Statistical estimation of the efficiency of quantum state tomography protocols.

A novel operational method for estimating the efficiency of quantum state tomography protocols is suggested. It is based on a priori estimation of the quality of an arbitrary protocol by means of universal asymptotic fidelity distribution and condition number, which takes minimal value for better protocol. We prove the adequacy of the method both with numerical modeling and through the experimental realization of several practically important protocols of quantum state tomography.

[1]  A. Lvovsky,et al.  Quantum state reconstruction of the single-photon Fock state. , 2001, Physical Review Letters.

[2]  V. I. Man'ko,et al.  Generalized tomographic maps , 2008, 0802.4140.

[3]  R. Penrose A Generalized inverse for matrices , 1955 .

[4]  Meng Khoon Tey,et al.  Statistical reconstruction of qutrits , 2004 .

[5]  S. Olivares,et al.  State reconstruction by on/off measurements , 2009, 0903.0104.

[6]  Marco Genovese,et al.  Experimental estimation of entanglement at the quantum limit. , 2009, Physical review letters.

[7]  Alessandro Zavatta,et al.  Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection , 2004, quant-ph/0406090.

[8]  Marco Genovese,et al.  Experimental reconstruction of photon statistics without photon counting. , 2005, Physical review letters.

[9]  C. Kurtsiefer,et al.  Experimental Polarization State Tomography using Optimal Polarimeters , 2006, quant-ph/0603126.

[10]  Giacomo Mauro D'Ariano,et al.  Generating qudits with d=3,4 encoded on two-photon states , 2005, quant-ph/0503227.

[11]  Yu. I. Bogdanov,et al.  Unified statistical method for reconstructing quantum states by purification , 2009 .

[12]  R. Kress Numerical Analysis , 1998 .

[13]  Gleb Maslennikov,et al.  Polarization states of four-dimensional systems based on biphotons , 2006 .

[14]  Alexei Gilchrist,et al.  Choice of measurement sets in qubit tomography , 2007, 0706.3756.

[15]  Andrew G. White,et al.  Measurement of qubits , 2001, quant-ph/0103121.

[16]  D. Kaszlikowski,et al.  Minimal qubit tomography , 2004, quant-ph/0405084.

[17]  M. Genovese Research on hidden variable theories: A review of recent progresses , 2005, quant-ph/0701071.