341 research outputs found

### Quantum mechanical probabilities and general probabilistic constraints for Einstein-Podolsky-Rosen-Bohm experiments

Relativistic causality, namely, the impossibility of signaling at
superluminal speeds, restricts the kinds of correlations which can occur
between different parts of a composite physical system. Here we establish the
basic restrictions which relativistic causality imposes on the joint
probabilities involved in an experiment of the Einstein-Podolsky-Rosen-Bohm
type. Quantum mechanics, on the other hand, places further restrictions beyond
those required by general considerations like causality and consistency. We
illustrate this fact by considering the sum of correlations involved in the
CHSH inequality. Within the general framework of the CHSH inequality, we also
consider the nonlocality theorem derived by Hardy, and discuss the constraints
that relativistic causality, on the one hand, and quantum mechanics, on the
other hand, impose on it. Finally, we derive a simple inequality which can be
used to test quantum mechanics against general probabilistic theories.Comment: LaTeX, 16 pages, no figures; Final version, to be published in Found.
Phys. Letter

### Local hidden-variable models and negative-probability measures

Elaborating on a previous work by Han et al., we give a general,
basis-independent proof of the necessity of negative probability measures in
order for a class of local hidden-variable (LHV) models to violate the
Bell-CHSH inequality. Moreover, we obtain general solutions for LHV-induced
probability measures that reproduce any consistent set of probabilities.Comment: LaTeX file, 10 page

### A simple proof of the converse of Hardy's theorem

In this paper we provide a simple proof of the fact that for a system of two
spin-1/2 particles, and for a choice of observables, there is a unique state
which shows Hardy-type nonlocality. Moreover, an explicit expression for the
probability that an ensemble of particle pairs prepared in such a state
exhibits a Hardy-type nonlocality contradiction is given in terms of two
independent parameters related to the observables involved. Incidentally, a
wrong statement expressed in Mermin's proof of the converse [N.D. Mermin, Am.
J. Phys. 62, 880 (1994)] is pointed out.Comment: LaTeX, 16 pages + 2 eps figure

### Bernoulli and Faulhaber

In a recent work, Zielinski used Faulhaber's formula to explain why the odd
Bernoulli numbers are equal to zero. Here, we assume that the odd Bernoulli
numbers are equal to zero to explain Faulhaber's formula.Comment: 5 pages; accepted in The Fibonacci Quarterl

### Generalization of the Deutsch algorithm using two qudits

Deutsch's algorithm for two qubits (one control qubit plus one auxiliary
qubit) is extended to two $d$-dimensional quantum systems or qudits for the
case in which $d$ is equal to $2^n$, $n=1,2,...$ . This allows one to classify
a certain oracle function by just one query, instead of the $2^{n-1}+1$ queries
required by classical means. The given algorithm for two qudits also solves
efficiently the Bernstein-Vazirani problem. Entanglement does not occur at any
step of the computation.Comment: LaTeX file, 7 page

### Chained Clauser-Horne-Shimony-Holt inequality for Hardy's ladder test of nonlocality

Relativistic causality forbids superluminal signaling between distant
observers. By exploiting the non-signaling principle, we derive the exact
relationship between the chained Clauser-Horne-Shimony-Holt sum of correlations
CHSH_K and the success probability P_K associated with Hardy's ladder test of
nonlocality for two qubits and K+1 observables per qubit. Then, by invoking the
Tsirelson bound for CHSH_K, the derived relationship allows us to establish an
upper limit on P_K. In addition, we draw the connection between CHSH_K and the
chained version of the Clauser-Horne (CH) inequality.Comment: 12 pages, 1 figur

### Quantum perfect correlations and Hardy's nonlocality theorem

In this paper the failure of Hardy's nonlocality proof for the class of
maximally entangled states is considered. A detailed analysis shows that the
incompatibility of the Hardy equations for this class of states physically
originates from the fact that the existence of quantum perfect correlations for
the three pairs of two-valued observables (D_11,D_21), (D_11,D_22) and
(D_12,D_21) [in the sense of having with certainty equal (different) readings
for a joint measurement of any one of the pairs (D_11,D_21), (D_11,D_22), and
(D_12,D_21)], necessarily entails perfect correlation for the pair of
observables (D_12,D_22) [in the sense of having with certainty equal
(different) readings for a joint measurement of the pair (D_12,D_22)]. Indeed,
the set of these four perfect correlations is found to satisfy the CHSH
inequality, and then no violations of local realism will arise for the
maximally entangled state as far as the four observables D_ij, i,j = 1,2, are
concerned. The connection between this fact and the impossibility for the
quantum mechanical predictions to give the maximum possible theoretical
violation of the CHSH inequality is pointed out. Moreover, it is generally
proved that the fulfillment of all the Hardy nonlocality conditions necessarily
entails a violation of the resulting CHSH inequality. The largest violation of
this latter inequality is determined.Comment: LaTeX, 24 pages, 1 figur

### Quantum dense coding using three qubits

We consider a situation in which two parties, Alice and Bob, share a 3-qubit
system coupled in an initial maximally entangled, GHZ state. By manipulating
locally two of the qubits, Alice can prepare any one of the eight 3-qubit GHZ
states. Thus the sending of Alice's two qubits to Bob, entails 3 bits of
classical information which can be recovered by Bob by means of a measurement
distinguishing the eight (orthonormal) GHZ states. This contrasts with the
2-qubit case, in which Alice can prepare any of the four Bell states by acting
locally only on one of the qubits.Comment: LaTeX file, 6 page

### Identification of all Hardy-type correlations for two photons or particles with spin 1/2

By using an alternative, equivalent form of the CHSH inequality and making
extensive use of the experimentally testable property of physical locality we
determine the 64 different Bell-type inequalities (each one involving four
joint probabilities) into which Hardy's nonlocality theorem can be cast. This
allows one to identify all the two-qubit correlations which can exhibit
Hardy-type nonlocality.Comment: LaTeX file, 22 pages, no figures. Forthcoming in Found. Phys. Letter

### Comment on "Quantum nonlocality for a three-particle nonmaximally entangled state without inequalities"

In a recent Brief Report, Zheng [S-B. Zheng, PRA 66, 014103 (2002)] has given
a proof of nonlocality without using inequalities for three spin-1/2 particles
in the nonmaximally entangled state |psi> = cos\theta |+++> + i sin\theta |-->.
Here we show that Zheng's proof is not correct. Indeed it is the case that, for
the experiment considered by Zheng, the only state that admits a nonlocality
proof without inequalities is the maximally entangled state.Comment: REVTeX4, 2 page

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