Speaker
Dr
Igor Ivanovic
(Carleton University)
Description
**On a minimal set of separable measurements
for a pure state determination in a two-qubit system.**
I.D. Ivanovic, Department of Physics, Carleton University
In this note I will address the problem of minimum set of separable measurements necessary to determine a pure state of a two-qubit system. A set of measurements for a complete state determination of a 2x2 system was given in[1], later it was expanded to arbitrary 2^(⊗n) in [2], and 2x2 was experimentally confirmed in [3]. Besides, a question of determining an unknown pure state was always present, and as recently as this year, it was discussed e.g. in [4] and [5]. In [5] a set of measurements was suggested aiming at determining an unknown pure state P,({P≥0,tr(P)=1,P^2=P }) of a two-qubit system. The set of nine operators allows pure state determination. The set of seven expected values for operators σ_i⊗σ_j ,tr(Pσ_i⊗σ_j ), plus normalization, where σ_i∈{I,σ_x,σ_y,σ_z } are Pauli matrices,
{ σ_x⊗I,σ_y⊗σ_x ,σ_y⊗σ_y ,σ_y⊗σ_z ,σ_z⊗σ_x ,σ_z⊗σ_y ,σ_z⊗σ_z }
does not. It is shown, by construction, that this particular choice of operators is inadequate. Some other possible solutions are discussed.
Email: igor@physics.carleton.ca
References:
[1] I.D. Ivanovic , in CISM Courses and lectures No.294 Proceedings of “Information complexity and control in quantum physics”, Editors Blaquiere et al –Udine,1985, Springer Verlag 1987, p 67-76.
[2] W. K. Wooters and B. D. Fields, Ann. Phys (NY) 191 (189) p.363
[3] Adamson R.B.A and A.M. Steinberg arxiv: 0808.0944v4[quant-ph]
[4] Chapman R. J. et al arxiv:1602.04194v1[quant-ph]
[5] Xian Ma, et al arXiv: 1601.05379v1 [quant-ph]
Author
Dr
Igor Ivanovic
(Carleton University)
