arXiv subjects

Areeya Chantasri

Publications and source records attributed to Areeya Chantasri.

27 records · Page 2Linked to original sources

arXiv2018

Quantum state tomography with time-continuous measurements: reconstruction with resource limitations

We propose and analyze quantum state estimation (tomography) using continuous quantum measurements with resource limitations, allowing the global state of many qubits to be constructed from only measuring a few. We give a proof-of-principle investigation demonstrating successful tomographic reconstruction of an arbitrary initial quantum state for three different situations: single qubit, remote qubit, and two interacting qubits. The tomographic reconstruction utilizes only a continuous weak probe of a single qubit observable, a fixed coupling Hamiltonian, together with single-qubit controls. In the single qubit case, a combination of the continuous measurement of an observable and a Rabi oscillation is sufficient to find all three unknown qubit state components. For two interacting qubits, where only one observable of the first qubit is measured, the control Hamiltonian can be implemented to transfer all quantum information to the measured observable, via the qubit-qubit interaction and Rabi oscillation controls applied locally on each qubit. We discuss different sets of controls by analyzing the unitary dynamics and the Fisher information matrix of the estimation in the limit of weak measurement, and simulate tomographic results numerically. As a result, we obtained reconstructed state fidelities in excess of 0.98 with a few thousand measurement runs.

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arXiv2017

Linear feedback stabilization of a dispersively monitored qubit

The state of a continuously monitored qubit evolves stochastically, exhibiting competition between coherent Hamiltonian dynamics and diffusive partial collapse dynamics that follow the measurement record. We couple these distinct types of dynamics together by linearly feeding the collected record for dispersive energy measurements directly back into a coherent Rabi drive amplitude. Such feedback turns the competition cooperative, and effectively stabilizes the qubit state near a target state. We derive the conditions for obtaining such dispersive state stabilization and verify the stabilization conditions numerically. We include common experimental nonidealities, such as energy decay, environmental dephasing, detector efficiency, and feedback delay, and show that the feedback delay has the most significant negative effect on the feedback protocol. Setting the measurement collapse timescale to be long compared to the feedback delay yields the best stabilization.

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arXiv2017

Simultaneous continuous measurement of non-commuting observables: quantum state correlations

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.

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arXiv2017

Prediction and Characterization of Multiple Extremal Paths in Continuously Monitored Qubits

We examine most-likely paths between initial and final states for diffusive quantum trajectories in continuously monitored pure-state qubits, obtained as extrema of a stochastic path integral. We demonstrate the possibility of "multipaths" in the dynamics of continuously-monitored qubit systems, wherein multiple most-likely paths travel between the same pre- and post-selected states over the same time interval. Most-likely paths are expressed as solutions to a Hamiltonian dynamical system. The onset of multipaths may be determined by analyzing the evolution of a Lagrange manifold in this phase space, and is mathematically analogous to the formation of caustics in ray optics or semiclassical physics. Additionally, we develop methods for finding optimal traversal times between states, or optimal final states given an initial state and evolution time; both give insight into the measurement dynamics of continuously-monitored quantum states. We apply our methods in two systems: a qubit with two non-commuting observables measured simultaneously, and a qubit measured in one observable while subject to Rabi drive. In the two-observable case we find multipaths due to caustics, bounded by a diverging Van-Vleck determinant, and their onset time. We also find multipaths generated by paths with different "winding numbers" around the Bloch sphere in both systems.

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arXiv2016

Arrow of Time for Continuous Quantum Measurement

We investigate the statistical arrow of time for a quantum system being monitored by a sequence of measurements. For a continuous qubit measurement example, we demonstrate that time-reversed evolution is always physically possible, provided that the measurement record is also negated. Despite this restoration of dynamical reversibility, a statistical arrow of time emerges, and may be quantified by the log-likelihood difference between forward and backward propagation hypotheses. We then show that such reversibility is a universal feature of non-projective measurements, with forward or backward Janus measurement sequences that are time-reversed inverses of each other.

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arXiv2016

Rapid estimation of drifting parameters in continuously measured quantum systems

We investigate the determination of a Hamiltonian parameter in a quantum system undergoing continuous measurement. We demonstrate a computationally rapid yet statistically optimal method to estimate an unknown and possibly time-dependent parameter, where we maximize the likelihood of the observed stochastic readout. By dealing directly with the raw measurement record rather than the quantum state trajectories, the estimation can be performed while the data is being acquired, permitting continuous tracking of the parameter during slow drifts in real time. Furthermore, we incorporate realistic nonidealities, such as decoherence processes and measurement inefficiency. As an example, we focus on estimating the value of the Rabi frequency of a continuously measured qubit, and compare maximum likelihood estimation to a simpler fast Fourier transform. Using this example, we discuss how the quality of the estimation depends on both the strength and duration of the measurement; we also discuss the trade-off between the accuracy of the estimate and the sensitivity to drift as the estimation duration is varied.

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arXiv2016

Quantum trajectories and their statistics for remotely entangled quantum bits

We experimentally and theoretically investigate the quantum trajectories of jointly monitored transmon qubits embedded in spatially separated microwave cavities. Using nearly quantum-noise limited superconducting amplifiers and an optimized setup to reduce signal loss between cavities, we can efficiently track measurement-induced entanglement generation as a continuous process for single realizations of the experiment. The quantum trajectories of transmon qubits naturally split into low and high entanglement classes corresponding to half-parity collapse. The distribution of concurrence is found at any given time and we explore the dynamics of entanglement creation in the state space. The distribution exhibits a sharp cut-off in the high concurrence limit, defining a maximal concurrence boundary. The most likely paths of the qubits' trajectories are also investigated, resulting in three probable paths, gradually projecting the system to two even subspaces and an odd subspace. We also investigate the most likely time for the individual trajectories to reach their most entangled state, and find that there are two solutions for the local maximum, corresponding to the low and high entanglement routes. The theoretical predictions show excellent agreement with the experimental entangled qubit trajectory data.

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arXiv2015

Anatomy of Fluorescence: Quantum trajectory statistics from continuously measuring spontaneous emission

We investigate the continuous quantum measurement of a superconducting qubit undergoing fluorescence. The fluorescence of the qubit is detected via a phase-preserving heterodyne measurement, giving the fluorescence quadrature signals as two continuous qubit readout results. By using the stochastic path integral approach to the measurement physics, we derive most likely paths between boundary conditions on the state, and compute approximate time correlation functions between all stochastic variables via diagrammatic perturbation theory. We focus on paths that increase in energy during the continuous measurement. Our results are compared to Monte Carlo numerical simulation of the trajectories, and we find close agreement between direct simulation and theory. We generalize this analysis to arbitrary diffusive quantum systems that are continuously monitored.

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arXiv2015

Stochastic path integral formalism for continuous quantum measurement

We generalize and extend the stochastic path integral formalism and action principle for continuous quantum measurement introduced in [A. Chantasri, J. Dressel and A. N. Jordan, Phys. Rev. A {\bf 88}, 042110 (2013)], where the optimal dynamics, such as the most-likely paths, are obtained by extremizing the action of the path integral. In this work, we apply exact functional methods as well as develop a perturbative approach to investigate the statistical behaviour of continuous quantum measurement, with examples given for the qubit case. For qubit measurement with zero qubit Hamiltonian, we find analytic solutions for average trajectories and their variances while conditioning on fixed initial and final states. For qubit measurement with unitary evolution, we use the perturbation method to compute expectation values, variances, and multi-time correlation functions of qubit trajectories in the short-time regime. Moreover, we consider continuous qubit measurement with feedback control, using the action principle to investigate the global dynamics of its most-likely paths, and finding that in an ideal case, qubit state stabilization at any desired pure state is possible with linear feedback. We also illustrate the power of the functional method by computing correlation functions for the qubit trajectories with a feedback loop to stabilize the qubit Rabi frequency.

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