TY - JOUR

T1 - Single-qubit tests of Bell-like inequalities

AU - De Zela, F.

PY - 2007/10/23

Y1 - 2007/10/23

N2 - This paper discusses some tests of Bell-like inequalities not requiring entangled states. The proposed tests are based on consecutive measurements on a single qubit. Available hidden-variable models for a single qubit [see, e.g., J. S. Bell, Rev. Mod. Phys. 38, 447 (1966)] reproduce the predictions of quantum mechanics and hence violate the Bell-like inequalities addressed in this paper. It is shown how this fact is connected with the state â€œ collapseâ€ and with its random nature. Thus, it becomes possible to test truly realistic and deterministic hidden-variable models. In this way, it can be shown that a hidden-variable model should entail at least one of the following features: (i) nonlocality, (ii) contextuality, or (iii) discontinuous measurement-dependent probability functions. The last two features are put to the test with the experiments proposed in this paper. A hidden-variable model that is noncontextual and deterministic would be at variance with some predictions of quantum mechanics. Furthermore, the proposed tests are more likely to be loophole-free, as compared to former ones.

AB - This paper discusses some tests of Bell-like inequalities not requiring entangled states. The proposed tests are based on consecutive measurements on a single qubit. Available hidden-variable models for a single qubit [see, e.g., J. S. Bell, Rev. Mod. Phys. 38, 447 (1966)] reproduce the predictions of quantum mechanics and hence violate the Bell-like inequalities addressed in this paper. It is shown how this fact is connected with the state â€œ collapseâ€ and with its random nature. Thus, it becomes possible to test truly realistic and deterministic hidden-variable models. In this way, it can be shown that a hidden-variable model should entail at least one of the following features: (i) nonlocality, (ii) contextuality, or (iii) discontinuous measurement-dependent probability functions. The last two features are put to the test with the experiments proposed in this paper. A hidden-variable model that is noncontextual and deterministic would be at variance with some predictions of quantum mechanics. Furthermore, the proposed tests are more likely to be loophole-free, as compared to former ones.

UR - http://www.scopus.com/inward/record.url?scp=35548975240&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.76.042119

DO - 10.1103/PhysRevA.76.042119

M3 - Article

AN - SCOPUS:35548975240

SN - 1050-2947

VL - 76

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 4

M1 - 042119

ER -