Bell inequality for pairs of superselection rule restricted states

Todd Gilmore, James L Park

H. Bechmann-Pasquinucci

Libby Heaney, Seung-Woo Lee, Dieter Jaksch

Proposals for Bell-inequality tests on systems restricted by the particle-number-superselection rule often require operations that are difficult to implement in practice. In this article, we derive a Bell inequality, where measurements on pairs of states are used as a method to bypass this superselection rule. In particular, we focus on mode entanglement of an arbitrary number of massive particles and show that our Bell inequality detects the entanglement in an identical pair of states when other inequalities fail. However, as the number of particles in the system increases, the violation of our Bell inequality decreases due to the restriction in the measurement space caused by the superselection rule. This Bell test can be implemented using techniques that are routinely used in current experiments.

Tomasz Paterek, Paweł Kurzyński, Daniel K. L. Oi +1 more

Superselection rules (SSRs) constrain the allowable physical operations and consequently the ability to observe violations of local realism. Not only do SSRs restrict the type of states which can be prepared, equally they restrict the reference frames which are necessary for measurements. Here, we derive quantitative conditions under which a Bell inequality is violated in the presence of SSRs which reveal the critical role of reference frames. In particular, references prepared only locally in accordance with SSRs cannot be used to violate a Bell inequality. We discuss the optimal reference frames, their minimal size and reusability. Finally we comment on experiments related to Bell inequality and single photon non-locality, and propose a new experiment showing violation under an induced SSR. ‡ Corresponding author. ar X iv :1 00 4. 51 84 v2 [ qu an tph ] 1 6 Ju n 20 10 Violation of Bell’s inequality in the presence of superselection rules 2

Jose Luis Cereceda

Asmita Kumari, Ujjwal Sen

We consider violations of a Clauser-Horne-Shimony-Holt-type steering inequality for quantum states of systems of indistinguishable particles restricted by a particle-number-superselection rule. We check for violations in non-interacting Bose-Einstein condensate and N00N states, by using two copies of the states for bypassing the superselection rule. The superselection rule prevents the states from maximally violating the steering inequality. But the steering inequality violations are higher than Bell inequality violations for the same states. This in particular implies, in certain cases, that visibilities of the steering inequality violations are higher than the same for Bell inequality violations, for admixtures with white noise. We also found that an increase in the number of particles in the non-interacting condensate states results in a decrease of the violation amount of the steering inequality.