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arXiv:1011.6202 · Physical Review Letters

Projection of Two Biphoton Qutrits onto a Maximally Entangled State

A. Halevy, E. Megidish, Tomer Shacham, Liat Dovrat, H. S. Eisenberg

Published Mar 29, 2011• 17 citations
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Abstract

Bell state measurements, in which two quantum bits are projected onto a maximally entangled state, are an essential component of quantum information science. We propose and experimentally demonstrate the projection of two quantum systems with three states (qutrits) onto a generalized maximally entangled state. Each qutrit is represented by the polarization of a pair of indistinguishable photons-a biphoton. The projection is a joint measurement on both biphotons using standard linear optics elements. This demonstration enables the realization of quantum information protocols with qutrits, such as teleportation and entanglement swapping.

DOI
10.1103/physrevlett.106.130502

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Abstract. We propose a scheme for building a heralded two-qutrit entangled state from polarized photons. An optical circuit is presented to build the maximally entangled two-qutrit state from two heralded Bell pairs and ideal threshold detectors. Several schemes are discussed for constructing the two Bell pairs. We also show how one can produce an unbalanced two-qutrit state that could be of general purpose use in some protocols. In terms of applications of the maximally entangled qutrit state, we mainly focus on how to use the state to demonstrate a violation of the Collins-Gisin-Linden-Massar-Popescu inequality under the restriction of measurements which can be performed using linear optical elements and photon counting. Other possible applications of the state, such as for higher dimensional quantum cryptography, teleportation, and generation of heralded two-qudit states are also briefly discussed. PACS numbers: 03.67.Bg, 03.65.Ud, 42.50DvA heralded two-qutrit entangled state 2 1.
We propose a scheme for building a heralded two-qutrit entangled state from polarized photons. An optical circuit is presented to build the maximally entangled two-qutrit state from two heralded Bell pairs and ideal threshold detectors. Several schemes are discussed for constructing the two Bell pairs. We also show how one can produce an unbalanced two-qutrit state that could be of general purpose use in some protocols. In terms of the applications of the maximally entangled qutrit state, we mainly focus on how to use the state to demonstrate a violation of the Collins–Gisin–Linden–Massar–Popescu inequality under the restriction of measurements which can be performed using linear optical elements and photon counting. Other possible applications of the state, such as for higher dimensional quantum cryptography, teleportation and generation of heralded two-qudit states, are also briefly discussed.
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.
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