Systematic and statistical errors in homodyne measurements of the density matrix

Abstract

We study both systematic and statistical errors in radiation density matrix measurements. First we estimate the minimum number of scanning phases needed to reduce systematic errors below a fixed threshold. Then, we calculate the statistical errors, intrinsic in the procedure that gives the density matrix. We present a detailed study of such errors versus the detectors quantum efficiency $\eta$ and the matrix indexes in the number representation, for different radiation states. For unit quantum efficiency, and for both coherent and squeezed states, the statistical errors of the diagonal matrix elements saturate for large n. On the contrary, off-diagonal errors increase with the distance from the diagonal. For non unit quantum efficiency the statistical errors along the diagonal do not saturate, and increase dramatically versus both $1-\eta$ and the matrix indexes.

16 pages, LaTeX, 9 postscript figures included

Cited by in corpus (11)

• Maximum-likelihood estimation of the density matrix
• Quantum Tomography
• Systematic errors in current quantum state tomography tools
• Self-homodyne tomography of a twin-beam state
• Comment on "Loss-error compensation in quantum-state measurements"
• Adaptive Quantum Homodyne Tomography
• Evading Vacuum Noise: Wigner Projections or Husimi Samples?
• Quantum homodyne tomography with a priori constraints
• Secure Coherent-state Quantum Key Distribution Protocols with Efficient Reconciliation
• Statistical uncertainty in quantum optical photodetection measurements
• Quantum tomography of mesoscopic superpositions of radiation states