We derive the optimal trade-off between the estimation fidelity and the fidelity of the state after the estimation for a single copy of an unknown pure state of a $d$ -level system belonging to a specific subset of the set of all pure states. The set of states to be considered here is formed by all pure states of a $d$ -level system produced by $d$ -independent phase shifts of some reference state. We also propose a measurement scheme realizing such an optimal partial estimation of multiple phases in which the trade-off between the fidelities can be controlled by the state of the ancilla.We derive the optimal trade-off between the estimation fidelity and the fidelity of the state after the estimation for a single copy of an unknown pure state of a $d$-level system belonging to a specific subset of the set of all pure states. The set of states to be considered here is formed by all pure states of a $d$-level system produced by $d$-independent phase shifts of some reference state. We also propose a measurement scheme realizing such an optimal partial estimation of multiple phases in which the trade-off between the fidelities can be controlled by the state of the ancilla.

Physical Review AJul 12, 200529 citations

Optimal measurements in phase estimation: simple examples

Tomasz Wasak, Augusto Smerzi, Luca Pezzè +1 more

arXiv:1310.2844Quantum Information ProcessingFeb 4, 201613 citations

We derive the optimal trade-off between the estimation fidelity and the fidelity of the state after the estimation for a single copy of an unknown pure state of a

d

-level system belonging to a specific subset of the set of all pure states. The set of states to be considered here is formed by all pure states of a

d

-level system produced by

d

-independent phase shifts of some reference state. We also propose a measurement scheme realizing such an optimal partial estimation of multiple phases in which the trade-off between the fidelities can be controlled by the state of the ancilla.