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J. Sperling

Publications and source records attributed to J. Sperling.

60 records · Page 4Linked to original sources
arXiv2011

Determination of the Schmidt number

Optimized, necessary and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure delivers equations similar to the eigenvalue problem of an operator. The properties of the solution of these equations will be studied. We solve these equations for classes of operators. The solutions will be applied to phase randomized two-mode squeezed-vacuum states in continuous variable systems.

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arXiv2009

Dirac's Quantum Phase Problem

In 1927 the great physicist Paul A. M. Dirac failed to provide a consistent quantum description of the phase of a radiation field. Only one year later, he developed the famous Dirac theory of the electron, which led to the anti-particle -- the positron. We show that the reason for Dirac's failure with the phase problem bears a striking resemblance to his ingenious insight into the nature of the electron. For a correct quantum description of the phase of a radiation field it is necessary to take the polarisation into account. Similarly to the introduction of the anti-particle of the electron, the inclusion of the second polarisation resolves the inconsistency of the quantum phase problem. This also leads to new insight into the quantum measurement problem of time.

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arXiv2009

Representation of entanglement by negative quasi-probabilities

Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one may reconstruct such quasi-propabilities from experimental data. Because of ambiguity, the quasi-probabilities obtained by the bare reconstruction are insufficient to identify entanglement. An optimization procedure is introduced to derive quasi-probabilities with a minimal amount of negativity. Negativities of optimized quasi-probabilities unambiguously prove entanglement, their positivity proves separability.

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arXiv2009

Necessary and sufficient conditions for bipartite entanglement

Necessary and sufficient conditions for bipartite entanglement are derived, which apply to arbitrary Hilbert spaces. Motivated by the concept of witnesses, optimized entanglement inequalities are formulated solely in terms of arbitrary Hermitian operators, which makes them useful for applications in experiments. The needed optimization procedure is based on a separability eigenvalue problem, whose analytical solutions are derived for a special class of projection operators. For general Hermitian operators, a numerical implementation of entanglement tests is proposed. It is also shown how to identify bound entangled states with positive partial transposition.

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arXiv2008

Verifying continuous-variable entanglement in finite spaces

Starting from arbitrary Hilbert spaces, we reduce the problem to verify entanglement of any bipartite quantum state to finite dimensional subspaces. Hence, entanglement is a finite dimensional property. A generalization for multipartite quantum states is also given.

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