Fetching the paper…

Reading the bibliography…

2012

Symmetric minimal quantum tomography by successive measurements

Kalev, Amir, Shang, Jiangwei, Englert, Berthold-Georg

Original
PDF
Post on X

Understand

We consider the implementation of a symmetric informationally complete probability-operator measurement (SIC POM) in the Hilbert space of a d-level system by a two-step measurement process: a diagonal-operator measurement with high-rank outcomes, followed by a rank-1 measurement in a basis chosen in accordance with the result of the first measurement.

We find that any Heisenberg-Weyl group-covariant SIC POM can be realized by such a sequence where the second measurement is simply a measurement in the Fourier basis, independent of the result of the first measurement.
Furthermore, at least for the particular cases studied, of dimension 2, 3, 4, and 8, this scheme reveals an unexpected operational relation between mutually unbiased bases and SIC POMs; the former are used to construct the latter.
As a laboratory application of the two-step measurement process, we propose feasible optical experiments that would realize SIC POMs in various dimensions.

Symmetric minimal quantum tomography by successive measurements · Around

Built on

E. Prugovečki, Int. J. Theor. Phys. 16
1977
Earlier work this paper cites.
P. Busch, Int. J. Theor. Phys. 30
1991
Earlier work this paper cites.
M. Reck, A. Zeilinger, H.J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73
1994
Earlier work this paper cites.
S.G. Hoggar, Geom. Det. 69
1998
Earlier work this paper cites.
B.-G. Englert, C. Kurtsiefer, and H. Weinfurter, Phys. Rev. A 63
2001
Earlier work this paper cites.
G. M. D’Ariano, P. Perinotti, and M. F. Sacchi, J. Opt. B: Quantum Semiclassical Opt. 6
2004
Earlier work this paper cites.

Similar

J. Řeháček, B.-G. Englert, and D. Kaszlikowski, Phys. Rev. A 70
2004
Cited alongside, same era.
J.M. Renes, R. Blume-Kohout, A.J. Scott, and C.M. Caves, J. Math. Phys. 45
2004
Cited alongside, same era.
D.M. Appleby, J. Math. Phys. 46
2005
Cited alongside, same era.
A.J. Scott, J. Phys. A: Math. Gen. 39
2006
Cited alongside, same era.
A. Ling, K.P. Soh, A. Lamas-Linares, and C. Kurtsiefer, Phys. Rev. A 74
2006
Cited alongside, same era.
A.J. Scott and M. Grassl, J. Math. Phys. 51
2010
Cited alongside, same era.
A. Kalev, J. Shang, and B.-G. Englert, submitted
Cited in the paper.

Then

W.M. Pimenta, B. Marques, M.A. Carvalho, M.R. Barros, J.G. Fonseca, J. Ferraz, M. Terra Cunha, and S. Pádua, Opt. Express 18
2010
Later among the works it cites.
T. Durt, B.-G. Englert, I. Bengtsson, and K. Życzkowski, Int. J. Quant. Inf. 8
2010
Later among the works it cites.
I. Bengtsson, J. Phys.: Conf. Ser., 254
2010
Later among the works it cites.
G. Zauner, Int. J. Quant. Inf. 9
2011
Later among the works it cites.
Z.E.D. Medendorp, F.A. Torres-Ruiz, L.K. Shalm, G.N.M. Tabia, C.A. Fuchs, and A.M. Steinberg, Phys. Rev. A 83
2011
Later among the works it cites.
C. Carmeli, T. Heinosaari, and A. Toigo, arXiv:1111.3509 (2011)
Original
2011

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Later among the works it cites.