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Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)

Biphoton ququarts and their entanglement

Yoon-Ho Kim

Published Aug 1, 2007• 0 citations
Publisher

Abstract

A four-dimensional quantum system (ququart) can be constructed by using the biphoton polarization states of frequency-nondegenerate spontaneous parametric down-conversion. We first discuss how to generate and characterize general single-ququart states with varying degrees of mixedness. We then discuss schemes to entangle multiple biphoton ququarts using linear optics and coincidence post-selection.

DOI
10.1109/cleopr.2007.4391556

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A four-dimensional quantum system (ququart) can be constructed by using the biphoton polarization states of frequency-nondegenerate spontaneous parametric down-conversion. We first discuss how to generate and characterize general single-ququart states with varying degrees of mixedness. We then discuss schemes to entangle multiple biphoton ququarts using linear optics and coincidence post-selection.
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Recently, quantum systems with D-dimensional bases states (D > 2) or quDits have attracted much attention in the context of fundamental tests of quantum theory and potential applications in quantum information. In this paper, we discuss several schemes for generating entangled states of two ququarts (four-dimensional quantum systems). The ququart in our scheme is based on frequency-nondegenerate biphoton states of spontaneous parametric down-conversion and we show how the entangled states between two ququarts can be generated with simple linear optical elements, such as an ordinary 50/50 beamsplitter, a polarizing beamsplitter, or a dichroic beamsplitter. We also show that our scheme is capable of generating postselection-free two-ququart entangled states efficiently.
We investigate, in a general form, entanglement of biphoton qutrits and ququarts, i.e. states formed in the processes of, correspondingly, degenerate and non-degenerate spontaneous parametric down-conversion. Indistinguishability of photons and, for ququarts, joint presence of the frequency and polarization entanglement are fully taken into account. In the case of qutrits, the most general three-parametric families of maximally entangled and non-entangled states are found, and anticorrelation of the degree of entanglement and polarization is shown to occur and to be characterized by a rather simple formula. Biphoton ququarts are shown to be two-qudits with the single-photon Hilbert space dimensionality d =4, which differentiates them significantly from the often used two-qubit model ( d =2). New expressions for entanglement quantifiers of biphoton ququarts are derived and discussed. Rather simple procedures for a direct measurement of the degree of entanglement are described for both qutrits and ququarts.
We investigate in a general form entanglement of biphoton qutrits and ququarts, i.e. states formed in the processes of collinear and, correspondingly, degenerate and non-degenerate Spontaneous Parametric Down-Conversion. Indistinguishability of photons and, for ququarts, joint presence of the frequency and and polarization entanglement are fully taken into account. In the case of qutrits the most general 3-parametric families of maximally entangled and non-entangled states are found, and anti-correlation of the degree of entanglement and polarization is shown to occur and to be characterized by a rather simple formula. Biphoton ququarts are shown to be two-qudits with the single-photon Hilbert space dimensionality d=4d=4d=4, which differs them significantly from the often used two-qubit model (d=2d=2d=2). New expressions for entanglement quantifiers of biphoton ququarts are derived and discussed. Rather simple procedures for a direct measurement of the degree of entanglement are described for both qutrits and ququarts.