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Tomography of a displacement photon counter for discrimination of single-rail optical qubits

Shuro Izumi, Jonas Schou Neergaard-Nielsen, Ulrik L. Andersen

Published Jan 1, 2018• 4 citations
OpenAlex

Abstract

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.

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Abstract 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 σ ˆ x 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.

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We investigate schemes for conversion between qubits encoded into superpositions of vacuum and single-photon states and qubits encoded into states of single photons. The analyzed schemes combine linear optics, homodyne or heterodyne detection, single-photon detection, and electro-optical feedforward, and are designed to be suitable for signals with arbitrary temporal profiles. To achieve perfect conversion, quantum filtering is utilized based on conditioning on no-clicks of single-photon detectors, which makes the conversion probabilistic. High-quality conditional conversion is nevertheless possible even without single-photon detectors, by conditioning on outcomes of a homodyne or heterodyne detector. Deterministic high-quality conversion of dual-rail qubits to single-rail qubits is possible with an array of homodyne detectors where the phases of the measured quadratures are controlled by a feedforward scheme, which represents an alternative to conversion via homodyne detection with a real-time continuous feedback [T. C. Ralph, A. P. Lund, and H. M. Wiseman, J. Opt. B 7, S245 (2005)].

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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.
Abstract 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 σ ˆ x 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.
Measurement and discrimination of quantum states are essential tasks in quantum information processing. A measurement strategy consisting of photon detection preceded by a displacement operation, that is actively feedback-controlled depending on the photon detection outcomes, is known to be a powerful measurement technique for quantum state discrimination [1] . In our work, we experimentally develop such a feedback measurement with photon detection and characterize its positive operator valued measure (POVM) via quantum detector tomography using coherent states. Quantum detector tomography has been demonstrated for various types of static measurements [3] , but not before for a dynamically updated measurement. As a potential application of the feedback measurement for quantum state discrimination, we analyze the performance of our measurement for the discrimination of the two orthogonal superpositions of vacuum and single photon states $| \pm \rangle = (|0\rangle \pm |1\rangle )/\sqrt 2 $ , which are the conjugate basis states of the optical single-rail qubit.
Quantum measurement is essential to both the foundations and practical applications of quantum information science. Among many possible models of quantum measurement, feedback measurements that dynamically update their physical structure are highly interesting due to their flexibility, which enables a wide range of measurements that might otherwise be hard to implement. Here we investigate by detector tomography a measurement consisting of a displacement operation combined with photon detection followed by a real time feedback operation. We design the measurement in order to discriminate the superposition of vacuum and single photon states-the single-rail qubit-and find that it can discriminate the superposition states with a certainty of 96%. Such a feedback-controlled photon counter will facilitate the realization of quantum information protocols with single-rail qubits as well as the nonlocality test of certain entangled states.
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.
We investigate schemes for conversion between qubits encoded into superpositions of vacuum and single-photon states and qubits encoded into states of single photons. The analyzed schemes combine linear optics, homodyne or heterodyne detection, single-photon detection, and electro-optical feedforward, and are designed to be suitable for signals with arbitrary temporal profiles. To achieve perfect conversion, quantum filtering is utilized based on conditioning on no-clicks of single-photon detectors, which makes the conversion probabilistic. High-quality conditional conversion is nevertheless possible even without single-photon detectors, by conditioning on outcomes of a homodyne or heterodyne detector. Deterministic high-quality conversion of dual-rail qubits to single-rail qubits is possible with an array of homodyne detectors where the phases of the measured quadratures are controlled by a feedforward scheme, which represents an alternative to conversion via homodyne detection with a real-time continuous feedback [T. C. Ralph, A. P. Lund, and H. M. Wiseman, J. Opt. B 7, S245 (2005)].
We experimentally demonstrate a new measurement scheme for the discrimination of two coherent states. The measurement scheme is based on a displacement operation followed by a photon-number-resolving detector, and we show that it outperforms the standard homodyne detector which we, in addition, prove to be optimal within all Gaussian operations including conditional dynamics. We also show that the non-Gaussian detector is superior to the homodyne detector in a continuous variable quantum key distribution scheme.