State estimation on correlated copies

Abstract

State estimation is usually analyzed in the situation when copies are in a product state, either mixed or pure. We investigate here the concept of state estimation on correlated copies. We analyze state estimation on correlated N qubit states, which are permutationally invariant. Using a correlated state we try to estimate as good as possible the direction of the Bloch vector of a single particle reduced density matrix. We derive the optimal fidelity for all permutation invariant states. We find the optimal state, which yields the highest estimation fidelity among the states with the same reduced density matrix. Interestingly this state is not a product state. We also point out that states produced by optimal universal cloning machines are the worst form the point of view of estimating the reduced density matrix.

9 pages, 1 figure. Previous results were correct only in special cases. New correct formula for the fidelity has an absolute value sign added. New states optimal for state estimation are derived. Slightly changed notation

References in corpus (5)

• Efficient use of quantum resources for the transmission of a reference frame
• Optimal encoding and decoding of a spin direction
• Collective vs local measurements in qubit mixed state estimation
• Optimal scheme for estimating a pure qubit state via local measurements
• Communication of Spin Directions with Product States and Finite Measurements

Cited by in corpus (11)

• Permutationally invariant state reconstruction
• Asymptotic quantum cloning is state estimation
• Investigating macroscopic quantum superpositions and the quantum-to-classical transition by optical parametric amplification
• Efficient Quantum Compression for Ensembles of Identically Prepared Mixed States
• Experimental test of the no signaling theorem
• Optimal convex approximations of quantum states
• Erasable and unerasable correlations
• The Quantum Cocktail Party
• Quantum state decorrelation
• Superbroadcasting and classical information
• How to hide a secret direction