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arXiv:1812.11462

Entanglement of multiphoton polarization Fock states and their superpositions

Stephen Vintskevich, D. A. Grigoriev, Nikolai Miklin, Mikhail Vladimirovich Fedorov

Published Dec 30, 2018• 0 citations
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Abstract

Density matrices of pure multiphoton Fock polarization states and of arising from them reduced density matrices of mixed states are expressed in similar ways in terms of matrices of correlators defined as averaged products of equal numbers of creation and annihilation operators. Degree of entanglement of considered states is evaluated for various combinations of parameters of states and character of their reduction.

DOI
10.48550/arxiv.1812.11462

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Density matrices of pure multiphoton Fock polarization states and of arising from them reduced density matrices of mixed states are expressed in similar ways in terms of matrices of correlators defined as averaged products of equal numbers of creation and annihilation operators. Degree of entanglement of considered states is evaluated for various combinations of parameters of states and character of their reduction.
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We analyze features of mixed biphoton polarization states, which arise from pure states of polarization-frequency biphoton ququarts after averaging over frequencies of photons. For mixed states, we find their concurrence CCC, Schmidt parameter KKK, degree of polarization PPP, as well as the von Neumann mutual information III. In some simple cases, we also find the relative entropy Srel{S}_{\mathrm{rel}}Srel​ and the degree of classical correlations Ccl{C}_{\mathrm{cl}}Ccl​. In mixed states, the Schmidt parameter does not characterize the degree of entanglement anymore, as it does in pure states. Nevertheless, the Schmidt parameter remains useful even in the case of mixed states because it remains directly related to the degree of polarization. We compare results occurring in the cases of full pure polarization-frequency states of ququarts and mixed states (averaged over frequencies). Differences between these results can be seen in experiments with and without frequency filters in front of a detector.
We analyze features of mixed biphoton polarization states which arise from pure states of polarization-frequency biphoton ququarts after averaging over frequencies of photons. For mixed states we find their concurrence C, Schmidt parameter K and degree of polarization P, as well as the von Neumann mutual information I. In some simple cases we find also the relative entropy S_{rel} and the degree of classical correlations C_{cl}. We show that in mixed states the Schmidt parameter does not characterize anymore the degree of entanglement, as it does in pure states. Nevertheless, the Schmidt parameter remains useful even in the case of mixed states because it remains directly related to the degree of polarization. We compare results occurring in the cases of full pure polarization-frequency states of ququarts, mixed states (averaged over frequencies) and states with separated high- and low-frequency parts. Differences between these results can be seen in experiments with and without a dichroic beam-splitter, as well as with and without frequency filters in front of detector.