This paper studies the covariance geometry of filter-integrated observables in dynamical-decoupling spectroscopy. We show that the covariance admits a non-commuting additive decomposition,Ctotal=λCflat+CdevC^{\rm total}=\lambda C^{\rm flat}+C^{\rm dev}Ctotal=λCflat+Cdev,where CflatC^{\rm flat}Cflat represents flat filter-overlap geometry and CdevC^{\rm dev}Cdev encodes spectral deformation induced by power-law noise weights. Numerical analysis of CPMG filters reveals persistent but diluted non-commutativity under protocol enlargement, selective intermediate-mode hybridization, and horizon-precursor growth of covariance ill-conditioning.This paper studies the covariance geometry of filter-integrated observables in dynamical-decoupling spectroscopy. We show that the covariance admits a non-commuting additive decomposition,Ctotal=λCflat+CdevC^{\rm total}=\lambda C^{\rm flat}+C^{\rm dev}Ctotal=λCflat+Cdev,where CflatC^{\rm flat}Cflat represents flat filter-overlap geometry and CdevC^{\rm dev}Cdev encodes spectral deformation induced by power-law noise weights. Numerical analysis of CPMG filters reveals persistent but diluted non-commutativity under protocol enlargement, selective intermediate-mode hybridization, and horizon-precursor growth of covariance ill-conditioning.

May 24, 20260 citations

Conditional Gaussian filtering by Arthurs--Kelly readout in a three-mode cluster wire

B. M. Rodríguez-Lara, J. A. Mendoza-Fierro

Measurement readout programs the Gaussian operation implemented by a continuous-variable cluster wire. For the standard three-node wire, momentum homodyne readout gives an additive parity channel with finite-squeezing noise. We classify the pattern-resolved input--output covariance transformations generated by calibrated uncorrelated Arthurs--Kelly readout on one or both consumed nodes. Any finite Arthurs--Kelly position record produces a conditional Gaussian filter whose gain and residual covariance depend on the input covariance entries, rather than an input-independent additive Gaussian channel. Writing $\mathrm{A}$ for Arthurs--Kelly readout and $\mathrm{H}$ for homodyne readout, the readout pattern selects the filtered sector, with $\mathrm{AH}$ selecting position, $\mathrm{HA}$ selecting momentum, and $\mathrm{AA}$ retaining both. The hierarchy $0 < τ_{\mathrm{AA}} < \min \left\{ τ_{\mathrm{AH}}, τ_{\mathrm{HA}} \right\} < 1 = τ_{\mathrm{HH}}$ shows that finite Arthurs--Kelly position records contract the gain-transferred covariance area. Our results identify calibrated uncorrelated Arthurs--Kelly readout as a measurement-level method for covariance-sensitive Gaussian filtering inside a fixed cluster graph.Measurement readout programs the Gaussian operation implemented by a continuous-variable cluster wire. For the standard three-node wire, momentum homodyne readout gives an additive parity channel with finite-squeezing noise. We classify the pattern-resolved input--output covariance transformations generated by calibrated uncorrelated Arthurs--Kelly readout on one or both consumed nodes. Any finite Arthurs--Kelly position record produces a conditional Gaussian filter whose gain and residual covariance depend on the input covariance entries, rather than an input-independent additive Gaussian channel. Writing $\mathrm{A}$ for Arthurs--Kelly readout and $\mathrm{H}$ for homodyne readout, the readout pattern selects the filtered sector, with $\mathrm{AH}$ selecting position, $\mathrm{HA}$ selecting momentum, and $\mathrm{AA}$ retaining both. The hierarchy $0 < τ_{\mathrm{AA}} < \min \left\{ τ_{\mathrm{AH}}, τ_{\mathrm{HA}} \right\} < 1 = τ_{\mathrm{HH}}$ shows that finite Arthurs--Kelly position records contract the gain-transferred covariance area. Our results identify calibrated uncorrelated Arthurs--Kelly readout as a measurement-level method for covariance-sensitive Gaussian filtering inside a fixed cluster graph.

quant-pharXiv:2608.22043Aug 25, 20260 citations

Quantum Invariance

Васил Пенчев

Jul 30, 20200 citations

Optimal filtering for a giant cavity in waveguide QED systems

Guangpu Wu, Shibei Xue, Yuting Zhu +2 more

In waveguide quantum electrodynamics (QED) systems, a giant cavity can be engineered to interact with quantum fields by multiple distant coupling points so that its non-Markovian dynamics are quite different from traditional quantum optical cavity systems. Towards feedback control this system, this paper designs an optimal filter for the giant cavity systems to estimate its state evolution under continuous quantum measurements. Firstly, the Langevin equation in the Heisenberg picture are derived, which is a linear continuous-time system with both states and inputs delays resulting from the unconventional distant couplings. Compared to existing modeling approaches, this formulation effectively preserves the nonlocal coupling and multiple delay dynamic characteristics inherent in the original system. In particular, the presence of coupling and propagation delays leads to noncommutativity among the system operators at different times, which prevents the direct application of existing quantum filtering methods. To address this issue, an optimal filter is designed, in which the delayed-state covariance matrices are computed. By iteratively evaluating the delayed-state covariance over successive time intervals, the resulting optimal filter can be implemented in an interval-wise backward recursion algorithm. Finally, numerical simulations are conducted to evaluate the tracking performance of the proposed optimal filter for the giant cavity. By comparing between the evolutions of Wigner functions of coherent and cat states and the filter, the effectiveness of the optimal filter is validated.In waveguide quantum electrodynamics (QED) systems, a giant cavity can be engineered to interact with quantum fields by multiple distant coupling points so that its non-Markovian dynamics are quite different from traditional quantum optical cavity systems. Towards feedback control this system, this paper designs an optimal filter for the giant cavity systems to estimate its state evolution under continuous quantum measurements. Firstly, the Langevin equation in the Heisenberg picture are derived, which is a linear continuous-time system with both states and inputs delays resulting from the unconventional distant couplings. Compared to existing modeling approaches, this formulation effectively preserves the nonlocal coupling and multiple delay dynamic characteristics inherent in the original system. In particular, the presence of coupling and propagation delays leads to noncommutativity among the system operators at different times, which prevents the direct application of existing quantum filtering methods. To address this issue, an optimal filter is designed, in which the delayed-state covariance matrices are computed. By iteratively evaluating the delayed-state covariance over successive time intervals, the resulting optimal filter can be implemented in an interval-wise backward recursion algorithm. Finally, numerical simulations are conducted to evaluate the tracking performance of the proposed optimal filter for the giant cavity. By comparing between the evolutions of Wigner functions of coherent and cat states and the filter, the effectiveness of the optimal filter is validated.

quant-pharXiv:2603.22710Mar 25, 20260 citations

Quantum Invariance

Vasil Dinev Penchev

Jan 1, 20200 citations

\mathrm{A}

for Arthurs--Kelly readout and

\mathrm{H}

for homodyne readout, the readout pattern selects the filtered sector, with

\mathrm{AH}

selecting position,

\mathrm{HA}

selecting momentum, and

\mathrm{AA}

retaining both. The hierarchy

0 < τ_{\mathrm{AA}} < \min \left\{ τ_{\mathrm{AH}}, τ_{\mathrm{HA}} \right\} < 1 = τ_{\mathrm{HH}}

shows that finite Arthurs--Kelly position records contract the gain-transferred covariance area. Our results identify calibrated uncorrelated Arthurs--Kelly readout as a measurement-level method for covariance-sensitive Gaussian filtering inside a fixed cluster graph.