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Polarization entropy of the two-photon system

Moorad Alexanian, Vanik E. Mkrtchian

Published Apr 5, 2018• 0 citations
OpenAlex

Abstract

We consider the bipartite state of a two-photon polarization system and obtain the exact analytical expression for the von Neumann entropy in the particular case of polarization when the entropy depends on only five parameters rather than the full fifteen parameters. We investigate and graphically illustrate the dependence of the entropy on these five parameters, in particular, theexistence of exotic to nonexotic statetransitions in single- and two-photon correlations.

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We consider the bipartite state of a two-photon polarization system and obtain the exact analytical expression for the von Neumann entropy in the particular case of polarization when the entropy depends on only five parameters rather than the full fifteen parameters. We investigate and graphically illustrate the dependence of the entropy on these five parameters, in particular, theexistence of exotic to nonexotic statetransitions in single- and two-photon correlations.
We consider the bipartite state of a two-photon polarization system and obtain the exact analytical expression for the von Neumann entropy in the particular case of a five-parameter polarization density matrix. We investigate and graphically illustrate the dependence of the entropy on these five parameters, in particular, the existence of exotic, transition from exotic to nonexotic, and nonexotic states, where the quantum conditional entropy is negative, both positive and negative, and positive, respectively. We study the ``cooling'' or ``heating'' effect that follows from the reduced density of photon 2 when a measurement is performed on photon 1.
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.
We study the entropy of small subsystems in thermalizing quantum many-body systems governed by local Hamiltonians. Assuming the eigenstate thermalization hypothesis, we derive an analytical formula for the von Neumann entropy of equilibrated subsystems. This formula reveals how subsystem entropy depends on the microscopic parameters of the Hamiltonian and the macroscopic properties of the initial state. Furthermore, our results provide a theoretical explanation for recent numerical findings by Maceira and Läuchli, obtained via exact diagonalization.