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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Continuous-variable experiments with optical qubits

С. А. Бабичев, Juergen Appel, Alexander I. Lvovsky

Published Jan 11, 2005• 0 citations
Publisher

Abstract

We present experimental homodyne tomography of an optical quantum bit represented by a single photon split into two optical modes. The reconstructed four-dimensional density matrix extends over the entire Hilbert space and thus reveals, for the first time, complete information about the dual-rail optical qubit as a state of the electromagnetic field. The experimental data violate the Bell inequality albeit with a loophole similar to the detection loophole in photon counting experiments. We also show that a homodyne measurement on just one of the modes leads to remote preparation of a single-rail optical qubit in the other mode.

DOI
10.1117/12.577717

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We present experimental homodyne tomography of an optical quantum bit represented by a single photon split into two optical modes. The reconstructed four-dimensional density matrix extends over the entire Hilbert space and thus reveals, for the first time, complete information about the dual-rail optical qubit as a state of the electromagnetic field. The experimental data violate the Bell inequality albeit with a loophole similar to the detection loophole in photon counting experiments. We also show that a homodyne measurement on just one of the modes leads to remote preparation of a single-rail optical qubit in the other mode.
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This review covers the latest developments in continuous-variable quantum-state tomography of optical fields and photons, placing a special emphasis on its practical aspects and applications in quantum-information technology. Optical homodyne tomography is reviewed as a method of reconstructing the state of light in a given optical mode. A range of relevant practical topics is discussed, such as state-reconstruction algorithms (with emphasis on the maximum-likelihood technique), the technology of time-domain homodyne detection, mode-matching issues, and engineering of complex quantum states of light. The paper also surveys quantum-state tomography for the transverse spatial state (spatial mode) of the field in the special case of fields containing precisely one photon.
We have developed a technique for dual-temporal-mode, ultrafast, time-domain, balanced homodyne detection. We have tested it by performing homodyne measurements on pairs of picosecond-duration temporal modes (or “time bins”) carrying a delocalized single photon. The experimental homodyne data have been used to reconstruct both the density matrix and the two-mode Wigner function of the delocalized state, thus showing the correlations existing between the pair of temporal modes carrying the single photon.
We investigate the performance of a detection strategy composed of a displacement operation and a photon counter, which is known as a beneficial tool in optical coherent communications, to the quantum state discrimination of the two superpositions of vacuum and single photon states corresponding to the σx eigenstates in the single-rail encoding of photonic qubits.We experimentally characterize the detection strategy in vacuum-single photon two-dimensional space using quantum detector tomography and evaluate the achievable discrimination error probability from the reconstructed measurement operators.We furthermore derive the minimum error rate obtainable with Gaussian transformations and homodyne detection.Our proof of principle experiment shows that the proposed scheme can achieve a discrimination error surpassing homodyne detection.