ISSN 1063-7397, Russian Microelectronics, 2006, Vol. 35, No. 1, pp. 47–52. © Pleiades Publishing, Inc., 2006.
Original Russian Text © S.N. Molotkov, 2006, published in Mikroelektronika, 2006, Vol. 35, No. 1, pp. 55–60.
Quantum mechanics opens up new vistas for infor-
mation processing and transmission, leading to a revo-
lutionary departure from classical techniques. The
basic unit of quantum information is called the quan-
tum bit (qubit) . It can be associated with any two-
level quantum system (such as a particle of spin 1/2),
two orthogonal states of which are assigned Boolean
zero and unity, respectively, as with a classical bit. One
difference is that the state of a qubit can be an arbitrary
superposition of states 0 and 1. Moreover, different
qubits are also subject to superposition and can form
entangled states. A qubit not known in advance cannot
be cloned . This is forbidden by the no-cloning the-
orem of quantum information science [2, 3].
It is possible to reliably measure an unknown state
of a bit (a two-state classical system) without disturbing
the state; strictly, the amount of disturbance can be
made as small as desired. Then any number of copies of
the state can be produced and transmitted.
With a qubit, the above procedure is impossible, for
any measurement disturbs a quantum system signiﬁ-
cantly . Furthermore, it is not possible to obtain reli-
able information on the state of a qubit in one measure-
ment. Nevertheless, the state of a qubit can be reliably
communicated for a long distance by making a replica
of the qubit, i.e., a faithful copy of the qubit up to a uni-
tary rotation, a procedure known as quantum teleporta-
. A replica and a clone of a qubit differ essen-
tially in that the party that has produced the replica is
unaware of its state, nor does it know the state of the
Quantum teleportation makes use of nonlocal quan-
tum correlations known as Einstein–Podolsky–Rosen
(EPR) correlations . To produce a replica of an
unknown state of a two-level quantum system (such as
a particle of spin 1/2), a party
ﬁrst generates a pair of
A qubit itself can in principle be transferred, but this is not possi-
ble in, e.g., the transmission between two nodes of a distributed
quantum cryptographically secure system.
two-level particles in an entangled state, or an EPR pair.
One of the particles is then sent to a party
, and the
other is retained by the party
. Afterward, the party
makes joint measurements on the EPR member and a
particle in an unknown state. This procedure is per-
formed in a Bell basis . A measurement has one of
four possible outcomes of equal probability, and any
outcome can be recognized reliably because the basis is
orthogonal (the postmeasurement state of the two parti-
cles is known). Owing to EPR correlations, the EPR
member possessed by the party
is brought to a state
that is a replica  of the state in which the other EPR
member occurs. The outcome is coded in two classical
bits (four outcomes are possible) that form a message to
be sent to the party
over a classical communication
channel. This message will tell the party
tary rotation must be applied to the EPR member in
order to obtain a state identical to the unknown input
state. Note that the party
remains unaware of the tele-
ported state, because the input state was destroyed.
Thus, the reliable teleportation of the state of a qubit
requires one EPR pair and a two-bit classical message.
Two qubits in an entangled state are called an entangled
bit (ebit) .
Recently, quantum teleportation has been demon-
strated experimentaly with a photon in an unknown
state of polarization .
The question naturally arises as to whether it is pos-
sible to teleport states that are characterized by contin-
uous dynamical variables, such as coordinate or
momentum, and therefore belong to an inﬁnite-dimen-
sional Hilbert space. With a continuous set of possible
measurement outcomes, one can hardly expect that
continuous-variable teleportation will be perfectly reli-
able and effective.
Vaidman  discussed the teleportation of a parti-
cle’s wave function in a one-dimensional case, the con-
tinuous dynamical variables being coordinate and
momentum. Effectively, the wave function of an EPR
pair was taken as
Quantum Teleportation with a Single-Photon Wave Packet
S. N. Molotkov
Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, Russia
Received August 10, 2005
—A scheme of energy–time quantum teleportation using an entangled photon pair is proposed. The
teleportation of a multimode state of a single-photon wave packet is investigated theoretically.