Latest Article
A Method of Estimating the Eigenstates of Density Operator
GAO Jingliang
State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an 710071, Shaanxi, China
We describe a mathematical structure which corresponds to the eigenstates of a density operator. For an unknown density operator, we propose an estimating procedure which uses successive “yes/no” measurements to scan the Bloch sphere and approximately yields the eigenstates. This result is based on the quantum method of types and implies a relationship between the typical subspace and the Young frame.
Key words:quantum state estimation; eigenstate; density operator
CLC number:TP 305
[1] Bennett C H, Harrow A W, Lloyd S. Universal quantum data compression via nondestructive tomography[J]. Physical Review A, 2006, 73(3): 032336.
[2] James D F V, Kwiat P G , Munro W J, et al. Measurement of qubits [J]. Physical Review A, 2001, 64(5): 052312.
[3] Adamson R B A, Steinberg A M. Improving quantum state estimation with mutually unbiased bases[J]. Physical Review Letters, 2010, 105(3): 030406.
[4] Lvovsky A I, Raymer M G. Continuous-variable optical quantum-state tomography [J]. Reviews of Modern Physics, 2009, 81(1): 299.
[5] Gross D, Liu Y K, Flammia S T, et al. Quantum state tomography via compressed sensing [J]. Physical Review Letters, 2010, 105(15): 150401.
[6] Christandl M, Renner R. Reliable quantum state tomography[J]. Physical Review Letters, 2012, 109(12): 120403.
[7] Keyl M, Werner R F. Estimating the spectrum of a density operator [J]. Physical Review A, 2001, 64(5): 052311.
[8] Vidal G , Latorre J I, Pascual P, et al. Optimal minimal measurements of mixed states [J]. Physical Review A, 1999, 60(1): 126.
[9] Keyl M. Quantum state estimation and large deviations [J]. Reviews in Mathematical Physics, 2006, 18(1): 19-60.
[10] Bagan E, Ballester M A, Gill R D, et al. Optimal full estimation of qubit mixed states [J]. Physical Review A, 2006, 73(3): 032301.
[11] Schumacher B. Quantum coding [J]. Physical Review A, 1995, 51: 2738.
[12] Nielsen M A, Chuang I L. Quantum Computation and Quantum Information [M]. Cambridge : Cambridge University Press, 2010.
[13] Cover T M, Thomas J A. Elements of Information Theory [M]. New York: John Wiley & Sons, 2012.
[14] Csiszar I, Körner J. Information Theory: Coding Theorems for Discrete Memoryless Systems [M]. Cambridge: Cambridge University Press, 2011.