Optimal probabilistic estimation of quantum states

Abstract

We extend the concept of probabilistic unambiguous discrimination of quantum states to quantum state estimation. We consider a scenario where the measurement device can output either an estimate of the unknown input state or an inconclusive result. We present a general method how to evaluate the maximum fidelity achievable by the probabilistic estimation strategy. We illustrate our method on two explicit examples: estimation of a qudit from a pair of conjugate qudits and phase covariant estimation of a qubit from N copies. We show that by allowing for inconclusive results it is possible to reach estimation fidelity higher than that achievable by the best deterministic estimation strategy.

7 pages, 2 figures, ReVTeX4

References in corpus (20)

• Probabilistic cloning and identification of linearly independent quantum states
• Unambiguous Discrimination Between Linearly-Independent Quantum States
• Optimum Unambiguous Discrimination Between Linearly Independent Symmetric States
• Universal Algorithm for Optimal Estimation of Quantum States from Finite Ensembles
• Spin flips and quantum information for anti-parallel spins
• Quantum benchmark for storage and transmission of coherent states
• Unambiguous discrimination of mixed states
• Optimal state estimation for d-dimensional quantum systems
• Optimal discrimination of mixed quantum states involving inconclusive results
• Finding optimal strategies for minimum-error quantum-state discrimination
• Unambiguous discrimination between quantum mixed states
• Reduction Theorems for Optimal Unambiguous State Discrimination of Density Matrices
• Optimum unambiguous discrimination among linearly-independent non-orthogonal quantum states and its optical realization
• Optimal minimal measurements of mixed states
• Optimal probabilistic cloning and purification of quantum states
• Quantum reverse-engineering and reference frame alignment without non-local correlations
• Distinguishing mixed quantum states: Minimum-error discrimination versus optimum unambiguous discrimination
• Optimal quantum detectors for unambiguous detection of mixed states
• Collective versus local measurements on two parallel or antiparallel spins
• Optimal estimation of multiple phases

Cited by in corpus (20)

• Quantum limits on post-selected, probabilistic quantum metrology
• The power of symmetric extensions for entanglement detection
• Quantum replication at the Heisenberg limit
• Quantum Metrology Assisted with Abstention
• Memory effects in quantum metrology
• Optimal quantum operations at zero energy cost
• Quantum amplification and purification of noisy coherent states
• Beating noise with abstention in state estimation
• Postselected quantum hypothesis testing
• Optimal parameter estimation with a fixed rate of abstention
• Probabilistic metrology or how some measurement outcomes render ultra-precise estimates
• Probabilistic Metrology Attains Macroscopic Cloning of Quantum Clocks
• Probabilistic metrology defeats ultimate deterministic bound
• No-signaling bounds for quantum cloning and metrology
• Ultimate limits of approximate unambiguous discrimination
• State estimation from pair of conjugate qudits
• Postselected communication over quantum channels
• Phase Estimation of Coherent States with a Noiseless Linear Amplifier
• Characterizing non-deterministic noiseless linear amplifiers at the quantum limit
• Cost-effective temperature estimation strategies for thermal states with probabilistic quantum metrology