Chained Bell Inequalities Research Articles

Minimum detection efficiency required for a loophole-free violation of the Braunstein-Caves chained Bell inequalities

The chained Bell inequalities of Braunstein and Caves involving $N$ settings per observer have some interesting applications. Here we obtain the minimum detection efficiency required for a loophole-free violation of the Braunstein-Caves inequalities for any $N\ensuremath{\ge}2$. We discuss both the case in which both particles are detected with the same efficiency and the case in which the particles are detected with different efficiencies.

Randomness vs. non-locality in a no-signalling world

We introduce a version of the chained Bell inequality for an arbitrary number of measurement outcomes, and use it to show that any non-signalling model that reproduces the correlations of maximally entangled states has the following property: for every hidden state, the outcomes of any measurement are completely undetermined and occur all with the same probability 1/d.

Maximally Nonlocal and Monogamous Quantum Correlations

We introduce a version of the chained Bell inequality for an arbitrary number of measurement outcomes and use it to give a simple proof that the maximally entangled state of two d-dimensional quantum systems has no local component. That is, if we write its quantum correlations as a mixture of local correlations and general (not necessarily quantum) correlations, the coefficient of the local correlations must be zero. This suggests an experimental program to obtain as good an upper bound as possible on the fraction of local states and provides a lower bound on the amount of classical communication needed to simulate a maximally entangled state in dxd dimensions. We also prove that the quantum correlations violating the inequality are monogamous among nonsignaling correlations and, hence, can be used for quantum key distribution secure against postquantum (but nonsignaling) eavesdroppers.

Wringing out better Bell inequalities

Local realism implies constraints on the statistics of two physically separated systems. These constraints, known collectively as Bell inequalities, can be violated by quantum mechanics. The standard Bell inequalities apply to a pair of two-state systems and constrain the value of some linear combination of correlation functions between the two systems. We generalize these standard Bell inequalities in two ways. First, we “chain” the Clauser-Horne-Shimony-Holt Bell inequality to obtain chained correlation Bell inequalities for two-state systems; we model a real experiment to show that these chained Bell inequalities lead to stronger quantum violations. Second, we formulate information-theoretic Bell inequalities, which are written in terms of the average information obtained in several measurements on a pair of physically separated systems (not just two-state systems); these information Bell inequalities have an appealing interpretation: if local realism holds, the two systems must carry an amount of information consistent with the inequality.