Local commutativity versus Bell inequality violation for entangled states and versus non-violation for separable states
| dc.creator | Seevinck, Michael | |
| dc.creator | Uffink, Jos | |
| dc.date | 2007-03-15 | |
| dc.date | 2007-10-09 | |
| dc.date.accessioned | 2026-07-07T08:34:51Z | |
| dc.date.available | 2026-07-07T08:34:51Z | |
| dc.description | By introducing a quantitative `degree of commutativity' in terms of the angle between spin-observables we present two tight quantitative trade-off relations in the case of two qubits: First, for entangled states, between the degree of commutativity of local observables and the maximal amount of violation of the Bell inequality: if both local angles increase from zero to π/2 (i.e., the degree of local commutativity decreases), the maximum violation of the Bell inequality increases. Secondly, a converse trade-off relation holds for separable states: if both local angles approach π/2 the maximal value obtainable for the correlations in the Bell inequality decreases and thus the non-violation increases. As expected, the extremes of these relations are found in the case of anti-commuting local observables where respectively the bounds of 2\sqrt{2} and \sqrt{2} hold for the expectation of the Bell operator. The trade-off relations show that non-commmutativity gives ``a more than classical result" for entangled states, whereas "a less than classical result" is obtained for separable states. The experimental relevance of the trade-off relation for separable states is that it provides an experimental test for two qubit entanglement. Its advantages are twofold: in comparison to violations of Bell inequalities it is a stronger criterion and in comparison to entanglement witnesses it needs to make less strong assumptions about the observables implemented in the experiment. | |
| dc.description | V2: Most important change: we have greatly extended the discussion of the theoretical and experimental relevance of the results. v3: Published version | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0703134 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0703134 | |
| dc.identifier | Phys. Rev. A 76, 042105 (2007) | |
| dc.identifier | doi:10.1103/PhysRevA.76.042105 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139579 | |
| dc.subject | Quantum Physics | |
| dc.title | Local commutativity versus Bell inequality violation for entangled states and versus non-violation for separable states | |
| dc.type | text |