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Register a new userFull distribution of work done on a quantum system for arbitrary initial states
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We propose a novel approach to define and measure the statistics of work, internal energy and dissipated heat in a driven quantum system. In our framework the presence of a physical detector arises naturally and work and its statistics can be investigated in the most general case. In particular, we show that the quantum coherence of the initial state can lead to measurable effects on the moments of the work done on the system. At the same time, we recover the known results if the initial state is a statistical mixture of energy eigenstates. Our method can also be applied to measure the dissipated heat in an open quantum system. By sequentially coupling the system to a detector, we can track the energy dissipated in the environment while accessing only the system degrees of freedom.
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We investigate the generic bound on the minimal evolution time of the open dynamical quantum system. This quantum speed limit time is applicable to both mixed and pure initial states. We then apply this result to the damped Jaynes-Cummings model and the Ohimc-like dephasing model starting from a general time-evolution state. The bound of this time-dependent state at any point in time can be found. For the damped Jaynes-Cummings model, the corresponding bound first decreases and then increases in the Markovian dynamics. While in the non-Markovian regime, the speed limit time shows an interesting periodic oscillatory behavior. For the case of Ohimc-like dephasing model, this bound would be gradually trapped to a fixed value. In addition, the roles of the relativistic effects on the speed limit time for the observer in non-inertial frames are discussed.
Grovers algorithm for quantum searching is generalized to deal with arbitrary initial complex amplitude distributions. First order linear difference equations are found for the time evolution of the amplitudes of the marked and unmarked states. These equations are solved exactly. New expressions are derived for the optimal time of measurement and the maximal probability of success. They are found to depend on the averages and variances of the initial amplitude distributions of the marked and unmarked states, but not on higher moments. Our results imply that Grovers algorithm is robust against modest noise in the amplitude initialization procedure.
We present a proposal of a set-up to measure the work distribution due to an arbitrary unitary process acting on the spatial transverse degrees of freedom of a light beam. Hermite-Gaussian optical modes representing a quantum harmonic oscillator are prepared in a thermal state and sent through an interferometer. We show that the Fourier transform of the work distribution, or the characteristic function, can be obtained by measuring the intensity at the output of the interferometer. The usefulness of the approach is illustrated by calculating the work distribution for a unitary operation that displaces the linear momentum of the oscillator. We discuss the feasibility of the experiment, which can be realized with simple linear optical components.
Grovers algorithm for quantum searching of a database is generalized to deal with arbitrary initial amplitude distributions. First order linear difference equations are found for the time evolution of the amplitudes of the r marked and N-r unmarked states. These equations are solved exactly. An expression for the optimal measurement time T sim O(sqrt{N/r}) is derived which is shown to depend only on the initial average amplitudes of the marked and unmarked states. A bound on the probability of measuring a marked state is derived, which depends only on the standard deviation of the initial amplitude distributions of the marked or unmarked states.
Research on the out-of-equilibrium dynamics of quantum systems has so far produced important statements on the thermodynamics of small systems undergoing quantum mechanical evolutions. Key examples are provided by the Crooks and Jarzynski relations: taking into account fluctuations in non-equilibrium dynamics, such relations connect equilibrium properties of thermodynamical relevance with explicit non-equilibrium features. Although the experimental verification of such fundamental relations in the classical domain has encountered some success, their quantum mechanical version requires the assessment of the statistics of work performed by or onto an evolving quantum system, a step that has so far encountered considerable difficulties in its implementation due to the practical difficulty to perform reliable projective measurements of instantaneous energy states. In this paper, by exploiting a radical change in the characterization of the work distribution at the quantum level, we report the first experimental verification of the quantum Jarzynski identity and the Tasaki-Crooks relation following a quantum process implemented in a Nuclear Magnetic Resonance (NMR) system. Our experimental approach has enabled the full characterisation of the out-of-equilibrium dynamics of a quantum spin in a statistically significant way, thus embodying a key step towards the grounding of quantum-systems thermodynamics.
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