Abstract
Device-independent quantum cryptography protocols exploit quantum correlations generated by ``black box'' quantum devices. The physical dimensionality of such devices may act as a constraint. But which quantum correlations are fundamentally attainable and can be exploited under this constraint? Scientists now develop a new and timely numerical method that answers this question.
Highlights
The realization by John Bell in his 1964 seminal paper [1] that the correlations arising from measuring spacelike separated quantum systems can be nonlocal represents one of the most outstanding discoveries of modern physics
The characterization of quantum nonlocality provided by the NavascuésPironio-Acín (NPA) hierarchy [14] played a pivotal role in assessing the security of many such protocols
By exploiting a previously unnoticed connection with the separability problem, we show how to use tools from entanglement detection to characterize the strength of bipartite quantum correlations under local dimension constraints via hierarchies of semidefinite programming relaxations
Summary
The realization by John Bell in his 1964 seminal paper [1] that the correlations arising from measuring spacelike separated quantum systems (quantum correlations) can be nonlocal represents one of the most outstanding discoveries of modern physics. In order to certify the security of semi-deviceindependent communication protocols, or the existence of high-dimensional entanglement in a device-independent way, a characterization of quantum correlations under local dimension constraints is needed. In this respect, seesaw variational techniques have proven very useful to characterize such a set of correlations from the inside [23,24]. We use our method to bound the maximal violation attainable via measurements on two-qubit states of a number of bipartite Bell inequalities This question arises naturally in quantum information science [18,19] and convex optimization theory [33], where high-performance algorithms to solve the problem are still missing. We make use of our new numerical tools to prove that such a scheme works, i.e., that the linear witness presented in Ref. [35] does discriminate separable from entangled measurement operators
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