We study the problem of mapping an unknown mixed quantum state onto a known pure state without the use of unitary transformations. This is achieved with the help of sequential measurements of two non-commuting observables only. We show that the overall success probability is maximized in the case of measuring two observables whose eigenstates define mutually unbiased bases. We find that for this optimal case the success probability quickly converges to unity as the number of measurement processes increases and that it is almost independent of the initial state. In particular, we show that to guarantee a success probability close to one the number of consecutive measurements must be larger than the dimension of the Hilbert space. We connect these results to quantum copying, quantum deleting and entanglement generation.
We investigate an explicitly time-dependent quantum system driven by a secant-pulse external field. By solving the Schrödinger equation exactly, we elucidate exotic properties of the system with respect to its dynamical evolution: on the one hand, the system is shown to be essentially nonadiabatic, which prohibits an adiabatic approximation for its dynamics; on the other hand, the loop evolution of the model can induce a geometric phase which, analogous to the Berry phase of the cyclic adiabatic evolution, is in direct proportion to the solid angle subtended by the path of the state vector. Mo…
A variety of dynamics in nature and society can be approximately treated as a driven and damped parametric oscillator. An intensive investigation of this time-dependent model from an algebraic point of view provides a consistent method to resolve the classical dynamics and the quantum evolution in order to understand the time-dependent phenomena that occur not only in the macroscopic classical scale for the synchronized behaviors but also in the microscopic quantum scale for a coherent state evolution. By using a Floquet U-transformation on a general time-dependent quadratic Hamiltonian, we ex…
We analyze the quantum evolution of a weakly nonlinear resonator due to a classical near-resonant drive and damping. The resonator nonlinearity leads to squeezing and heating of the resonator state. Using a hybrid phase-space--Fock-space representation for the resonator state within the Gaussian approximation, we derive evolution equations for the four parameters characterizing the Gaussian state. Numerical solution of these four ordinary differential equations is much simpler and faster than simulation of the full density matrix evolution, while providing good accuracy for the system analysis…
We discuss a self-contained spin-boson model for a measurement-driven engine, in which a demon generates work from thermal excitations of a quantum spin via measurement and feedback control. Instead of granting it full direct access to the spin state and to Landauer's erasure strokes for optimal performance, we restrict this demon's action to pointer measurements, i.e. random or continuous interrogations of a damped mechanical oscillator that assumes macroscopically distinct positions depending on the spin state. The engine can reach simultaneously the power and efficiency benchmarks and opera…
It is widely known that spin-locking noise-spectroscopy is a powerful technique for the characterization of low-frequency noise mechanisms in superconducting qubits. Here we show that the relaxation rate of the driven spin-locking state of a qubit can be significantly affected by the presence of an off-resonant high-frequency two-level-system defect. Thus, both low- and high-frequency defects should be taken into account in the interpretation of spin-locking measurements and other types of driven-state noise-spectroscopy.
Driven-Dissipative Dynamics of Measurement-Induced State Transitions
National Taiwan University（台湾大学）；National Tsing Hua University（清华大学）；National Center for Excellence in Quantum Information Science and Engineering, National Tsing Hua University（国家量子信息与工程卓越中心）；National Center for Theoretical Sciences（国家理论科学中心）
The spinor condensate with spin states degenerated in the ground spin-space provides a unique platform for investigating the edge of quantum mechanics and statistical physics. We study the evolution of the condensate under the scattering of a coherent atom beam. The time-dependent magnetization, entanglement entropy, thermal entropy and the entropy production rate are calculated. A novel spontaneous symmetry breaking is found during the evolution, It is shown that the stationary spin distribution can be controlled by the incoming coherent spin state of the incident atom beam, therefore the ato…
The dynamics of the next quantum jump for a qubit [two level system] coupled to a readout resonator [damped driven harmonic oscillator] is calculated. A quantum mechanical treatment of readout resonator reveals non exponential short time behavior which could facilitate detection of the state of the qubit faster than the resonator lifetime.
A universal scheme is introduced to speed up the dynamics of a driven open quantum system along a prescribed trajectory of interest. This framework generalizes counterdiabatic driving to open quantum processes. Shortcuts to adiabaticity designed in this fashion can be implemented in two alternative physical scenarios: one characterized by the presence of balanced gain and loss, the other involves non-Markovian dynamics with time-dependent Lindblad operators. As an illustration, we engineer superadiabatic cooling, heating, and isothermal strokes for a two-level system, and provide a protocol fo…
We consider the real-time evolution of a strongly coupled system of lattice fermions whose dynamics is driven entirely by dissipative Lindblad processes, with linear or quadratic quantum jump operators. The fermion 2-point functions obey a closed set of differential equations, which can be solved with linear algebra methods. The staggered occupation order parameter of the t-V model decreases exponentially during the dissipative time evolution. The structure factor associated with the various Fourier modes shows the slowing down of low-momentum modes, which is due to particle number conservatio…
We study the entanglement behavior of a random unitary circuit punctuated by projective measurements at the measurement-driven phase transition in one spatial dimension. We numerically study the logarithmic entanglement negativity of two disjoint intervals and find that it scales as a power of the cross-ratio. We investigate two systems: (1) Clifford circuits with projective measurements, and (2) Haar random local unitary circuit with projective measurements. Remarkably, we identify a power-law behavior of entanglement negativity at the critical point. Previous results of entanglement entropy …
