The precise estimation of unknown parameters in physical systems is
crucial to both scientific research and technological advancement.
Quantum metrology provides a framework to determine the ultimate
precision limits in estimating one or multiple parameters by exploiting
quantum mechanical principles and resources. In this talk, I discuss the
role of resources across different encoding paradigms and present a
universal framework that extends beyond the standard metrological
approach.<\/p>\n\n\n\n
First, we investigate the role of resources in the simultaneous
estimation of two phases encoded through arbitrary Hamiltonians with
arbitrary weight matrices. We show that the optimal probe is a coherent
superposition of the eigenstates corresponding to the largest and
smallest eigenvalues of the total encoding Hamiltonian, with a fixed \u2014
and not arbitrary \u2014 relative phase. Strikingly, this probe is
independent of the specific weight matrix, rendering it universally
optimal for estimating any pair of SU(2) parameters.<\/p>\n\n\n\n
Second, we examine whether the optimal probe is entangled when
estimating the noise parameter of a broad class of local quantum
encoding processes termed \u201cvector encoding,\u201d and if so, characterize its
nature and amount. We show that vector encoding is invariably
\u201ccontinuously commutative\u201d for optimal probes and use this structure to
characterize entanglement in representative cases, including local
depolarizing and bit-flip channels.<\/p>\n\n\n\n
Third, we consider estimation scenarios where the encoding is
implemented via a quantum measurement. Comparing strategies that retain
or discard measurement outcomes, we derive conditions under which
retaining outcomes improves precision. Furthermore, we establish
necessary and sufficient criteria for the simultaneous estimation of two
parameters encoded by an arbitrary quantum process and identify when the
quantum Cram\u00e9r\u2013Rao bound is valid and achievable.<\/p>\n\n\n\n
Finally, we propose a general framework to compare the values of a
physical quantity pertaining to two \u2014 or more \u2014 physical setups in the
finite-precision scenario. Instead of comparing sharp values, one
compares \u201cpatches\u201d on the real line, whose extents are universally
characterized by percentiles of the estimator\u2019s distribution, unlike the
standard deviation used in conventional metrology, and independent of
symmetry assumptions. As an application, we introduce the concept of
finite-precision cooling.<\/p>\n\n\n\n
The talk will be based on the following works:
(i) Role of phase of optimal probe in noncommutativity vs coherence in
quantum multiparameter estimation, arXiv:2507.04824
(ii) Optimal quantum precision in noise estimation: Is entanglement
necessary?, arXiv:2507.22413 (accepted in Phys. Rev. A)
(iii) Encoding parameters by measurement: Forgetting can be better in
quantum metrology, arXiv:2512.10541
(iv) Comparing physical quantities with finite-precision: beyond
standard metrology and an illustration for cooling in quantum processes,
arXiv:2510.24484<\/p>\n","protected":false},"excerpt":{"rendered":"
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