Quantum State Measurement Based On A Single Quantum Probe

Quantum information science is a novel interdisciplinary field covering quantum optics,quantum physics and information science,as well as many more.Quantum information science provides the remarkable capability to process information far beyond classical techniques by controlling and measuring the quantum states of quantum systems.However,quantum information technology requires a high-precision preparation,manipulation and readout of these quantum states.Therefore,measuring the unknown quantum states of the quantum systems is prerequisite to realize and verify applications of quantum information technology.Quantum states are usually determined through a tomographic process that estimates the density matrix on the basis of a diverse collection of measurements.However,despite the rapid development of quantum control and quantum measurement,some quantum systems still remain difficult to access for a direct observation of their states.These systems we will refer to as dark systems.Usually,the response of these dark quantum systems to external driving fields and the coupling with their surroundings are very weak,which makes the direct measurement and manipulation utterly difficult to perform.In order to overcome these technical difficulties of direct access,an indirect measurement approach based on a fully controllable quantum probe is an intuitive and promising alternative.We employ a quantum probe that is weakly coupled with the dark quantum systems and design a pulse control sequence applied to the probe in order to tailor the information we can measure from the quantum probe.Thereby,we can reconstruct the dark-system quantum states with the extracted information.To demonstrate the applicability and feasibility of the experimental proposals,we design high-precision reconstruction schemes for the quantum states of both discrete and continuous-variable dark systems.(1)Quantum state tomography of a discrete variable system.We illustrate our proposal in a qubit system.A qubit is one of the most widely studied systems in quantum mechanics.In our proposal,the Bloch vector of the quantum state of a single qubit can be determined through manipulating and measuring the quantum probe,which is utilized to reconstruct the quantum state.Additionally,in a two-qubit system,relevant correlation functions can be detected usuing our proposal.Furthermore,in terms of experimental realization,this can be applied to measure the quantum state of a nuclear spin in a solid spin system.(2)Quantum state tomography of a continuous variable system.In a continuous variable system,we illustrate our proposal in a quantum harmonic oscillator system.Here,the Wigner characteristic function contains all the information of the quantum state of the harmonic oscillator.In our proposal,we can determine the whole distribution of the characteristic function in reciprocal phase space of either a free or a damped harmonic oscillator through the local manipulation and measurement of the quantum probe.To show the feasibility of experimental demonstration for the harmonic oscillator system,one can reconstruct the motional state of a single trapped ion,where the quantum probe employed is formed by two electronic sublevels of the trapped ion.Our proposal only relies on the pulsed control and readout of a quantum probe,while circumventing the requirement for direct manipulation and measurement of the dark systems.It is also not necessary to adjust the form and strength of the interaction during the entire reconstruction process.Additionally,our proposal inherits the feature of robustness against slow noise acting on the probe from pulsed dynamical decoupling.The proposal provides a versatile tool for quantum-state measurement and can be extended to more general scenarios,such as dark systems formed by higher spins,many-body systems,and novel mechanical systems.