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Register a new userProbability distributions of continuous measurement results for two non-commuting variables and conditioned quantum evolution
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Added by
Albert Franquet Gonz\\'alez
Publication date
2017
fields
Physics
and research's language is
English
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We address the statistics of a simultaneous CWLM of two non-commuting variables on a few-state quantum system subject to a conditioned evolution. Both conditioned quantum measurement and that of two non-commuting variables differ drastically for either classical or quantum projective measurement, and we explore the peculiarities brought by the combination of the two. We put forward a proper formalism for the evaluation of the distributions of measurement outcomes. We compute and discuss the statistics in idealized and experimentally relevant setups. We demonstrate the visibility and manifestations of the interference between initial and final states in the statistics of measurement outcomes for both variables in various regimes. We analytically predict the peculiarities at the circle ${cal O}^2_1+{cal O}^2_2=1$ in the distribution of measurement outcomes in the limit of short measurement times and confirm this by numerical calculation at longer measurement times. We demonstrate analytically anomalously large values of the time-integrated output cumulants in the limit of short measurement times(sudden jump) and zero overlap between initial and final states, and give the detailed distributions. We present the numerical evaluation of the probability distributions for experimentally relevant parameters in several regimes and demonstrate that interference effects in the conditioned measurement can be accurately predicted even if they are small.
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We address the statistics of continuous weak linear measurement on a few-state quantum system that is subject to a conditioned quantum evolution. For a conditioned evolution, both the initial and final states of the system are fixed: the latter is achieved by the post-selection in the end of the evolution. The statistics may drastically differ from the non-conditioned case, and the interference between initial and final states can be observed in the probability distributions of measurement outcomes as well as in the average values exceeding the conventional range of non-conditioned averages. We develop a proper formalism to compute the distributions of measurement outcomes, evaluate and discuss the distributions in experimentally relevant setups. We demonstrate the manifestations of the interference between initial and final states in various regimes. We consider analytically simple examples of non-trivial probability distributions. We reveal peaks (or dips) at half-quantized values of the measurement outputs. We discuss in detail the case of zero overlap between initial and final states demonstrating anomalously big average outputs and sudden jump in time-integrated output. We present and discuss the numerical evaluation of the probability distribution aiming at extend- ing the analytic results and describing a realistic experimental situation of a qubit in the regime of resonant fluorescence.
The possibility of performing simultaneous measurements in quantum mechanics is investigated in the context of the Curie-Weiss model for a projective measurement. Concretely, we consider a spin-$frac{1}{2}$ system simultaneously interacting with two magnets, which act as measuring apparatuses of two different spin components. We work out the dynamics of this process and determine the final state of the measuring apparatuses, from which we can find the probabilities of the four possible outcomes of the measurements. The measurement is found to be non-ideal, as (i) the joint statistics do not coincide with the one obtained by separately measuring each spin component, and (ii) the density matrix of the spin does not collapse in either of the measured observables. However, we give an operational interpretation of the process as a generalised quantum measurement, and show that it is fully informative: The expected value of the measured spin components can be found with arbitrary precision for sufficiently many runs of the experiment.
We consider the temporal correlations of the quantum state of a qubit subject to simultaneous continuous measurement of two non-commuting qubit observables. Such qubit state correlators are defined for an ensemble of qubit trajectories, which has the same fixed initial state and can also be optionally constrained by a fixed final state. We develop a stochastic path integral description for the continuous quantum measurement and use it to calculate the considered correlators. Exact analytic results are possible in the case of ideal measurements of equal strength and are also shown to agree with solutions obtained using the Fokker-Planck equation. For a more general case with decoherence effects and inefficiency, we use a diagrammatic approach to find the correlators perturbatively in the quantum efficiency. We also calculate the state correlators for the quantum trajectories which are extracted from readout signals measured in a transmon qubit experiment, by means of the quantum Bayesian state update. We find an excellent agreement between the correlators based on the experimental data and those obtained from our analytical and numerical results.
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and study their mutual relationships. Additionally, we prove that quantum query complexity of distinguishing two probability distributions is given by their inverse Hellinger distance, which gives a quadratic improvement over classical query complexity for any pair of distributions. The results are obtained by using the adversary method for state-generating input oracles and for distinguishing probability distributions on input strings.
Entanglement distillation is an essential ingredient for long distance quantum communications. In the continuous variable setting, Gaussian states play major roles in quantum teleportation, quantum cloning and quantum cryptography. However, entanglement distillation from Gaussian states has not yet been demonstrated. It is made difficult by the no-go theorem stating that no Gaussian operation can distill Gaussian states. Here we demonstrate the entanglement distillation from Gaussian states by using measurement-induced non-Gaussian operations, circumventing the fundamental restriction of the no-go theorem. We observed a gain of entanglement as a result of conditional local subtraction of a single photon or two photons from a two-mode Gaussian state. Furthermore we confirmed that two-photon subtraction also improves Gaussian-like entanglement as specified by the Einstein-Podolsky-Rosen (EPR) correlation. This distilled entanglement can be further employed to downstream applications such as high fidelity quantum teleportation and a loophole-free Bell test.
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