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Revealing Quantum Entanglement via Locally Noneffective Operations
Abstract
Quantum entanglement is at the heart of quantum information processing. Various methods for the detection of entanglement have been developed. Here, we will explain an approach that uses locally noneffective unitary operations which, however, do cause a change of the global density matrix - an indication for the existence of correlations. We investigate whether this method can distinguish between classical and quantum correlations.
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A theorem of Bell, proving that certain predictions of quantum mechanics are inconsistent with the entire family of local hidden-variable theories, is generalized so as to apply to realizable experiments. A proposed extension of the experiment of Kocher and Commins, on the polarization correlation of a pair of optical photons, will provide a decisive test between quantum mechanics and local hidden-variable theories.
The state of a bipartite system may be changed by a cyclic operation applied on one of its subsystems. The change is a nonlocal effect, and can be detected only by measuring the two parts jointly. By employing the Hilbert-Schmidt metric, we can quantify such nonlocal effects via measuring the distance between the initial and final state. We show that this nonlocal property can be manifested not only by entangled states but also by the disentangled states which are classically correlated. Furthermore, we study the effect for the system of two qubits in detail. It is interesting that the nonlocal effect of disentangled states is limited by 1/√2, while the entangled states can exceed this limit and reach 1 for maximally entangled states.
A state of a composite quantum system is called classically correlated if it can be approximated by convex combinations of product states, and Einstein-Podolsky-Rosen correlated otherwise. Any classically correlated state can be modeled by a hidden-variable theory and hence satisfies all generalized Bell’s inequalities. It is shown by an explicit example that the converse of this statement is false.