Implementing one-photon three-qubit quantum gates using spatial light modulators

Abstract

Increasing the information-carrying capacity of a single photon may be achieved by utilizing multiple degrees of freedom. We describe here an approach that utilizes two degrees of freedom to encode three qubits per photon: one in polarization and two in the spatial-parity symmetry of the transverse field. In this conception, a polarization-sensitive spatial light modulator corresponds to a three-qubit controlled-unitary gate with one control qubit (polarization) and two target (spatial-parity-symmetry) qubits. We describe the construction of controlled-not (cnot), n\ cnot, controlled-phase, and Fredkin gates, and the preparation of one-photon, three-qubit Greenberger-Horne-Zeilinger (GHZ) and W states. This approach enables simple optical implementations of few-qubit tasks in quantum information processing

Optical coherency matrix tomography

“…In this Article, we present a methodical approach—optical coherency matrix tomography (OC m T)—for measuring the complex elements of 4 × 4 coherency matrices G by appropriating the quantum-state-tomography strategy. To demonstrate the universality of our approach, we implement it with coherent and partially coherent fields having coupled or uncoupled DoFs in three distinct settings involving pairs of points 9 10 11 , spatial-parity modes 40 41 42 43 44 , and orbital angular momentum (OAM) modes 45 —each together with polarization. We identify the minimal set of linearly independent, joint spatial-polarization projective measurements that enable a unique reconstruction of G .…”

“…1(b) ]: (i) the scalar field at two points and , E a and E b ; (ii) the spatial-parity even ‘e’ and odd ‘o’ modes of a scalar field E e and E o refs. 40 , 41 , 42 , 43 , 44 ; or (iii) a pair of OAM modes, e.g., E 0 and E 1 corresponding to OAM and 1, respectively 45 47 .…”

“…The corresponding procedure for multi-DoF beams in classical optics has been studied theoretically 11 , but has not been demonstrated experimentally heretofore. Even in the simplest case of two binary DoFs 6 (e.g., polarization, a bimodal waveguide 36 37 , two coupled single-mode waveguides 38 39 , spatial-parity modes 40 41 42 43 44 , etc. ), the associated 4 × 4 coherency matrix G , which is a complete representation of second-order coherence 10 11 , has not been measured in its entirety to date.…”

Universal hybrid three-qubit quantum gates assisted by a nitrogen-vacancy center coupled with a whispering-gallery-mode microresonator

“…The information-carrying capacity of single photons can be increased largely by encoding logic qubits on more than one degree of freedom (DOF), such as polarization, orbital angular momentum [9], discrete path [10], spatial position [11], time bin [12], frequency [13], and global spatial symmetry [14]. Fascinating applications in the field of multiple-DOF QIP have also attracted much attention recently, e.g., beating the channel capacity limit with superdense coding [15,16], significantly reducing physical * wangchuan@bupt.edu.cn qubits required in distributed quantum computing [17], and constructing efficient qutrit gates using ancillary DOFs [18].…”

Characterization of a spatial light modulator as a polarization quantum channel

“…Spatial light modulators (SLM) are ever more popular devices that have recently been employed for phase modulation of a light beam in a vast variety of classical and quantum optics [1][2][3][4], atom optics [5], optical tweezers [6,7], quantum chaos [8], quantum metrology [9], quantum information [10][11][12][13][14][15][16], and quantum communication experiments [17,18]. The increasing popularity of this device is mainly due to its versatility: SLMs have been used to produce different orbital angular momentum (OAM) states of light; they can act as digital lenses or holograms, tunable filters, among other applications.…”