Saturating the quantum Cramér–Rao bound using LOCC
Sisi Zhou, Chang-Ling Zou, Liang Jiang
Abstract
Abstract The quantum Cramér–Rao bound (QCRB) provides an ultimate precision limit allowed by quantum mechanics in parameter estimation. Given any quantum state dependent on a single parameter, there is always a positive-operator valued measurement (POVM) saturating the QCRB. However, the QCRB-saturating POVM cannot always be implemented efficiently, especially in multipartite systems. In this paper, we show that the POVM based on local operations and classical communication is QCRB-saturating for arbitrary pure states or rank-two mixed states with varying probability distributions over fixed eigenbasis. Local measurements without classical communication, however, is not QCRB-saturating in general.
Topics & Concepts
POVMMultipartiteLOCCLimit (mathematics)State (computer science)QuantumMathematicsQuantum stateQuantum mechanicsUpper and lower boundsQuantum systemPhysicsQuantum measurementStatistical physicsQuantum discordQuantum operationW stateMeasure (data warehouse)Quantum entanglementQuantum limitMultipartite entanglementQuantum channelQuantum processClassical limitBound stateQuantum informationQuantum statistical mechanicsQuantum teleportationQuantum information scienceQuantum Information and CryptographyQuantum Computing Algorithms and ArchitectureQuantum Mechanics and Applications