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Physical Review A

Interconversion between single-rail and dual-rail photonic qubits

Jaromı́r Fiurášek

Published Mar 3, 2017• 7 citations
Publisher

Abstract

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)].

DOI
10.1103/physreva.95.033802

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IEEE photonics journal•Oct 22, 2012•4 citations
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 show how to convert between partially coherent superpositions of a single photon with the vacuum by using linear optics and postselection based on homodyne measurements. We introduce a generalized quantum efficiency for such states and show that any conversion that decreases this quantity is possible. We also prove that our scheme is optimal by showing that no linear optical scheme with generalized conditional measurements, and with one single-rail qubit input, can improve the generalized efficiency.
Today's most widely used method of encoding quantum information in optical qubits is the dual-rail basis, often carried out through the polarisation of a single photon. On the other hand, many stationary carriers of quantum information - such as atoms - couple to light via the single-rail encoding in which the qubit is encoded in the number of photons. As such, interconversion between the two encodings is paramount in order to achieve cohesive quantum networks. In this paper, we demonstrate this by generating an entangled resource between the two encodings and using it to teleport a dual-rail qubit onto its single-rail counterpart. Our results yield an average fidelity of F=(92.8±2.2)%\mathcal{F}= (92.8\pm2.2)\%F=(92.8±2.2)% for the teleportation and F=(89.7±2.1)%\mathcal{F}= (89.7\pm2.1)\%F=(89.7±2.1)% for entanglement swapping, thus confirming the applicability of this scheme for a real-world implementation. This work completes the set of tools necessary for the interconversion between the three primary encodings of the qubit in the optical field: single-rail, dual-rail and continuous-variable.
This DPhil thesis presents two key works towards practical applications of quantum optics. Both works are novel and achieve competitive state-of-the-art results. Today's most widely used method of encoding quantum information in optical qubits is the dual-rail basis, often carried out through the polarisation of a single photon. On the other hand, many stationary carriers of quantum information | such as atoms | couple to light via the single-rail encoding in which the qubit is encoded in the number of photons. As such, interconversion between the two encodings is paramount in order to achieve cohesive quantum networks. In the first part of this thesis, we demonstrate this by generating a hybrid entangled resource between the two encodings and using it to teleport a dual-rail qubit onto its singlerail counterpart. Our key results yield an average fidelity of F = (92:8±2:2)% for the teleportation and F = (89:7 ± 2:1)% for entanglement swapping, thus confirming the applicability of this scheme towards a real-world implementation. This work completes the set of tools necessary for the interconversion between the three primary encodings of a qubit in the optical field: single-rail, dual-rail and continuous-variable. A remarkable aspect of quantum theory is that certain measurement outcomes are entirely unpredictable to all possible observers. Such quantum events can be harnessed to generate numbers whose randomness is asserted based upon the underlying physical processes. In the second part of this thesis, we formally introduce and experimentally demonstrate an ultrafast optical quantum randomness generator that uses a totally untrusted photonic source and whose idea we have patented. While considering completely general quantum attacks, we certify randomness at a rate of 1:1 Gbps with a rigorous security parameter of 10-20. Our security proof is entirely composable, thereby allowing the generated randomness to be utilised for arbitrary applications in cryptography and beyond.
Today's most widely used method of encoding quantum information in optical qubits is the dual-rail basis, often carried out through the polarisation of a single photon. On the other hand, many stationary carriers of quantum information – such as atoms – couple to light via the single-rail encoding in which the qubit is encoded in the number of photons. As such, interconversion between the two encodings is paramount in order to achieve cohesive quantum networks. In this paper, we demonstrate this by generating an entangled resource between the two encodings and using it to teleport a dual-rail qubit onto its single-rail counterpart. This work completes the set of tools necessary for the interconversion between the three primary encodings of the qubit in the optical field: single-rail, dual-rail and continuous-variable.
Photon counting induces an effective non-linear optical phase shift in certain states derived by linear optics from single photons. Although this non-linearity is non-deterministic, it is sufficient in principle to allow scalable linear optics quantum computation (LOQC). The most obvious way to encode a qubit optically is as a superposition of the vacuum and a single photon in one mode—so-called ‘single-rail’ logic. Until now this approach was thought to be prohibitively expensive (in resources) compared to ‘dual-rail’ logic where a qubit is stored by a photon across two modes. Here we attack this problem with real-time feedback control, which can realize a quantum-limited phase measurement on a single mode, as has been recently demonstrated experimentally. We show that with this added measurement resource, the resource requirements for single-rail LOQC are not substantially different from those of dual-rail LOQC. In particular, with adaptive phase measurements an arbitrary qubit state can be prepared deterministically .
In a recent paper, have developed a scheme for the stochastic implementation of arbitrary quantum operations on multimode single-photon qudit states by using reconfigurable linear-optic systems. Based on this idea, we explore the use of phase modulation for the realization of qubit channels in the frequency basis. Single-photon states belonging to two different frequency modes differing by the modulator's driving frequency represent the input dual-rail qubit states. The channel is implemented by a phase modulator followed by a fiber Bragg grating, taking advantage of the high degree of reconfigurability and microwave bandwidth shown by electrooptic modulation technology. The channels are realized by a combination of three techniques: 1) suitably designed driving waveforms, which are probabilistically addressed to the modulator; 2) the corresponding addressing probabilities; and 3) the grating transmittance at the values of the frequency basis. The proposed scheme results in nonoptimal success probabilities but is shown to allow for a compact implementation of the conventional qubit random unitary channels and the qubit amplitude-damping channel.