REVIEW 6 cited by
Multiparameter quantum estimation with Gaussian states: efficiently evaluating Holevo, RLD and SLD Cram\'er-Rao bounds
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
Multiparameter quantum estimation theory is crucial for many applications involving infinite-dimensional Gaussian quantum systems, since they can describe many physical platforms, e.g., quantum optical and optomechanical systems and atomic ensembles. In the multiparameter setting, the most fundamental estimation error (quantified by the trace of the estimator covariance matrix) is given by the Holevo Cram\'er-Rao bound (HCRB), which takes into account the asymptotic detrimental impact of measurement incompatibility on the simultaneous estimation of parameters encoded in a quantum state. However, the difficulty of evaluating the HCRB for infinite-dimensional systems weakens the practicality of applying this tool in realistic scenarios. In this paper, we introduce an efficient numerical method to evaluate the HCRB for general Gaussian states, by solving a semidefinite program involving only the covariance matrix and first moment vector and their parametric derivatives. This approach follows similar techniques developed for finite-dimensional systems, and hinges on a phase-space evaluation of inner products between observables that are at most quadratic in the canonical bosonic operators. From this vantage point, we can also understand symmetric and right logarithmic derivative scalar Cram\'er-Rao bounds under the same common framework, showing how they can similarly be evaluated as semidefinite programs. To exemplify the relevance and applicability of this methodology, we consider two paradigmatic applications, where the parameter dependence appears both in the first moments and in the covariance matrix of Gaussian states: estimation of phase and loss, and estimation of squeezing and displacement.
Forward citations
Cited by 6 Pith papers
-
Measurement incompatibility in Bayesian multiparameter quantum estimation
Measurement incompatibility at most doubles the minimum mean-square loss in Bayesian multiparameter quantum estimation, relative to the symmetric-posterior-mean bound.
-
Efficient learning of bosonic Gaussian unitaries
We present the first provably efficient algorithm, in both query and time complexity, for learning arbitrary multi-mode bosonic Gaussian unitaries under the energy-constrained diamond distance.
-
From the Hong-Ou-Mandel Effect to Quantum Sensing: Interference of Nonclassical Light with Partial Distinguishability and Noise
New Fock-state suppression laws, a partial-distinguishability extension of Gaussian Boson Sampling via overlap matrices, and a proof that measurement incompatibility survives even when probe incompatibility vanishes f...
-
Stochastic Quantum Information Geometry and Speed Limits at the Trajectory Level
The authors introduce a conditional quantum Fisher information whose average equals the standard QFI, and use it to derive single-trajectory speed limits with a possible negative interference term.
-
Multiparameter quantum estimation in a photon system induced by gravitational redshift
For a photon redshifted in curved spacetime and subjected to amplitude-damping or Ohmic-like dephasing, the Nagaoka bound is the tightest multiparameter estimation limit, with best precision in the strong-coupling and...
-
Beating joint quantum estimation limits with stepwise multiparameter metrology
Stepwise, one-parameter-at-a-time quantum estimation can beat the joint-estimation precision limit when the quantum Fisher information matrix is near singular.
Discussion (0). Continue with ORCID to comment.