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Quantum XOR operation using macroscopic polarization states of light in Mach-Zehnder interferometer

A. Yu. Leksin, A. P. Alodjants, A.V. Prokhorov, Sergei M Arakelyan

Published Nov 30, 2003• 0 citations
Publisher

Abstract

In the paper we discuss the quantum optical element XOR (XOR-gate) on the basis of switching of macroscopic polarization states in Mach-Zehnder interferometer for single-photon pulses. It is shown that the state at the output of the optical system has the Schrödinger cat macroscopic superposition properties in polarization characteristics. PACS numbers: 42.50.Dv, 03.67.Lx

DOI
10.1201/9781482269079-93

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In the paper we discuss the quantum optical element XOR (XOR-gate) on the basis of switching of macroscopic polarization states in Mach-Zehnder interferometer for single-photon pulses. It is shown that the state at the output of the optical system has the Schrödinger cat macroscopic superposition properties in polarization characteristics. PACS numbers: 42.50.Dv, 03.67.Lx
A method for producing macroscopic quantum superposition states (generally known as Schr\"odinger cat) states for optical fields is presented. The proposed method involves two modes of the field interacting dispersively in a Kerr medium where one of the modes is an arm of a Mach-Zehnder interferometer and the other mode is external to it. If the external mode initially contains a macroscopic quantum state, such as a coherent state, and the vacuum and a single photon state are the inputs to the interferometer, the external field state becomes entangled with the number states associated with the two paths of the interferometer. Selective measurement at the output ports of the interferometer project the external mode into the desired cat states. It is pointed out that the method can also be used to generate cat states out of multimode states initially containing correlations.
Combining the recent progress in semiconductor nanostructures along with the versatility of photonic crystals in confining and manipulating light, quantum networks allow for the prospect of an integrated and low power quantum technology. Within quantum networks, which consist of a system of waveguides and nanocavities with embedded quantum dots, it has been demonstrated in theory that many-qubit states stored in electron spins could be teleported from one quantum dot to another via a single photon using the single-photon Faraday effect. However, in addition to being able to transfer quantum information from one location to another, quantum networks need added functionality such as (1) controlling the flow of the quantum information and (2) performing specific operations on qubits that can be easily integrated. In this paper, we show how a single-photon Mach–Zehnder interferometer (SMZI), that uses the concept of the single-photon Faraday effect to manipulate the polarization of a single photon, can be operated both as a switch to control the flow of quantum information inside the quantum network and as various single-qubit quantum gates to perform operations on a single photon. Given that the X gate, the Z gate, and the XZ gate are essential for the implementation of quantum teleportation, we show explicitly their implementation by means of our proposed SMZI. We also present the implementation of the Hadamard gate and the single-qubit phase gate, which are needed to complete the universal set of quantum gates for integrated quantum computing in a quantum network. Finally, the expected fidelity and robustness of the proposed SMZI are quantitatively explored by considering the phase errors within the SMZI.
A Mach–Zehnder interferometer with a nonlinear medium in each arm is treated as an all-optical switching device. In a classical treatment, the interferometer can, in principle, operate as an ideal switch, but quantization of the electromagnetic fields limits the switching capability. In this treatment we illustrate the fundamental quantum limits that apply to switching in all-optical devices by studying the nonlinear Mach–Zehnder interferometer. In particular the input states are assumed to be coherent states and the reduction in the quality of the switching device is discussed.
Polarized photons have properties that can be explained, among others, by their indistinguishability. This includes superposition and entanglement. We propose that the superposition state can be understood as the entirety of all mixtures of indistinguishable perpendicularly polarized photon beams. The photon beams, whose polarization correspond to the position of the polarizer, are filtered out by selection using a polarizer. There are no nonlocal effects with the entangled photons. This is because the physical states of the photons are defined before each measurement. The model replicates the predictions of quantum mechanics for entangled photons and also explains entanglement swapping and teleportation. The superposition of indistinguishable photon beams can be experimentally demonstrated using a Mach-Zehnder interferometer. This explains how the polarization of the input state reappears at the output of the Mach-Zehnder interferometer.
Abstract The superposition states, allowed by quantum theory, are dramatically diverse with respect to classical states and represent the true quantum states. By using a Mach-Zehnder interferometer we experimentally show how a single photon in a polarization superposition state can produce interference. The experimental setup includes a strongly attenuated laser source, polarizing beam splitters, half-waveplates, polarizers and single-photon detectors. The experimental activity has been performed with high-school students and teachers in several different contexts.