246 research outputs found
Incompatibility of Observables as State-Independent Bound of Uncertainty Relations
For a pair of observables, they are called "incompatible", if and only if the
commutator between them does not vanish, which represents one of the key
features in quantum mechanics. The question is, how can we characterize the
incompatibility among three or more observables? Here we explore one possible
route towards this goal through Heisenberg's uncertainty relations, which
impose fundamental constraints on the measurement precisions for incompatible
observables. Specifically, we quantify the incompatibility by the optimal
state-independent bounds of additive variance-based uncertainty relations. In
this way, the degree of incompatibility becomes an intrinsic property among the
operators, but not on the quantum state. To justify our case, we focus on the
incompatibility of spin systems. For an arbitrary setting of two or three
linearly-independent Pauli-spin operators, the incompatibility is analytically
solved, the spins are maximally incompatible if and only if they are orthogonal
to each other. On the other hand, the measure of incompatibility represents a
versatile tool for applications such as testing entanglement of bipartite
states, and EPR-steering criteria.Comment: Comments are welcom
Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems
The effect of quantum steering describes a possible action at a distance via
local measurements. Whereas many attempts on characterizing steerability have
been pursued, answering the question as to whether a given state is steerable
or not remains a difficult task. Here, we investigate the applicability of a
recently proposed method for building steering criteria from generalized
entropic uncertainty relations. This method works for any entropy which satisfy
the properties of (i) (pseudo-) additivity for independent distributions; (ii)
state independent entropic uncertainty relation (EUR); and (iii) joint
convexity of a corresponding relative entropy. Our study extends the former
analysis to Tsallis and R\'enyi entropies on bipartite and tripartite systems.
As examples, we investigate the steerability of the three-qubit GHZ and W
states.Comment: 27 pages, 8 figures. Published version. Title change
Analog of the Clauser-Horne-Shimony-Holt inequality for steering
The Clauser-Horne-Shimony-Holt (CHSH) inequality (and its permutations), are
necessary and sufficient criteria for Bell nonlocality in the simplest
Bell-nonlocality scenario: 2 parties, 2 measurements per party and 2 outcomes
per measurement. Here we derive an inequality for EPR-steering that is an
analogue of the CHSH, in that it is necessary and sufficient in this same
scenario. However, since in the case of steering the device at Bob's site must
be specified (as opposed to the Bell case in which it is a black box), the
scenario we consider is that where Alice performs two (black-box) dichotomic
measurements, and Bob performs two mutually unbiased qubit measurements. We
show that this inequality is strictly weaker than the CHSH, as expected, and
use it to decide whether a recent experiment [Phys. Rev. Lett. 110, 130401
(2013).] involving a single-photon split between two parties has demonstrated
EPR-steering.Comment: Expanded v2, new results, new figure. 9 pages, 2 figure
Steering is an essential feature of non-locality in quantum theory
A physical theory is called non-local when observers can produce
instantaneous effects over distant systems. Non-local theories rely on two
fundamental effects: local uncertainty relations and steering of physical
states at a distance. In quantum mechanics, the former one dominates the other
in a well-known class of non-local games known as XOR games. In particular,
optimal quantum strategies for XOR games are completely determined by the
uncertainty principle alone. This breakthrough result has yielded the
fundamental open question whether optimal quantum strategies are always
restricted by local uncertainty principles, with entanglement-based steering
playing no role. In this work, we provide a negative answer to the question,
showing that both steering and uncertainty relations play a fundamental role in
determining optimal quantum strategies for non-local games. Our theoretical
findings are supported by an experimental implementation with entangled
photons.Comment: 16 pages, 5 figure
Multidimensional quantum entanglement with large-scale integrated optics
The ability to control multidimensional quantum systems is key for the
investigation of fundamental science and for the development of advanced
quantum technologies. Here we demonstrate a multidimensional integrated quantum
photonic platform able to robustly generate, control and analyze
high-dimensional entanglement. We realize a programmable bipartite entangled
system with dimension up to on a large-scale silicon-photonics
quantum circuit. The device integrates more than 550 photonic components on a
single chip, including 16 identical photon-pair sources. We verify the high
precision, generality and controllability of our multidimensional technology,
and further exploit these abilities to demonstrate key quantum applications
experimentally unexplored before, such as quantum randomness expansion and
self-testing on multidimensional states. Our work provides a prominent
experimental platform for the development of multidimensional quantum
technologies.Comment: Science, (2018
Bell nonlocality
Bell's 1964 theorem, which states that the predictions of quantum theory
cannot be accounted for by any local theory, represents one of the most
profound developments in the foundations of physics. In the last two decades,
Bell's theorem has been a central theme of research from a variety of
perspectives, mainly motivated by quantum information science, where the
nonlocality of quantum theory underpins many of the advantages afforded by a
quantum processing of information. The focus of this review is to a large
extent oriented by these later developments. We review the main concepts and
tools which have been developed to describe and study the nonlocality of
quantum theory, and which have raised this topic to the status of a full
sub-field of quantum information science.Comment: 65 pages, 7 figures. Final versio
Environmental effects on nonlocal correlations
Environmental interactions are ubiquitous in practical instances of any
quantum information processing protocol. The interaction results in depletion
of various quantum resources and even complete loss in numerous situations.
Nonlocality, which is one particular quantum resource marking a significant
departure of quantum mechanics from classical mechanics, meets the same fate.
In the present work we study the decay in nonlocality to the extent of the
output state admitting a local hidden state model. Using some fundamental
quantum channels we also demonstrate the complete decay in the resources in the
purview of the Bell-CHSH inequality and a 3-settings steering inequality. We
also obtain bounds on the parameter of the depolarizing map for which it
becomes steerability breaking pertaining to a general class of two qubit
states.Comment: Accepted in Quanta. Accepted versio
Self-testing of binary observables based on commutation
We consider the problem of certifying binary observables based on a Bell
inequality violation alone, a task known as self-testing of measurements. We
introduce a family of commutation-based measures, which encode all the distinct
arrangements of two projective observables on a qubit. These quantities by
construction take into account the usual limitations of self-testing and since
they are "weighted" by the (reduced) state, they automatically deal with
rank-deficient reduced density matrices. We show that these measures can be
estimated from the observed Bell violation in several scenarios and the proofs
rely only on standard linear algebra. The trade-offs turn out to be tight and,
in particular, they give non-trivial statements for arbitrarily small
violations. On the other extreme, observing the maximal violation allows us to
deduce precisely the form of the observables, which immediately leads to a
complete rigidity statement. In particular, we show that for all the
-partite Mermin-Ardehali-Belinskii-Klyshko inequality self-tests the
-partite Greenberger-Horne-Zeilinger state and maximally incompatible qubit
measurements on every party. Our results imply that any pair of projective
observables on a qubit can be certified in a truly robust manner. Finally, we
show that commutation-based measures give a convenient way of expressing
relations among more than two observables.Comment: 5 + 4 pages. v2: published version; v3: formatting errors fixe
- …