342 research outputs found
Rotationally invariant proof of Bell's theorem without inequalities
The singlet state of two spin-3/2 particles allows a proof of Bell's theorem
without inequalities with two distinguishing features: any local observable can
be regarded as an Einstein-Podolsky-Rosen element of reality, and the
contradiction with local realism occurs not only for some specific local
observables but for any rotation whereof.Comment: REVTeX4, 3 page
Characterization of Binary Constraint System Games
We consider a class of nonlocal games that are related to binary constraint
systems (BCSs) in a manner similar to the games implicit in the work of Mermin
[N.D. Mermin, "Simple unified form for the major no-hidden-variables theorems,"
Phys. Rev. Lett., 65(27):3373-3376, 1990], but generalized to n binary
variables and m constraints. We show that, whenever there is a perfect
entangled protocol for such a game, there exists a set of binary observables
with commutations and products similar to those exhibited by Mermin. We also
show how to derive upper bounds strictly below 1 for the the maximum entangled
success probability of some BCS games. These results are partial progress
towards a larger project to determine the computational complexity of deciding
whether a given instance of a BCS game admits a perfect entangled strategy or
not.Comment: Revised version corrects an error in the previous version of the
proof of Theorem 1 that arises in the case of POVM measurement
Three-particle entanglement versus three-particle nonlocality
The notions of three-particle entanglement and three-particle nonlocality are
discussed in the light of Svetlichny's inequality [Phys. Rev. D 35, 3066
(1987)]. It is shown that there exist sets of measurements which can be used to
prove three-particle entanglement, but which are nevertheless useless at
proving three-particle nonlocality. In particular, it is shown that the quantum
predictions giving a maximal violation of Mermin's three-particle Bell
inequality [Phys. Rev. Lett. 65, 1838 (1990)] can be reproduced by a hybrid
hidden variables model in which nonlocal correlations are present only between
two of the particles. It should be possible, however, to test the existence of
both three-particle entanglement and three-particle nonlocality for any given
quantum state via Svetlichny's inequality.Comment: REVTeX4, 4 pages, journal versio
Spacetime and Euclidean Geometry
Using only the principle of relativity and Euclidean geometry we show in this
pedagogical article that the square of proper time or length in a
two-dimensional spacetime diagram is proportional to the Euclidean area of the
corresponding causal domain. We use this relation to derive the Minkowski line
element by two geometric proofs of the "spacetime Pythagoras theorem".Comment: 11 pages, 9 figures; for a festschrift honoring Michael P. Ryan; v.2:
References to related work adde
Relational Hidden Variables and Non-Locality
We use a simple relational framework to develop the key notions and results
on hidden variables and non-locality. The extensive literature on these topics
in the foundations of quantum mechanics is couched in terms of probabilistic
models, and properties such as locality and no-signalling are formulated
probabilistically. We show that to a remarkable extent, the main structure of
the theory, through the major No-Go theorems and beyond, survives intact under
the replacement of probability distributions by mere relations.Comment: 42 pages in journal style. To appear in Studia Logic
Greenberger-Horne-Zeilinger-like proof of Bell's theorem involving observers who do not share a reference frame
Vaidman described how a team of three players, each of them isolated in a
remote booth, could use a three-qubit Greenberger-Horne-Zeilinger state to
always win a game which would be impossible to always win without quantum
resources. However, Vaidman's method requires all three players to share a
common reference frame; it does not work if the adversary is allowed to
disorientate one player. Here we show how to always win the game, even if the
players do not share any reference frame. The introduced method uses a 12-qubit
state which is invariant under any transformation
(where , where is a
unitary operation on a single qubit) and requires only single-qubit
measurements. A number of further applications of this 12-qubit state are
described.Comment: REVTeX4, 6 pages, 1 figur
An Operational Interpretation of Negative Probabilities and No-Signalling Models
Negative probabilities have long been discussed in connection with the
foundations of quantum mechanics. We have recently shown that, if signed
measures are allowed on the hidden variables, the class of probability models
which can be captured by local hidden-variable models are exactly the
no-signalling models. However, the question remains of how negative
probabilities are to be interpreted. In this paper, we present an operational
interpretation of negative probabilities as arising from standard probabilities
on signed events. This leads, by virtue of our previous result, to a systematic
scheme for simulating arbitrary no-signalling models.Comment: 13 pages, 2 figure
Bell inequalities as constraints on unmeasurable correlations
The interpretation of the violation of Bell-Clauser-Horne inequalities is
revisited, in relation with the notion of extension of QM predictions to
unmeasurable correlations. Such extensions are compatible with QM predictions
in many cases, in particular for observables with compatibility relations
described by tree graphs. This implies classical representability of any set of
correlations , , , and the equivalence of the
Bell-Clauser-Horne inequalities to a non void intersection between the ranges
of values for the unmeasurable correlation associated to different
choices for B. The same analysis applies to the Hardy model and to the "perfect
correlations" discussed by Greenberger, Horne, Shimony and Zeilinger. In all
the cases, the dependence of an unmeasurable correlation on a set of variables
allowing for a classical representation is the only basis for arguments about
violations of locality and causality.Comment: Some modifications have been done in order to improve clarity of
presentation and comparison with other approache
Bell's theorem without inequalities and without unspeakable information
A proof of Bell's theorem without inequalities is presented in which distant
local setups do not need to be aligned, since the required perfect correlations
are achieved for any local rotation of the local setups.Comment: REVTeX4, 4 pages, 1 figure; for Asher Peres' Festschrift, to be
published in Found. Phy
Entangled qutrits violate local realism stronger than qubits - an analytical proof
In Kaszlikowski [Phys. Rev. Lett. {\bf 85}, 4418 (2000)], it has been shown
numerically that the violation of local realism for two maximally entangled
-dimensional () quantum objects is stronger than for two maximally
entangled qubits and grows with . In this paper we present the analytical
proof of this fact for N=3.Comment: 5 page
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