12 research outputs found
A complementary relation between classical bits and randomness in local part in simulating singlet state
Recently Leggett's proposal of non-local model generates new interest in
simulating the statistics of singlet state. Singlet state statistics can be
simulated by 1 bit of classical communication without using any further
nonlocal correlation. But, interestingly, singlet state statistics can also be
simulated with no classical cost if a non-local box is used. In the first case,
the output is completely unbiased whereas in second case outputs are completely
random. We suggest a new (possibly) signaling correlation resource which
successfully simulates singlet statistics and this result suggests a new
complementary relation between required classical bits and randomness in local
output when the classical communication is limited by 1 cbit. This result
reproduces the above two models of simulation as extreme cases. This also
explains why Leggett's non-local model and the model presented by Branciard
et.al. should fail to reproduce the statistics of a singlet.Comment: v3: Typos corrected, few changed notations, some extensions to
earlier write-u
Degree of Complementarity Determines the Nonlocality in Quantum Mechanics
Complementarity principle is one of the central concepts in quantum mechanics
which restricts joint measurement for certain observables. Of course, later
development shows that joint measurement could be possible for such observables
with the introduction of a certain degree of unsharpness or fuzziness in the
measurement. In this paper, we show that the optimal degree of unsharpness,
which guarantees the joint measurement of all possible pairs of dichotomic
observables, determines the degree of nonlocality in quantum mechanics as well
as in more general no-signaling theories.Comment: Close to published versio
Local simulation of singlet statistics for restricted set of measurement
The essence of Bell's theorem is that, in general, quantum statistics cannot
be reproduced by local hidden variable (LHV) model. This impossibility is
strongly manifested while analyzing the singlet state statistics for Bell-CHSH
violations. In this work, we provide various subsets of two outcome POVMs for
which a local hidden variable model can be constructed for singlet state.Comment: 2 column, 5 pages, 4 figures, new references, abstract modified,
accepted in JP
Optimal free-will on one side in reproducing the singlet correlation
Bell's theorem teaches us that there are quantum correlations that can not be
simulated by just shared randomness (Local Hidden variable). There are some
recent results which simulate singlet correlation by using either 1 cbit or a
binary (no-signaling) correlation which violate Bell's inequality maximally.
But there is one more possible way to simulate quantum correlation by relaxing
the condition of independency of measurement on shared randomness. Recently,
MJW Hall showed that the statistics of singlet state can be generated by
sacrificing measurement independence where underlying distribution of hidden
variables depend on measurement direction of both parties [Phys. Rev. Lett.105
250404 (2010)]. He also proved that for any model of singlet correlation, 86%
measurement independence is optimal. In this paper, we show that 59%
measurement independence is optimal for simulating singlet correlation when the
underlying distribution of hidden variables depend only on measurements of one
party. We also show that a distribution corresponding to this optimal lack of
free will, already exists in literature which first appeared in the context of
detection efficiency loophole.Comment: 7 pages (single column), accepted in J. Phys. A: Math. Theo
Classical communication and non-classical fidelity of quantum teleportation
In quantum teleportation, the role of entanglement has been much discussed.
It is known that entanglement is necessary for achieving non-classical
teleportation fidelity. Here we focus on the amount of classical communication
that is necessary to obtain non-classical fidelity in teleportation. We
quantify the amount of classical communication that is sufficient for achieving
non-classical fidelity for two independent 1-bit and single 2-bits noisy
classical channels. It is shown that on average 0.208 bits of classical
communication is sufficient to get non-classical fidelity. We also find the
necessary amount of classical communication in case of isotropic
transformation. Finally we study how the amount of sufficient classical
communication increases with weakening of entanglement used in the
teleportation process.Comment: Accepted in Quantum Info. Proces
Local randomness in Hardy's correlations: Implications from information causality principle
Study of nonlocal correlations in term of Hardy's argument has been quite
popular in quantum mechanics. Recently Hardy's argument of non-locality has
been studied in the context of generalized non-signaling theory as well as
theory respecting information causality. Information causality condition
significantly reduces the success probability for Hardy's argument when
compared to the result based on non-signaling condition. Here motivated by the
fact that maximally entangled state in quantum mechanics does not exhibit
Hardy's non-local correlation, we do a qualitative study of the property of
local randomness of measured observable on each side reproducing Hardy's
non-locality correlation,in the context of information causality condition. On
applying the necessary condition for respecting the principle of information
causality, we find that there are severe restrictions on the local randomness
of measured observable in contrast to results obtained from no-signaling
condition.Still, there are some restrictions imposed by quantum mechanics that
are not obtained from information causality condition.Comment: 6 pages, 2 tables, new references adde