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arXiv:quant-ph/0308003 · Physical Review Letters

Maximally Entangled Mixed States: Creation and Concentration

Nicholas A. Peters, Joseph B. Altepeter, David A. Branning, Evan R. Jeffrey, Tzu-Chieh Wei, Paul G. Kwiat

Published Apr 2, 2004• 134 citations
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Abstract

Using correlated photons from parametric down-conversion, we extend the boundaries of experimentally accessible two-qubit Hilbert space. Specifically, we have created and characterized maximally entangled mixed states that lie above the Werner boundary in the linear entropy-tangle plane. In addition, we demonstrate that such states can be efficiently concentrated, simultaneously increasing both the purity and the degree of entanglement. We investigate a previously unsuspected sensitivity imbalance in common state measures, i.e., the tangle, linear entropy, and fidelity.

DOI
10.1103/physrevlett.92.133601

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Using correlated photons from parametric down-conversion, we extend the boundaries of experimentally accessible two-qubit Hilbert space. Specifically, we have created and characterized maximally entangled mixed states that lie above the Werner boundary in the linear entropy-tangle plane. In addition, we demonstrate that such states can be efficiently concentrated, simultaneously increasing both the purity and the degree of entanglement. We investigate a previously unsuspected sensitivity imbalance in common state measures, i.e., the tangle, linear entropy, and fidelity.
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Maximally entangled mixed states are those states that, for a given mixedness, achieve the greatest possible entanglement. For two-qubit systems and for various combinations of entanglement and mixedness measures, the form of the corresponding maximally entangled mixed states is determined primarily analytically. As measures of entanglement, we consider entanglement of formation, relative entropy of entanglement, and negativity; as measures of mixedness, we consider linear and von Neumann entropies. We show that the forms of the maximally entangled mixed states can vary with the combination of (entanglement and mixedness) measures chosen. Moreover, for certain combinations, the forms of the maximally entangled mixed states can change discontinuously at a specific value of the entropy. Along the way, we determine the states that, for a given value of entropy, achieve maximal violation of Bell's inequality.
We experimentally prepare bi-photon mixed states in polarization employing an entangled-classical hybrid photon emitter which can properly model solid-state entangled photon sources with uncorrelated background photons. Polarization-uncorrelated photon pairs in totally mixed (TM) states are embodied with classical thermal radiation, while the polarization-entangled ones in a Bell state are generated by conventional parametric down conversion. The bi-photon states generated from the hybrid photon emitter are characterized in terms of a linear entropy-tangle plane, which reveals the formation of two-qubit Werner states. We also propose a direct way for evaluating the Werner states by means of minimal coincidence counts measurements. This simple method can be widely applicable in examining the bi-photon states from solid-state entangled photon sources, in which the polarization-entangled photon pairs have temporal correlation while the background photons in the TM states do not.