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arXiv:quant-ph/0606191 · Physical Review A

Preparation of pure and mixed polarization qubits and the direct measurement of figures of merit

Robert B. A. Adamson, Lynden K. Shalm, Aephraim M. Steinberg

Published Jan 8, 2007• 15 citations
arXivHTMLPDF

Abstract

Nonclassical joint measurements can hugely improve the efficiency with which certain figures of merit of quantum systems are measured. We use such a measurement to determine a particular figure of merit, the purity, for a polarization qubit. In the process we highlight some of subtleties involved in common methods for generating decoherence in quantum optics.

DOI
10.1103/physreva.75.012104

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Nonclassical joint measurements can hugely improve the efficiency with which certain figures of merit of quantum systems are measured. We use such a measurement to determine a particular figure of merit, the purity, for a polarization qubit. In the process we highlight some of subtleties involved in common methods for generating decoherence in quantum optics.
Before we begin our detailed discussion of optical quantum information processing, we need to introduce certain figures of merit that quantify how well our information processor is performing. For a quantum computer, the time and resources it takes to complete a task are good measures, but we are faced with the problem that we do not know what the final design for a quantum computer will be. We therefore need additional figures of merit that are applicable in a wide range of situations. We first introduce the concept of the ‘density operator’, which will be used to describe quantum states about which we have incomplete knowledge. We then define the ‘fidelity’, which is used for assessing how close we are to a particular desired quantum state, and we discuss different measures of entanglement. The later part of the chapter will focus on figures of merit that are particularly relevant for assessing optical states, namely the first-order correlation functions, and the visibility of interference phenomena. Density operators and superoperators Classical physics often confronts us with situations where we can say only a limited amount about the state of a system: we can measure certain ‘bulk’ variables such as the temperature and pressure, but we do not know all of the details of the microscopic make-up of the state. For example, we typically have very little knowledge of the positions and velocities of all the atoms that constitute the system.
In quantum information processing, one of the most common methods to represent a qubit is by means of the polarization degree of freedom of a photon. Efficient methods to determine the photon polarization state are hence the fundamental tools in the studies of qubit systems. In fact, both theoretically optimal and practical polarization measurement schemes have been investigated extensively in the past two decades. These studies nevertheless focus on the situation when a definite number of photons are given and the results demonstrate the polarization estimation performance in terms of the mean fidelity [1, 2].
In this work, we consider an on-chip silicon device that prepares photonic qubits in mutually unbiased bases (MUBs), which can be used to realize quantum key distribution protocols. We present a realistic approach to dealing with generic imperfections in on-chip devices for generating MUBs, in particular, imperfections originating from fabrication. We show how to control the conversion of path to polarization qubits for sending MUBs, and conversely from polarization to path qubits when receiving them: we identify the so-called tilt angle at the conversion station as the parameter to control and improve the preparation of MUBs. We investigate the optimization of a tilt angle for various figures of merit, such as fidelities of MUBs, photon losses, and secret key rates in a practical realization. Our results suggest a realistic, cost-effective strategy for exploiting chip-based fiber-optic quantum communication.
ABSTRACT The design of nonlinear metasurfaces for quantum applications has traditionally focused on classical figures of merit such as tuning resonances at the pump and target frequencies. While these approaches can enhance nonlinear efficiency, they do not guarantee the precise phase control needed for generating pure quantum state. In this work, we present a hybrid quantum‐classical inverse design framework that directly incorporates quantum metrics into the optimization process. By leveraging an advanced multiobjective optimization, we optimized both entanglement fidelity and the spontaneous parametric down conversion (SPDC) rate, ensuring that high brightness and quantum purity are achieved simultaneously. In general, classical methods that rely on bound states in the continuum (BIC) modes or sharp resonances, can improve the SPDC rate but are often sensitive and difficult to control across the polarization channels leading to low quantum purity, uncontrolled correlations, and reduced entanglement fidelity. In contrast, our approach demonstrates that reliable, easy‐to‐fabricate metasurfaces can achieve superior quantum performance without these constraints. When applied to a [100] AlGaAs nanohole metasurface, our numerical simulations predict a Bell‐state fidelity of 0.989 combined with a collected SPDC rate of 55 Hz/mW, integrated over a wide angular emission range. Our optimized design represents a robust architecture for compact, high‐purity sources of entangled photon pairs.