MAXIMUM LIKELIHOOD ESTIMATION FOR A GROUP OF PHYSICAL TRANSFORMATIONS

The maximum likelihood strategy for the estimation of group parameters allows one to derive in a general fashion optimal measurements, optimal signal states, and their relations with other information theoretical quantities. These results provide deep insight into the general structure underlying optimal quantum estimation strategies. The entanglement between representation spaces and multiplicity spaces of the group action appears to be the unique kind of entanglement which is really useful for the optimal estimation of group parameters.

[1]  R. Gill,et al.  State estimation for large ensembles , 1999, quant-ph/9902063.

[2]  Tobias J. Hagge,et al.  Physics , 1929, Nature.

[3]  G Chiribella,et al.  Efficient use of quantum resources for the transmission of a reference frame. , 2004, Physical review letters.

[4]  T. Rudolph,et al.  Classical and quantum communication without a shared reference frame. , 2003, Physical review letters.

[5]  Giacomo Mauro D'Ariano,et al.  Optimal phase estimation for qubits in mixed states (4 pages) , 2005 .

[6]  S. Massar,et al.  Optimal quantum clocks , 1998, quant-ph/9808042.

[7]  H. Yuen Quantum detection and estimation theory , 1978, Proceedings of the IEEE.

[8]  L. Ballentine,et al.  Probabilistic and Statistical Aspects of Quantum Theory , 1982 .

[9]  P. Zanardi,et al.  Virtual quantum subsystems. , 2001, Physical review letters.

[10]  Giulio Chiribella,et al.  Covariant quantum measurements that maximize the likelihood , 2004, quant-ph/0403083.

[11]  D. Bruß,et al.  Optimal Universal Quantum Cloning and State Estimation , 1997, quant-ph/9712019.

[12]  N. J. Cerf,et al.  Phase conjugation of continuous quantum variables , 2001 .

[13]  Asher Peres,et al.  Transmission of a Cartesian frame by a quantum system. , 2001, Physical review letters.

[14]  E. Bagan,et al.  Entanglement-assisted alignment of reference frames using a dense covariant coding , 2004 .

[15]  G. D’Ariano,et al.  Optimal estimation of group transformations using entanglement , 2005, quant-ph/0506267.

[16]  N. Gisin,et al.  Spin Flips and Quantum Information for Antiparallel Spins , 1999 .

[17]  Asher Peres,et al.  Covariant quantum measurements may not be optimal , 2001, quant-ph/0107114.

[18]  E. Bagan,et al.  Quantum reverse engineering and reference-frame alignment without nonlocal correlations , 2004 .

[19]  Massar,et al.  Optimal extraction of information from finite quantum ensembles. , 1995, Physical review letters.

[20]  E Bagan,et al.  Aligning reference frames with quantum states. , 2001, Physical review letters.

[21]  T. Rudolph,et al.  Decoherence-full subsystems and the cryptographic power of a private shared reference frame , 2004, quant-ph/0403161.

[22]  Leonard Susskind,et al.  Quantum mechanical phase and time operator , 1964 .

[23]  Viola,et al.  Theory of quantum error correction for general noise , 2000, Physical review letters.

[24]  William K. Wootters,et al.  A ‘Pretty Good’ Measurement for Distinguishing Quantum States , 1994 .

[25]  C. M. Care Probabilistic and Statistical Aspects of Quantum Theory: North-Holland Series in Statistics and Probability Vol 1 , 1983 .

[26]  Asymptotic estimation theory for a finite dimensional pure state model , 1997, quant-ph/9704041.