of quantum nonlocality and elaborate the role of Uncertainty principle
and Complementarity principle in explaining this feature.Comment: 27 pages; This article is a modified version of the tutorial lecture
delivered by G. Kar at IPQI, February 17-28, 2014, Institute of Physics,
Bhubaneswar, Indi
Is an optimal quantum cloner the best choice for local copying in broadcasting entanglement?
The paper is temporarily withdrawn by the authors.Comment: temporarily withdrawn, email: [email protected]
Disentanglement of pure bipartite quantum states by local cloning
We discuss disentanglement of pure bipartite quantum states within the
framework of the schemes developed for entanglement splitting and broadcasting
of entanglement.Comment: 8 pages, Latex, to appear in Phys. Letts.
Probabilistic cloning and signalling
We give a proof of impossibility of probabilistic exact 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.Comment: Replaced with revised version, 3 pages, late
Distinguishability of maximally entangled states
In , 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 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 or
less no. of pairwise orthogonal maximally entangled states in (in
single copy case), which are in cannonical form, is also discussed.Comment: There were some mistakes in the previous versions, which have been
correcte
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 -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.Comment: New game included, title and abstract change, 9 pages, Revtex
Bell's inequality for a single spin 1/2 particle and quantum contextuality
We argue that for a \emph{single particle} Bell's inequality is a consequence
of noncontextuality and is \emph{incompatible} with statistical predictions of
quantum mechanics. Thus noncontextual models can be empirically falsified,
\emph{independent} of locality condition. For this an appropriate entanglement
between \emph{disjoint} Hilbert spaces pertaining to translational and spin
degrees of freedom of a single spin-1/2 particle is invokedComment: Latex, 7 pages, 2 Figs. published version with a note added to the
proo
Necessary Condition for Local Distinguishability of Maximally Entangled States: Beyond Orthogonality Preservation
The (im)possibility of local distinguishability of orthogonal multipartite
quantum states still remains an intriguing question. Beyond
, 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 to be perfectly
locally distinguishable. This condition is seen to be stronger than the OP
condition. This is particularly so for any set of number of pairwise
orthogonal MES in . When testing this
condition for the local distinguishability of all sets of four generalized Bell
states in , 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.Comment: 11 pages. The content is essentially the same as the previous
version, with the language having been simplified a bit. Also, the appendix
has been shortene
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