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arXiv:quant-ph/0305113 · Journal of Experimental and Theoretical Physics Letters

Operationalistic orthogonality condition for single-mode biphotons (qutrits)

Andrei A. Zhukov, Gleb Maslennikov, Maria V. Chekhova

Published Nov 1, 2002• 13 citations
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Abstract

An arbitrary polarization state of a single-mode biphoton is considered. The operationalistic criterion is formulated for the orthogonality of these states. It can be used to separate a biphoton with an arbitrary degree of polarization from a set of biphotons orthogonal to it. This is necessary for the implementation of quantum cryptography protocol based on the three-level systems. The experimental test of this criterion amounts to the observation of the anticorrelation effect for a biphoton with an arbitrary polarization state.

DOI
10.1134/1.1541042

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An arbitrary polarization state of a single-mode biphoton is considered. The operationalistic criterion is formulated for the orthogonality of these states. It can be used to separate a biphoton with an arbitrary degree of polarization from a set of biphotons orthogonal to it. This is necessary for the implementation of quantum cryptography protocol based on the three-level systems. The experimental test of this criterion amounts to the observation of the anticorrelation effect for a biphoton with an arbitrary polarization state.
Most protocols of quantum information transmission are based on qubits, or two-level quantum systems. However, in certain cases, it is reasonable to use quantum systems of higher dimensionality, such as, for instance, qutrits - three-level systems. In the present paper, it is shown that single-mode entangled pairs of polarized photons (biphotons) can be used for this purpose. Polarization state of a single-mode biphoton is considered and its representation on the Poincare sphere is suggested. An orthogonality criterion for two biphotons in arbitrary polarization states is formulated. Experiments on polarization transformations of biphotons are described. Finally, propagation of biphotons through fibres is considered.
The novel experimental realization of three-state optical quantum systems is presented. We use the polarization state of biphotons in single frequency- and spatial mode to generate an arbitrary qutrits. In particular the specific sequence of states that are used in the extended version of BB84 quantum key distribution protocol was generated and tested. We experimentally verify the orthogonality of the 12 basic states and demonstrate the ability of switching between them. The tomography procedure is applied to reconstruct the density matrices of generated states.