838 research outputs found
Quantum measurement incompatibility does not imply Bell nonlocality
We discuss the connection between the incompatibility of quantum
measurements, as captured by the notion of joint measurability, and the
violation of Bell inequalities. Specifically, we present explicitly a given a
set of non jointly measurable POVMs with the following
property. Considering a bipartite Bell test where Alice uses ,
then for any possible shared entangled state and any set of (possibly
infinitely many) POVMs performed by Bob, the resulting
statistics admits a local model, and can thus never violate any Bell
inequality. This shows that quantum measurement incompatibility does not imply
Bell nonlocality in general.Comment: See also arXiv:1705.10069 for a related work Small changes on the
main text. Some typos were fixe
Sufficient criterion for guaranteeing that a two-qubit state is unsteerable
Quantum steering can be detected via the violation of steering inequalities,
which provide sufficient conditions for the steerability of quantum states.
Here we discuss the converse problem, namely ensuring that a state is
unsteerable, and hence Bell local. We present a simple criterion, applicable to
any two-qubit state, which guarantees that the state admits a local hidden
state model for arbitrary projective measurements. We find new classes of
unsteerable entangled states, which can thus not violate any steering or Bell
inequality. In turn, this leads to sufficient conditions for a state to be only
one-way steerable, and provides the simplest possible example of one-way
steering. Finally, by exploiting the connection between steering and
measurement incompatibility, we give a sufficient criterion for a continuous
set of qubit measurements to be jointly measurable.Comment: 7 page
Incompatible quantum measurements admitting a local hidden variable model
The observation of quantum nonlocality, i.e. quantum correlations violating a
Bell inequality, implies the use of incompatible local quantum measurements.
Here we consider the converse question. That is, can any set of incompatible
measurements be used in order to demonstrate Bell inequality violation? Our
main result is to construct a local hidden variable model for an incompatible
set of qubit measurements. Specifically, we show that if Alice uses this set of
measurements, then for any possible shared entangled state, and any possible
dichotomic measurements performed by Bob, the resulting statistics are local.
This represents significant progress towards proving that measurement
incompatibility does not imply Bell nonlocality in general.Comment: A few small changes, closer to the published versio
Genuine hidden quantum nonlocality
The nonlocality of certain quantum states can be revealed by using local
filters before performing a standard Bell test. This phenomenon, known as
hidden nonlocality, has been so far demonstrated only for a restricted class of
measurements, namely projective measurements. Here we prove the existence of
genuine hidden nonlocality. Specifically, we present a class of two-qubit
entangled states, for which we construct a local model for the most general
local measurements (POVMs), and show that the states violate a Bell inequality
after local filtering. Hence there exist entangled states, the nonlocality of
which can be revealed only by using a sequence of measurements. Finally, we
show that genuine hidden nonlocality can be maximal. There exist entangled
states for which a sequence of measurements can lead to maximal violation of a
Bell inequality, while the statistics of non-sequential measurements is always
local.Comment: 5 pages, no figure
Entanglement without hidden nonlocality
We consider Bell tests in which the distant observers can perform local
filtering before testing a Bell inequality. Notably, in this setup, certain
entangled states admitting a local hidden variable model in the standard Bell
scenario can nevertheless violate a Bell inequality after filtering, displaying
so-called hidden nonlocality. Here we ask whether all entangled states can
violate a Bell inequality after well-chosen local filtering. We answer this
question in the negative by showing that there exist entangled states without
hidden nonlocality. Specifically, we prove that some two-qubit Werner states
still admit a local hidden variable model after any possible local filtering on
a single copy of the state.Comment: 16 pages, 2 figure
Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant
We consider the problem of reproducing the correlations obtained by arbitrary
local projective measurements on the two-qubit Werner state via a local hidden variable (LHV) model, where
denotes the singlet state. We show analytically that these
correlations are local for . In turn, as this problem is closely related to a purely
mathematical one formulated by Grothendieck, our result implies a new bound on
the Grothendieck constant . We also present a
LHV model for reproducing the statistics of arbitrary POVMs on the Werner state
for . The techniques we develop can be adapted to construct
LHV models for other entangled states, as well as bounding other Grothendieck
constants.Comment: 12 pages, typos correcte
Local hidden variable models for entangled quantum states using finite shared randomness
The statistics of local measurements performed on certain entangled states
can be reproduced using a local hidden variable (LHV) model. While all known
models make use of an infinite amount of shared randomness---the physical
relevance of which is questionable---we show that essentially all entangled
states admitting a LHV model can be simulated with finite shared randomness.
Our most economical model simulates noisy two-qubit Werner states using only
3.58 bits of shared randomness. We also discuss the case of POVMs, and the
simulation of nonlocal states with finite shared randomness and finite
communication. Our work represents a first step towards quantifying the cost of
LHV models for entangled quantum states.Comment: 9 pages, 2 figures. One graph changed, one typo correcte
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