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IEEE photonics journal

Realization of Single-Photon Frequency-Domain Qubit Channels Using Phase Modulators

J. Capmany, Carlos R. Fernández‐Pousa

Published Oct 22, 2012• 4 citations
Publisher

Abstract

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.

DOI
10.1109/jphot.2012.2226022

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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.
We propose and theoretically study a method for the stochastic realization of arbitrary quantum channels on multimode single-photon qudits. In order for our method to be undemanding in its implementation, we restrict our analysis to linear-optical techniques, vacuum ancillary states, and nonadaptive schemes, but we allow for random switching between different optical networks. With our method it is possible to deterministically implement random-unitary channels and to stochastically implement general channels. We provide an expression for the optimal probability of success of our scheme and calculate this quantity for specific examples such as the qubit amplitude-damping channel. The success probability is shown to be related to the entanglement properties of the Choi-Jamio\l{}kowski state isomorphic to the channel.
The technology of frequency coding in channels of quantum key distribution allows to determine the ground state of photons through the value of the amplitude of its carrier, frequency modulated in phase (PM) or amplitude (AM) by a radio-frequency signal, and the resulting side components. Over the past twenty years, it has been substantially modified and improved. At the same time, in recent works, an expanded understanding of the frequency coding principle is used, in which each photon state is associated not with the phase of the modulating signal at a certain frequency, but with one or more sideband frequencies or the carrier frequency of the photon itself. The known schemes of electro-optical modulation and remodulation are described by the symmetric pairs PM-PM, AM-AM and AM-PM (PM-AM), where the first component determines the modulator type on the Alice side (legal subscriber - transmitter), and the second one on the side of Bob legal subscriber - receiver). It is noted, that the smallest value of QBER is achieved in schemes with a passive definition of one or two basic states of a photon, i.e. without the use of remodulation processes. The formation of a filter system is carried out using fiber Bragg gratings (FBG) or arrayed waveguide gratings (AWG), tuned to the photon carrier or it sideband components. In this paper, we present the results of constructing a universal system of quantum key distribution (QKD) based on the electro-optical AMPM-PMAM scheme, which makes it possible to realize all the above-mentioned schemes and additionally combined version. At the heart of the AMPMPMAM system of the QKD system is the modulation transformation of the photon carrier based on the Il'inMorozov's method and its one- and two-modulator realizations. For the mathematical description of the scheme, the principles of constructing a single-port modulation microwave photonic link of a sequential type and photon modeling of electro-optical modulators were used. The use of the universal scheme will allow using several levels of cryptographic protection, including switching schemes and protocols, with remodulation and only passive detection. In addition, it should be noted the high spectral efficiency of the Il'in-Morozov's modulation conversion, its spectral purity and the stability of the received characteristics of the output radiation when the conversion parameters deviate from the optimal ones. The possibility of reducing the probability of achieving a positive result in PNS attacks by Eva (illegal subscriber) is shown by eliminating the carrier of the signal transmitted via the quantum channel from the structure of the key distribution.
The technology of frequency coding in channels of quantum key distribution allows to determine the ground state of photons through the value of the amplitude of its carrier, frequency modulated in phase (PM) or amplitude (AM) by a radio-frequency signal, and the resulting side components. Over the past twenty years, it has been substantially modified and improved. At the same time, in recent works, an expanded understanding of the frequency coding principle is used, in which each photon state is associated not with the phase of the modulating signal at a certain frequency, but with one or more sideband frequencies or the carrier frequency of the photon itself. In this paper, we present the results of constructing a frequency coding system of quantum key distribution (QKD) based on the serial electro-optical photon amplitude modulation and phase commutation. The possibility of reducing the probability of achieving a positive result in PNS attacks by Eva is shown by eliminating the carrier of the signal transmitted via the quantum channel from the structure of the key distribution. It was early noted, that the smallest value of QBER is achieved in schemes with a passive definition of one or two basic states of a photon, i.e. without the use of remodulation processes, that is realized in considering. Additionally it is not necessary to form a notch filter system, which is usually carried out using fiber Bragg gratings (FBG) or arrayed waveguide gratings (AWG) for discrimination the photon carrier and its sideband components.
We experimentally demonstrate a single-qubit decohering quantum channel using linear optics. We implement the channel, whose special cases include the familiar amplitude-damping channel and the bit-flip channel, using a single, static optical setup. Following a recent theoretical result (Piani et al 2011 Phys. Rev. A 84 032304), we realize the channel in an optimal way, maximizing the probability of success, i.e. the probability for the photonic qubit to remain in its encoding. Using a two-photon entangled resource, we characterize the channel using ancilla-assisted process tomography and find average process fidelities of 0.98 ± 0.01 and 0.976 ± 0.009 for amplitude-damping and the bit-flip case, respectively.