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Viewpoint: Mapping Out the State of a Quantum System

Andrew N. Jordan

Published Sep 12, 2016• 1 citation
OpenAlex

Abstract

Researchers have developed a new technique to measure the density matrix—a more general way of characterizing the state of a quantum system than that provided by the wave function.

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We propose a new method to directly measure a general multiparticle quantum wave function, a single matrix element in a multi-particle density matrix, by quantum teleportation. The density matrix element is embedded in a virtual logical qubit and is nondestructively teleported to a single physical qubit for readout. We experimentally implement this method to directly measure the wave function of a photonic mixed quantum state beyond a single photon using a single observable for the first time. Our method also provides an exponential advantage over the standard quantum state tomography in measurement complexity to fully characterize a sparse multiparticle quantum state.
Quantum computation depends on quantum entanglement, a correlation between subsystems that cannot occur classically. A variety of theoretical measures exist for quantifying the degree entanglement in such schemes, all of which are functions of the system density matrix. How can the entanglement be measured experimentally? Using quantum tomography techniques developed for two photon entangled states, the density matrix can be reconstructed from the appropriate experimental data. In this case the state tomography gives the complete characterization of the physical system (for the relevant degree of freedom, such as spin or polarization). It gives information on both the degree of nonclassical correlation, that is entanglement, as well as the amount of decoherence in the system. In this proceedings we discuss the general state tomography procedure required to characterize a few qubit quantum computer, for any architecture.
This chapter provides the relevant theory and techniques of quantum tomography. Quantum tomography aims to determine the state of the system by determining its density matrix by means of a series of measurements done on fairly a large number of identically prepared copies of the same system. Wolfgang Ernst Pauli problem asks the question whether measurements of probability densities of position and momentum of a particle determine its quantum state wave function. The chapter outlines the optical homodyne tomography technique of reconstruction of Wigner function. Polarized light wave is described by the commonly used Stokes parameters introduced by George Gabriel Stokes in 1852. Quantum process tomography (QPT) aims to give full information on the dynamics of a quantum state. QPT can be used to improve the design and control of quantum hardware. Direct characterization of quantum dynamics differs in many ways from standard quantum process tomography and ancilla-assisted process tomography.