A particularly startling discovery by Bennett et al. is the possibility for teleportation of a quantum state, whereby an unknown state of a spin-1/2 particle is transported by Alice from a sending station to Bob at a receiving terminal by conveying 2 bits of classical information. Beyond the context of dichotomic variables, Vaidman has analyzed teleportation of the wave function of a one-dimensional particle in a beautiful variation of the original EPR paradox. Here we extend Vaidman's analysis to incorporate finite (nonsingular) degrees of correlation among the relevant particles

Braunstein, S. L.

Furusawa, A.

Georgiades, N. P.

Kimble, H. J.

Sorensen, Y.

Caltech Authors - Main

WEDNESDAY AFTERNOON / IQEC'98 / 133 
White 
Light 
670 nm 
Laser 
670 nm Jris 
Filter ~ "" 
Fiber optic 
(single-mode) 
QWHl Fig. 2. Two methods to prepare nonpure quantum states. The simplest, a filtered white-light 
source, produces a completely unpolarized state. The laser-diode version allows one to make an arbitrary 
quantum state by varying the input polarization to the polarizing Mach-Zehnder interferometer (which 
is unbalanced much more than the coherence length of the laser). 
1. W.K. Wooters, W.H. Zurek, Phys. Rev. D 
19, 473 (1979). 
2. D.M. Greenberger, A. Yasin, Phys. Lett. A 
128, 391 (1988). 
3. B.-G. Englert, Phys. Rev. Lett. 77, 2154 
(1996). 
4. P. Mittlestaedt, A. Prieur, R. Schieder, 
Found. Phys. 17, 891 (1987). 
QWH2 2:45 pm 
Teleportation of continuous quantum 
variables 
S.L. Braunstein, H.J. Kimble, Y. Sorensen, 
A. Furusawa, N.Ph. Georgiades, Norman 
Bridge Laboratory of Physics, California 
Institute of Technology, 12-33, Pasadena, 
California 91125 
A particularly startling discovery by Bennett et 
al.' is the possibility for teleportation of a 
quantum state, whereby an unknown state of a 
spin-! particle is transported by 'Alice' from a 
sendibg station to 'Bob' at a receiving terminal 
by conveying 2 bits of classical information.1 
Beyond the context of dichotomic variables, 
Vaidman has analyzed teleportation of the 
wave function of a one-dimensional particle in 
a beautiful variation of the original EPR para-
dox.2 In this case, the nonlocal resource shared 
by Alice and Bob is the EPR state with perfect 
correlations in both position and momentum. 
Here we extend Vaidman's analysis to incor-
porate finite (nonsingular) degrees of correla-
tion among the relevant particles and to in-
clude inefficiencies in the measurement 
process. We quantify the "quality" of the re-
sulting protocol for teleportation with the first 
explicit computation of the fidelity of en-
tanglement for a process acting on an infinite 
dimensional Hilbert space. 3 Finally, we report 
on our experimental progress towards quan-
tum teleportation of continuous quantum 
variables, where now the entangled state 
shared by Alice and Bob is a highly squeezed 
two-mode state of the electromagnetic field, 
with the quadrature amplitudes of the field 
playing the roles of position and momentum 
as in Ou et al.4 Note that up until now, all 
experimental proposals for teleportation have 
involved dichotomic variables. 
As shown schematically in Fig. 1, an un-
known input state described by the Wigner 
function W;n( ex) is to be teleported to a remote 
station, with the teleported (output) state de-
noted by wou,(ex). Alice (at the sending sta-
tion) and Bob (at the receiving terminal) have 
previously arranged to share an entangled 
state, which is sent along paths 1 and 2, de-
scribed by the Wigner function WEPR(ex"ex2). 
The classical results (ix,' iPb) oflinear measure-
ments performed by Alice are sent to Bob and 
allow him to construct the teleported state 
W0 u,( ex2) from component 2 of the EPR state. 
Note that our analysis includes finite efficien-
cies in detection and propagation, as well as the 
finite degree of correlation of the state 
WEPR(ex1>exz).3 
To illustrate the protocol, we consider tele-
portation of the coherent superposition state 
[l\I) et:. [ + ex) + ei<f>[ - ex), with corresponding 
Wigner function W;n(a) illustrated in Fig. 2a. 
The teleported Wigner function W0 u,(ex) is 
shown in Fig. 2b for parameters corresponding 
to - lOdB of squeezing with overall detection 
efficiency 112 = 0.99, which should be com-
pared with the parameters of Ref. 6 (namely 
-6 dB of squeezing and detectors with effi-
ciency 'T]2 = 0.99 ± 0.02). The quantum char-
acter of the state survives teleportation, includ-
ing negative values for wout associated with 
quantum interference for the off-diagonal 
QWH2 Fig. 1. Illustration of setup for quan-
tum teleporation of an unknown quantum state 
W;n( ex) from Alice's sending station S to Bob's 
receiving terminal R, resulting in the teleported 
output state W0 j ex). 
a) b) c) 
QH2 Fig. 2. (a) Wigner function W;n(a) for 
the input state ltJi>"' l+a>+ei<l>[-a>, with a= 
l.5i. (b) Teleported output state W0 u,(a) for 
squeezing parameter r = 1.15 and efficiency 112 = 
0.99. (c) Output state W::uia) for classical tele-
portation with WEPR replaced by the vacuum 
state. 
components of Pin· For comparison, note that 
for classical teleporation, YV:;1ut consists of the 
incoherent superposition of two distributions 
centered at ±ex, as shown in Fig. 2c. 
We are currently working to realize a labo-
ratory implementation of our teleportation 
scheme based upon extensions of Ref. 4 and 6. 
The progress of this endeavor will be de-
scribed. 
SLB is funded in part by a Humboldt Fel-
lowship. We acknowledge support from 
DARPA via the QUIC Institute administered 
by ARO, from the Office of Naval Research, 
and from the National Science Foundation. 
1. C.H. Bennett, G. Brassard, C. Crepeau, R. 
Jozsa, A. Peres, W.K. Wootters, Phys. Rev. 
Lett. 70, 1895 (1993). 
2. L. Vaidman, Phys. Rev.A49, 1473 (1994). 
3. S.L. Braunstein, H.J. Kimble, Phys. Rev. 
Lett. (submitted, 1997). 
4. (a) Z.Y. Ou, S.F. Pereira, H.J. Kimble, K.C. 
Peng, Phys. Rev. Lett. 68, 3663(1992); (b) 
Appl. Phys. B 55, 265 (1992). 
5. L. Davidovich, N. Zagury, M. Brune, J.M. 
Raimond, S. Haroche, Phys. Rev. A 50, 
R895 
QWH3 3:00 pm 
Which-way information in an atom 
interferometer 
G. Rempe, S. Diirr, T. Nonn, Universitiit 
Konstanz, Fakultiit Physik, 78457 Konstanz, 
Germany 
Duality is often used to highlight the difference 
between quantum mechanics and classical 
physics. It expresses the fact, that observation 
ofinterference and which-way information are 
mutually exclusive. It has been vividly dis-
cussed 1•2 recently, whether or not the loss of 
interference in an arbitrary which-way experi-
ment can always be attributed to mechanical 
forces. While a lot of Gedanken experiments 
have been proposed, there are only a few ex-
perimental results. We now report on an ex-
periment that addresses precisely this ques-
tion.' 
Our atom interferometer is based on Bragg 
scattering from standing light waves. A first 
standing light wave splits the incoming beam 


Teleportation of continuous quantum variables

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Teleportation of continuous quantum variables

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