Fisher-symmetric informationally complete measurements for pure states

Abstract

We introduce a new kind of quantum measurement that is defined to be symmetric in the sense of uniform Fisher information across a set of parameters that injectively represent pure quantum states in the neighborhood of a fiducial pure state. The measurement is locally informationally complete---i.e., it uniquely determines these parameters, as opposed to distinguishing two arbitrary quantum states---and it is maximal in the sense of a multi-parameter quantum Cramer-Rao bound. For a $d$-dimensional quantum system, requiring only local informational completeness allows us to reduce the number of outcomes of the measurement from a minimum close to but below $4d-3$, for the usual notion of global pure-state informational completeness, to $2d-1$.

v2 has additional discussion of Fisher-symmetric measurements for mixed states and an additional example of a PFSIC that consists of coin flipping between two orthonormal bases. Two new authors. Additional minor changes throughout

References in corpus (1)

• Information complementarity: A new paradigm for decoding quantum incompatibility

Cited by in corpus (20)

• Multi-parameter Quantum Metrology
• Optimal measurements for simultaneous quantum estimation of multiple phases
• Characterizing nonclassical correlations via local quantum Fisher information
• Deterministic realization of collective measurements via photonic quantum walks
• Incorporating Heisenberg's Uncertainty Principle into Quantum Multiparameter Estimation
• Quantum state estimation with nuisance parameters
• Ultimate precision of multi-parameter quantum magnetometry under the parallel scheme
• Universally Fisher-Symmetric Informationally Complete Measurements
• Reaching for the quantum limits in the simultaneous estimation of phase and phase diffusion
• Quantum correlations as probes of chaos and ergodicity
• Optimal joint estimation of multiple Rabi frequencies
• Information geometry under hierarchical quantum measurement
• Experimental demonstration of topological bounds in quantum metrology
• Incompatibility measures in multi-parameter quantum estimation under hierarchical quantum measurements
• Statistical analysis of low rank tomography with compressive random measurements
• Quantum-state estimation problem via optimal design of experiments
• Randomized measurements for multi-parameter quantum metrology
• Efficient Experimental Qudit State Estimation via Point Tomography
• Holevo Cramér-Rao bound: How close can we get without entangling measurements?
• Multiparameter quantum metrology with postselection measurements