We show that the quantum state diffusion equation of Gisin and Percival, driven by complex Wiener noise, is equivalent up to a global stochastic phase to quantum trajectory models. With an appropriate feedback scheme, we set up an analog continuous measurement model which exactly simulates the Gisin-Percival quantum state diffusion.
REFERENCES
1.
J.
Kupsch
, “Open quantum systems
,” in Decoherence and the Appearance of a Classical World in Quantum Theory
, edited by E.
Joos
, H. D.
Zeh
, C.
Kiefer
, D. J. W.
Giulini
, J.
Kupsch
, and I.-O.
Stamatescu
(Springer-Verlag
, Berlin, Heidelberg
, 2003
), Chap. 7.2.
N.
Gisin
and I. C.
Percival
, J. Phys. A: Math. Gen.
25
, 5677
–5691
(1992
).3.
H. M.
Wiseman
and G. J.
Milburn
, Phys. Rev. A
47
, 1652
–1666
(1993
).4.
H. M.
Wiseman
and G. J.
Milburn
, Quantum Measurement and Control
(Cambridge University Press
, 2009
).5.
V. P.
Belavkin
, Lect. Notes Control Inf. Sci.
121
, 245
–265
(1989
).6.
V. P.
Belavkin
, Radiotechnika Electronika
25
, 1445
–1453
(1980
);V. P.
Belavkin
, “Stochastic calculus of input-output processes and non-demolition filtering
,” in Reviews of the Newest Achievements in Science and Technology
, Volume 36 of Current Problems of Mathematics, edited by A. S.
Holevo
(VINITI
, 1989
), pp. 29
–67
;V. P.
Belavkin
, J. Multivar. Anal.
42
, 171
–201
(1992
).7.
L. M.
Bouten
, M. I.
Guţă
, and H.
Maassen
, J. Phys. A
37
, 3189
–3209
(2004
).8.
L.
Bouten
and R.
van Handel
, “Quantum filtering: A reference probability approach
,” e-print arXiv:math-ph/0508006 (unpublished).9.
L.
Bouten
, R.
van Handel
, and M. R.
James
, SIAM J. Control Optim.
46
, 2199
–2241
(2007
).10.
R. L.
Hudson
and K. R.
Parthasarathy
, Commun. Math. Phys.
93
, 301
(1984
).11.
C. W.
Gardiner
and M. J.
Collett
, Phys. Rev. A
31
, 3761
(1985
).12.
K. R.
Parthasarathy
, An Introduction to Quantum Stochastic Calculus
(Birkhauser
, 1992
).13.
H. J.
Carmichael
, An Open Systems Approach to Quantum Optics
, Lecture Notes in Physics (Springer
, 1993
), Vol. 18.14.
J.
Dalibard
, Y.
Castin
, and K.
Molmer
, Phys. Rev. Lett.
68
, 580
–583
(1992
).15.
C. W.
Gardiner
and P.
Zoller
, Quantum Noise
(Springer
, Berlin
, 2000
).16.
G. C.
Ghirardi
, P.
Pearle
, and A.
Rimini
, Phys. Rev. A
42
, 78
–89
(1990
).17.
P.
Goetsch
and R.
Graham
, Phys. Rev. A
50
, 5242
–5255
(1994
).18.
D.
Gatarek
and N.
Gisin
, J. Math. Phys.
32
(8
), 2152
–2157
(1991
).19.
S.
Bochner
and K.
Chandrasekharan
, Fourier Transforms
(Princeton University Press
, 1949
).20.
K. R.
Parthasarathy
and A. R.
Usha Devi
, “From quantum stochastic differential equations to Gisin-Percival state diffusion
,” preprint arXiv:1705.00520v1.21.
C. M.
Mora
and R.
Rebolledo
, Ann. Appl. Probab.
18
(2
), 591
–619
(2008
).22.
F.
Fagnola
and C.
Mora
, Indian J. Pure Appl. Math.
46
(4
), 399
–414
(2015
).23.
F.
Fagnola
and C. M.
Mora
, ALEA, Lat. Am. J. Probab. Math. Stat.
10
(1
), 191
–223
(2013
).24.
J.
Gough
and M. R.
James
, Commun. Math. Phys.
287
, 1109
(2009
).25.
J.
Gough
and M. R.
James
, IEEE Trans. Autom. Control
54
, 2530
(2009
).26.
J. E.
Gough
, “Non-Markovian quantum feedback networks II: Controlled flows
,” J. Math. Phys.
58
, 063517
(2017
).© 2018 Author(s).
2018
Author(s)
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