536 research outputs found
Symmetry analysis of crystalline spin textures in dipolar spinor condensates
We study periodic crystalline spin textures in spinor condensates with
dipolar interactions via a systematic symmetry analysis of the low-energy
effective theory. By considering symmetry operations which combine real and
spin space operations, we classify symmetry groups consistent with non-trivial
experimental and theoretical constraints. Minimizing the energy within each
symmetry class allows us to explore possible ground states.Comment: 19 pages, 4 figure
Bounds on Quantum Correlations in Bell Inequality Experiments
Bell inequality violation is one of the most widely known manifestations of
entanglement in quantum mechanics; indicating that experiments on physically
separated quantum mechanical systems cannot be given a local realistic
description. However, despite the importance of Bell inequalities, it is not
known in general how to determine whether a given entangled state will violate
a Bell inequality. This is because one can choose to make many different
measurements on a quantum system to test any given Bell inequality and the
optimization over measurements is a high-dimensional variational problem. In
order to better understand this problem we present algorithms that provide, for
a given quantum state, both a lower bound and an upper bound on the maximal
expectation value of a Bell operator. Both bounds apply techniques from convex
optimization and the methodology for creating upper bounds allows them to be
systematically improved. In many cases these bounds determine measurements that
would demonstrate violation of the Bell inequality or provide a bound that
rules out the possibility of a violation. Examples are given to illustrate how
these algorithms can be used to conclude definitively if some quantum states
violate a given Bell inequality.Comment: 13 pages, 1 table, 2 figures. Updated version as published in PR
Better Bell Inequality Violation by Collective Measurements
The standard Bell inequality experiments test for violation of local realism
by repeatedly making local measurements on individual copies of an entangled
quantum state. Here we investigate the possibility of increasing the violation
of a Bell inequality by making collective measurements. We show that
nonlocality of bipartite pure entangled states, quantified by their maximal
violation of the Bell-Clauser-Horne inequality, can always be enhanced by
collective measurements, even without communication between the parties. For
mixed states we also show that collective measurements can increase the
violation of Bell inequalities, although numerical evidence suggests that the
phenomenon is not common as it is for pure states.Comment: 7 pages, 4 figures and 1 table; references update
Bell inequalities for three systems and arbitrarily many measurement outcomes
We present a family of Bell inequalities for three parties and arbitrarily
many outcomes, which can be seen as a natural generalization of the Mermin Bell
inequality. For a small number of outcomes, we verify that our inequalities
define facets of the polytope of local correlations. We investigate the quantum
violations of these inequalities, in particular with respect to the Hilbert
space dimension. We provide strong evidence that the maximal quantum violation
can only be reached using systems with local Hilbert space dimension exceeding
the number of measurement outcomes. This suggests that our inequalities can be
used as multipartite dimension witnesses.Comment: v1 6 pages, 4 tables; v2 Published version with minor typos correcte
Generating nonclassical correlations without fully aligning measurements
We investigate the scenario where spatially separated parties perform
measurements in randomly chosen bases on an N-partite
Greenberger-Horne-Zeilinger state. We show that without any alignment of the
measurements, the observers will obtain correlations that violate a Bell
inequality with a probability that rapidly approaches 1 as N increases and that
this probability is robust against noise. We also prove that restricting these
randomly chosen measurements to a plane perpendicular to a common direction
will always generate correlations that violate some Bell inequality.
Specifically, if each observer chooses their two measurements to be locally
orthogonal, then the N observers will violate one of two Bell inequalities by
an amount that increases exponentially with N. These results are also robust
against noise and perturbations of each observer's reference direction from the
common direction.Comment: v2: Essentially published version (with typos fixed, results updated
in Table 2 and Figure 4 replaced); v1: 16 pages, 5 figures, 2 tables,
comments welcom
Renormalization Group calculations with k|| dependent couplings in a ladder
We calculate the phase diagram of a ladder system, with a Hubbard interaction
and an interchain coupling . We use a Renormalization Group method, in
a one loop expansion, introducing an original method to include
dependence of couplings. We also classify the order parameters corresponding to
ladder instabilities. We obtain different results, depending on whether we
include dependence or not. When we do so, we observe a region with
large antiferromagnetic fluctuations, in the vicinity of small ,
followed by a superconducting region with a simultaneous divergence of the Spin
Density Waves channel. We also investigate the effect of a non local backward
interchain scattering : we observe, on one hand, the suppression of singlet
superconductivity and of Spin Density Waves, and, on the other hand, the
increase of Charge Density Waves and, for some values of , of triplet
superconductivity. Our results eventually show that is an influential
variable in the Renormalization Group flow, for this kind of systems.Comment: 20 pages, 19 figures, accepted in Phys. Rev. B 71 v. 2
Alternative fidelity measure for quantum states
We propose an alternative fidelity measure (namely, a measure of the degree
of similarity) between quantum states and benchmark it against a number of
properties of the standard Uhlmann-Jozsa fidelity. This measure is a simple
function of the linear entropy and the Hilbert-Schmidt inner product between
the given states and is thus, in comparison, not as computationally demanding.
It also features several remarkable properties such as being jointly concave
and satisfying all of "Jozsa's axioms". The trade-off, however, is that it is
supermultiplicative and does not behave monotonically under quantum operations.
In addition, new metrics for the space of density matrices are identified and
the joint concavity of the Uhlmann-Jozsa fidelity for qubit states is
established.Comment: 12 pages, 3 figures. v2 includes minor changes, new references and
new numerical results (Sec. IV
Neutral skyrmion configurations in the low-energy effective theory of spinor condensate ferromagnets
We study the low-energy effective theory of spinor condensate ferromagnets
for the superfluid velocity and magnetization degrees of freedom. This
effective theory describes the competition between spin stiffness and a
long-ranged interaction between skyrmions, topological objects familiar from
the theory of ordinary ferromagnets. We find exact solutions to the non-linear
equations of motion describing neutral configurations of skyrmions and
anti-skyrmions. These analytical solutions provide a simple physical picture
for the origin of crystalline magnetic order in spinor condensate ferromagnets
with dipolar interactions. We also point out the connections to effective
theories for quantum Hall ferromagnets.Comment: 13 pages, 7 figure
A phenomenological model of the superconducting state of the Bechgaard salts
We present a group theoretical analysis of the superconducting state of the
Bechgaard salts, e.g., (TMTSF)_2PF_6 or (TMTSF)_2ClO_6. We show that there are
eight symmetry distinct superconducting states. Of these only the (fully
gapped, even frequency, p-wave, triplet) 'polar state' is consistent with the
full range of the experiments on the Bechgaard salts. The gap of the polar
state is d(k) (psi_uk,0,0), where psi_uk may be any odd parity function that is
translationally invariant.Comment: 4 pages, no figure
Measurement-device-independent entanglement witnesses for all entangled quantum states
The problem of demonstrating entanglement is central to quantum information processing applications. Resorting to standard entanglement witnesses requires one to perfectly trust the implementation of the measurements to be performed on the entangled state, which may be an unjustified assumption. Inspired by the recent work of F. Buscemi [Phys. Rev. Lett. 108, 200401 (2012)], we introduce the concept of measurement-device-independent entanglement witnesses (MDI-EWs), which allow one to demonstrate entanglement of all entangled quantum states with untrusted measurement apparatuses. We show how to systematically obtain such MDI-EWs from standard entanglement witnesses. Our construction leads to MDI-EWs that are loss tolerant and can be implemented with current technology
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