53 research outputs found
Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality
We investigate the relation between the incompatibility of quantum
measurements and quantum nonlocality. We show that any set of measurements that
is not jointly measurable (i.e. incompatible) can be used for demonstrating EPR
steering, a form of quantum nonlocality. This implies that EPR steering and
(non) joint measurability can be viewed as equivalent. Moreover, we discuss the
connection between Bell nonlocality and joint measurability, and give evidence
that both notions are inequivalent. Specifically, we exhibit a set of
incompatible quantum measurements and show that it does not violate a large
class of Bell inequalities. This suggest the existence of incompatible quantum
measurements which are Bell local, similarly to certain entangled states which
admit a local hidden variable model.Comment: 6 pages, 1 figure, 2 tables, title slightly changed, one reference
adde
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
Transformations between arbitrary (quantum) objects and the emergence of indefinite causality
Many fundamental and key objects in quantum mechanics are linear mappings
between particular affine/linear spaces. This structure includes basic quantum
elements such as states, measurements, channels, instruments, non-signalling
channels and channels with memory, and also higher-order operations such as
superchannels, quantum combs, n-time processes, testers, and process matrices
which may not respect a definite causal order. Deducing and characterising
their structural properties in terms of linear and semidefinite constraints is
not only of foundational relevance, but plays an important role in enabling the
numerical optimization over sets of quantum objects and allowing simpler
connections between different concepts and objects. Here, we provide a general
framework to deduce these properties in a direct and easy to use way.
Additionally, while primarily guided by practical quantum mechanical
considerations, we extend our analysis to mappings between \textit{general}
linear/affine spaces and derive their properties, opening the possibility for
analysing sets which are not explicitly forbidden by quantum theory, but are
still not much explored. Together, these results yield versatile and readily
applicable tools for all tasks that require the characterization of linear
transformations, in quantum mechanics and beyond. As an application of our
methods, we discuss the emergence of indefinite causality in higher-order
quantum transformation.Comment: 31 pages, 8 figure
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
The minimal communication cost for simulating entangled qubits
We analyze the amount of classical communication required to reproduce the
statistics of local projective measurements on a general pair of entangled
qubits, (with ). We construct a classical protocol that perfectly simulates local
projective measurements on all entangled qubit pairs by communicating one
classical trit. Additionally, when , approximately , we present a classical protocol that requires only a single bit of
communication. The latter model even allows a perfect classical simulation with
an average communication cost that approaches zero in the limit where the
degree of entanglement approaches zero (). This proves that the
communication cost for simulating weakly entangled qubit pairs is strictly
smaller than for the maximally entangled one.Comment: 6 pages main text, 8 pages appendices, 3 figure
Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies
For minimum-error channel discrimination tasks that involve only unitary
channels, we show that sequential strategies may outperform parallel ones.
Additionally, we show that general strategies that involve indefinite causal
order are also advantageous for this task. However, for the task of
discriminating a uniformly distributed set of unitary channels that forms a
group, we show that parallel strategies are indeed optimal, even when compared
to general strategies. We also show that strategies based on the quantum switch
cannot outperform sequential strategies in the discrimination of unitary
channels. Finally, we derive an ultimate upper bound for the maximal
probability of successfully discriminating any set of unitary channels with any
number of copies, for the most general strategies that are suitable for channel
discrimination. Our bound is tight since it is saturated by sets of unitary
channels forming a group k-design.Comment: This version improves Thm. 5 by presenting a simple "closed formula"
for Eq. (23). 11 + 13 pages, 4 figures. Code available at
https://github.com/mtcq/unitary_channel_discriminatio
Device-independent tests of structures of measurement incompatibility
In contrast with classical physics, in quantum physics some sets of
measurements are incompatible in the sense that they can not be performed
simultaneously. Among other applications, incompatibility allows for
contextuality and Bell nonlocality. This makes of crucial importance developing
tools for certifying whether a set of measurements posses a certain structure
of incompatibility. Here we show that, for quantum or nonsignaling models, if
the measurements employed in a Bell test satisfy a given type of compatibility,
then the amount of violation of some specific Bell inequalities become limited.
Then, we show that correlations arising from local measurements on two-qubit
states violate these limits, which rules out in a device-independent way such
structures of incompatibility. In particular, we prove that quantum
correlations allow for a device-independent demonstration of genuine triplewise
incompatibility. Finally, we translate these results into a
semi-device-independent Einstein-Podolsky-Rosen-steering scenario.Comment: Substantial improvements, several new results added, new author
added. 18 pages, 4 figure
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