Collective versus local measurements in a qubit mixed-state estimation

2003/07/31 by E. Bagán, E. Bagan, M. Baig +4 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Random Matrices and Applications #quant-ph

paper · pdf · doi:10.1103/physreva.69.010304

published as Phys. Rev. A 69, 010304 (2004) · 4 pages, 1 figure, minor style changes, refs. added

arxiv created 2003/09/17 · openalex publication_date 2004/01/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04

Abstract

We discuss the problem of estimating a qubit mixed state. We give the optimal estimation that can be inferred from any given set of measurements. For collective measurements and for a large number N of copies, we show that the error in the estimation varies as 1/N. For local measurements, we focus on the simpler case of states lying on the equatorial plane of the Bloch sphere. We show that the error using plain tomography varies as 1/N^1/4, while our approach leads to an error proportional to 1/N^3/4.

Citations

• Quantum state estimation
• Fidelity for Mixed Quantum States
• Explicit computation of the Bures distance for density matrices
• Estimating mixed quantum states
• Optimal minimal measurements of mixed states
• Spin Flips and Quantum Information for Antiparallel Spins
• Optimal Purification of Single Qubits
• Adaptive quantum homodyne tomography

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