Role of phase of optimal probe in noncommutativity vs coherence in quantum multiparameter estimation

• URL: http://arxiv.org/abs/2507.04824v1
• Date: Mon, 07 Jul 2025 09:42:56 GMT
• Title: Role of phase of optimal probe in noncommutativity vs coherence in quantum multiparameter estimation
• Authors: Ritopriyo Pal, Priya Ghosh, Ahana Ghoshal, Ujjwal Sen,
• Abstract summary: We investigate simultaneous estimation of two phases encoded through arbitrary qubit Hamiltonians.<n>We also consider single-qutrit probes, for which the encoding Hamiltonians are chosen as SU(2) generators.<n>We find that in both the qubit and qutrit scenarios, the optimal probe is a coherent superposition of the eigenstates corresponding to the largest and smallest eigenvalues.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum multiparameter estimation offers a framework for the simultaneous estimation of multiple parameters, pertaining to possibly noncommutating observables. While the optimal probe for estimating a single unitary phase is well understood - being a pure state that is an equal superposition of the eigenvectors of the encoding Hamiltonian corresponding to its maximum and minimum eigenvalues - the structure of optimal probes in the multiparameter setting remains more intricate. We investigate the simultaneous estimation of two phases, each encoded through arbitrary qubit Hamiltonians, using arbitrary weight matrices, and considering single-qubit probes. We also consider single-qutrit probes, for which the encoding Hamiltonians are chosen as SU(2) generators. We find that in both the qubit and qutrit scenarios, 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 - and not arbitrary - relative phase. Remarkably, this optimal probe is independent of the specific choice of weight matrix, making it a universally optimal input state for the estimation of any pair of SU(2) parameters, which can be reparameterized to the phase estimation problem. Furthermore, we show that this probe also maximizes the determinant of the quantum Fisher information matrix, providing a handy tool for identifying the optimal probe state. We also examine the role of commutativity between the generators of the unitary encodings. Our results demonstrate that a high degree of commutativity degrades the achievable precision, rendering estimation infeasible in the extreme case. However, maximal noncommutativity does not necessarily yield optimal precision.

Related papers

• Entanglement-Constrained Quantum Metrology: Rapid Low-Entanglement Gains, Tapered High-Level Growth [0.0]
  We consider the potential experimental limitation on probe entanglement, and find a relation between achievable precision and initial probe entanglement.<n>For two-qubit probes, we analytically derive an exact relationship between the entanglement-constrained optimal quantum Fisher information and the limited initial entanglement.<n>We identify the specific states that realize maximum precision in these scenarios.
  arXiv  Detail & Related papers  (2025-07-04T12:09:37Z)
• Precision in estimating independent local fields: attainable bound and indispensability of genuine multiparty entanglement [0.0]
  We show that estimation of independent multiple field strengths of a local Hamiltonian requires the utility of genuine multipartite entangled state as the input probe.<n>For an arbitrary weight matrix and an arbitrary multiparty local encoding Hamiltonian, we prove that using a probe that is in any mixed state provides a precision lower than that obtainable using pure states.
  arXiv  Detail & Related papers  (2024-07-29T16:12:04Z)
• Finding the optimal probe state for multiparameter quantum metrology using conic programming [61.98670278625053]
  We present a conic programming framework that allows us to determine the optimal probe state for the corresponding precision bounds. We also apply our theory to analyze the canonical field sensing problem using entangled quantum probe states.
  arXiv  Detail & Related papers  (2024-01-11T12:47:29Z)
• Quantum multiparameter estimation with graph states [6.152619905686453]
  In the SU(2) dynamics, it is especially significant to achieve a simultaneous optimal multi parameter estimation. We propose a simultaneous multi parameter estimation scheme that investigates evolution in SU(N) dynamics. We prove that the graph state is the optimal state of quantum metrology, a set of optimal measurement basic can be found, and the precision limit of multi parameter estimation can attain the quantum Cram'er-Rao bound.
  arXiv  Detail & Related papers  (2023-06-05T00:50:24Z)
• Optimal Generators for Quantum Sensing [0.0]
  We show that the maximal sensitivity using a given quantum state is determined by the largest eigenvalue of the quantum Fisher information matrix (QFIM) Since we optimize the process of parameter encoding rather than focusing on state preparation protocols, our scheme is relevant for any quantum sensor.
  arXiv  Detail & Related papers  (2023-05-24T20:42:38Z)
• Importance sampling for stochastic quantum simulations [68.8204255655161]
  We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
  arXiv  Detail & Related papers  (2022-12-12T15:06:32Z)
• Tight Cram\'{e}r-Rao type bounds for multiparameter quantum metrology through conic programming [61.98670278625053]
  It is paramount to have practical measurement strategies that can estimate incompatible parameters with best precisions possible. Here, we give a concrete way to find uncorrelated measurement strategies with optimal precisions. We show numerically that there is a strict gap between the previous efficiently computable bounds and the ultimate precision bound.
  arXiv  Detail & Related papers  (2022-09-12T13:06:48Z)
• Quantum probes for the characterization of nonlinear media [50.591267188664666]
  We investigate how squeezed probes may improve individual and joint estimation of the nonlinear coupling $tildelambda$ and of the nonlinearity order $zeta$. We conclude that quantum probes represent a resource to enhance precision in the characterization of nonlinear media, and foresee potential applications with current technology.
  arXiv  Detail & Related papers  (2021-09-16T15:40:36Z)
• Bosonic field digitization for quantum computers [62.997667081978825]
  We address the representation of lattice bosonic fields in a discretized field amplitude basis. We develop methods to predict error scaling and present efficient qubit implementation strategies.
  arXiv  Detail & Related papers  (2021-08-24T15:30:04Z)
• High Probability Complexity Bounds for Non-Smooth Stochastic Optimization with Heavy-Tailed Noise [51.31435087414348]
  It is essential to theoretically guarantee that algorithms provide small objective residual with high probability. Existing methods for non-smooth convex optimization have complexity bounds with dependence on confidence level. We propose novel stepsize rules for two methods with gradient clipping.
  arXiv  Detail & Related papers  (2021-06-10T17:54:21Z)
• Quantum probes for universal gravity corrections [62.997667081978825]
  We review the concept of minimum length and show how it induces a perturbative term appearing in the Hamiltonian of any quantum system. We evaluate the Quantum Fisher Information in order to find the ultimate bounds to the precision of any estimation procedure. Our results show that quantum probes are convenient resources, providing potential enhancement in precision.
  arXiv  Detail & Related papers  (2020-02-13T19:35:07Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.