arXiv subjects

J. M. Geremia

Publications and source records attributed to J. M. Geremia.

5 recordsLinked to original sources

arXiv2008

Single shot parameter estimation via continuous quantum measurement

We present filtering equations for single shot parameter estimation using continuous quantum measurement. By embedding parameter estimation in the standard quantum filtering formalism, we derive the optimal Bayesian filter for cases when the parameter takes on a finite range of values. Leveraging recent convergence results [van Handel, arXiv:0709.2216 (2008)], we give a condition which determines the asymptotic convergence of the estimator. For cases when the parameter is continuous valued, we develop quantum particle filters as a practical computational method for quantum parameter estimation.

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arXiv2008

Suppression of Spin Projection Noise in Broadband Atomic Magnetometry

Our 2005 Physical Review Letter entitled "Suppression of Spin-Projection Noise in Broadband Atomic Magnetometry" (volume 94, 203002) relied heavily in its claims of experimental quantum-limited performance on the results of a prior publication from our group [1]. In subsequent work we have determined that the results of [1] were incorrect and must therefore retract this Physical Review Letter as well. The authors would like to emphasize that the broadband magnetometry approach taken in our work remains valid, as described in the theoretical paper [2], but we have lost confidence in the calibration procedures employed at the time to establish sensitivity relative to the spin-projection noise level. [1] JM Geremia, John K. Stockton and Hideo Mabuchi, "Real-Time Quantum Feedback Control of Atomic Spin-Squeezing," Science 304, 270, (2004). [2] John K. Stockton, JM Geremia, Andrew C. Doherty and Hideo Mabuchi, "Robust quantum parameter estimation: Coherent magnetometry with feedback," Phys. Rev. A 69, 032109, (2004).

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arXiv2008

Collective States and Symmetric Local Decoherence in Large Ensembles of Qubits

The symmetric collective states of an atomic spin ensemble (i.e., many-body states that are invariant under particle exchange) are not preserved by decoherence that acts identically but individually on members of the ensemble. We develop a class of collective states in an ensemble of N spin-1/2 particles that is invariant under symmetric local decoherence and find that the dimension of the Hilbert space spanned by these collective states scales only as N^2. We then investigate the open system dynamics of experimentally relevant non-classical collective atomic states, including Schroedinger cat and spin squeezed states, subject to various symmetric but local decoherence models.

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arXiv2008

Collective processes of an ensemble of spin-1/2 particles

When the dynamics of a spin ensemble are expressible solely in terms of symmetric processes and collective spin operators, the symmetric collective states of the ensemble are preserved. These many-body states, which are invariant under particle relabeling, can be efficiently simulated since they span a subspace whose dimension is linear in the number of spins. However, many open system dynamics break this symmetry, most notably when ensemble members undergo identical, but local, decoherence. In this paper, we extend the definition of symmetric collective states of an ensemble of spin-1/2 particles in order to efficiently describe these more general collective processes. The corresponding collective states span a subspace which grows quadratically with the number of spins. We also derive explicit formulae for expressing arbitrary identical, local decoherence in terms of these states.

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arXiv2008

Efficient feedback controllers for continuous-time quantum error correction

We present an efficient approach to continuous-time quantum error correction that extends the low-dimensional quantum filtering methodology developed by van Handel and Mabuchi [quant-ph/0511221 (2005)] to include error recovery operations in the form of real-time quantum feedback. We expect this paradigm to be useful for systems in which error recovery operations cannot be applied instantaneously. While we could not find an exact low-dimensional filter that combined both continuous syndrome measurement and a feedback Hamiltonian appropriate for error recovery, we developed an approximate reduced-dimensional model to do so. Simulations of the five-qubit code subjected to the symmetric depolarizing channel suggests that error correction based on our approximate filter performs essentially identically to correction based on an exact quantum dynamical model.

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