56,475 research outputs found

### Comment on "Separability of quantum states and the violation of Bell-type inequalities"

The statement of E.R. Loubenets, Phys. Rev. A 69, 042102 (2004), that
separable states can violate classical probabilistic constraints is based on a
misleading definition of classicality, which is much narrower than Bell's
concept of local hidden variables. In a Bell type setting the notion of
classicality used by Loubenets corresponds to the assumption of perfect
correlations if the same observable is measured on both sides. While it is
obvious that most separable states do not satisfy this assumption, this does
not constitute "non-classical" behaviour in any usual sense of the word.Comment: 1 page, accepted by Phys. Rev.

### Bell's theorem as a signature of nonlocality: a classical counterexample

For a system composed of two particles Bell's theorem asserts that averages
of physical quantities determined from local variables must conform to a family
of inequalities. In this work we show that a classical model containing a local
probabilistic interaction in the measurement process can lead to a violation of
the Bell inequalities. We first introduce two-particle phase-space
distributions in classical mechanics constructed to be the analogs of quantum
mechanical angular momentum eigenstates. These distributions are then employed
in four schemes characterized by different types of detectors measuring the
angular momenta. When the model includes an interaction between the detector
and the measured particle leading to ensemble dependencies, the relevant Bell
inequalities are violated if total angular momentum is required to be
conserved. The violation is explained by identifying assumptions made in the
derivation of Bell's theorem that are not fulfilled by the model. These
assumptions will be argued to be too restrictive to see in the violation of the
Bell inequalities a faithful signature of nonlocality.Comment: Extended manuscript. Significant change

### Not throwing out the baby with the bathwater: Bell's condition of local causality mathematically 'sharp and clean'

The starting point of the present paper is Bell's notion of local causality
and his own sharpening of it so as to provide for mathematical formalisation.
Starting with Norsen's (2007, 2009) analysis of this formalisation, it is
subjected to a critique that reveals two crucial aspects that have so far not
been properly taken into account. These are (i) the correct understanding of
the notions of sufficiency, completeness and redundancy involved; and (ii) the
fact that the apparatus settings and measurement outcomes have very different
theoretical roles in the candidate theories under study. Both aspects are not
adequately incorporated in the standard formalisation, and we will therefore do
so. The upshot of our analysis is a more detailed, sharp and clean mathematical
expression of the condition of local causality. A preliminary analysis of the
repercussions of our proposal shows that it is able to locate exactly where and
how the notions of locality and causality are involved in formalising Bell's
condition of local causality.Comment: 14 pages. To be published in PSE volume "Explanation, Prediction, and
Confirmation", edited by Dieks, et a

### Monogamy of Bell's inequality violations in non-signaling theories

We derive monogamy relations (tradeoffs) between strengths of violations of
Bell's inequalities from the non-signaling condition. Our result applies to
general Bell inequalities with an arbitrary large number of partners, outcomes
and measurement settings. The method is simple, efficient and does not require
linear programming. The results are used to derive optimal fidelity for
asymmetric cloning in nonsignaling theories.Comment: 4 pages, 2 figures, published versio

### Quantum interference and non-locality of independent photons from disparate sources

We quantitatively investigate the non-classicality and non-locality of a
whole new class of mixed disparate quantum and semiquantum photon sources at
the quantum-classical boundary. The latter include photon added thermal and
photon added coherent sources, experimentally investigated recently by Zavatta
et al. [Phys. Rev. Lett. 103, 140406 (2009)]. The key quantity in our
investigations is the visibility of the corresponding photon-photon correlation
function. We present explicit results on the violations of the Cauchy-Schwarz
inequality - which is a measure of nonclassicality - as well as of Bell-type
inequalities.Comment: 9 pages, 3 figure

### Loophole-free test of quantum non-locality using high-efficiency homodyne detectors

We provide a detailed analysis of the recently proposed setup for a
loophole-free test of Bell inequality using conditionally generated
non-Gaussian states of light and balanced homodyning. In the proposed scheme, a
two-mode squeezed vacuum state is de-gaussified by subtracting a single photon
from each mode with the use of an unbalanced beam splitter and a standard
low-efficiency single-photon detector. We thoroughly discuss the dependence of
the achievable Bell violation on the various relevant experimental parameters
such as the detector efficiencies, the electronic noise and the mixedness of
the initial Gaussian state. We also consider several alternative schemes
involving squeezed states, linear optical elements, conditional photon
subtraction and homodyne detection.Comment: 13 pages, 14 figures, RevTeX

### Class of bipartite quantum states satisfying the original Bell inequality

In a general setting, we introduce a new bipartite state property sufficient
for the validity of the perfect correlation form of the original Bell
inequality for any three bounded quantum observables. A bipartite quantum state
with this property does not necessarily exhibit perfect correlations. The class
of bipartite states specified by this property includes both separable and
nonseparable states. We prove analytically that, for any dimension d>2, every
Werner state, separable or nonseparable, belongs to this class.Comment: 6 pages, v.2: one reference added, the statement on Werner states
essentially extended; v.3: details of proofs inserte

### On the dimension of H-strata in quantum matrices

We study the topology of the prime spectrum of an algebra supporting a
rational torus action. More precisely, we study inclusions between prime ideals
that are torus-invariant using the $H$-stratification theory of Goodearl and
Letzter on one hand and the theory of deleting derivations of Cauchon on the
other. We apply the results obtained to the algebra of $m \times n$ generic
quantum matrices to show that the dimensions of the $H$-strata described by
Goodearl and Letzter are bounded above by the minimum of $m$ and $n$, and that
moreover all the values between 0 and this bound are achieved.Comment: New introduction; results improve

### Maximal violation of Bell inequality for any given two-qubit pure state

In the case of bipartite two qubits systems, we derive the analytical
expression of bound of Bell operator for any given pure state. Our result not
only manifest some properties of Bell inequality, for example which may be
violated by any pure entangled state and only be maximally violated for a
maximally entangled state, but also give the explicit values of maximal
violation for any pure state. Finally we point out that for two qubits systems
there is no mixed state which can produce maximal violation of Bell inequality.Comment: 3 pages, 1 figure

### Amplitude control of quantum interference

Usually, the oscillations of interference effects are controlled by relative
phases. We show that varying the amplitudes of quantum waves, for instance by
changing the reflectivity of beam splitters, can also lead to quantum
oscillations and even to Bell violations of local realism. We first study
theoretically a generalization of the Hong-Ou-Mandel experiment to arbitrary
source numbers and beam splitter transmittivity. We then consider a Bell type
experiment with two independent sources, and find strong violations of local
realism for arbitrarily large source number $N$; for small $N$, one operator
measures essentially the relative phase of the sources and the other their
intensities. Since, experimentally, one can measure the parity of the number of
atoms in an optical lattice more easily than the number itself, we assume that
the detectors measure parity.Comment: 4 pages; 4 figure

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