Optical Hybrid Quantum Teleportation

SHUNTARO TAKEDA AND AKIRA FURUSAWA

DEPARTMENT OF APPLIED PHYSICS

SCHOOL OF ENGINEERING
THE UNIVERSITY OF TOKYO

1. INTRODUCTION

The laws of quantum mechanics enable optical communications
with ultimate capacity and allow quantum
computers to solve certain problems with unprecedented
speed. A key ingredient in such quantum information
processing is quantum teleportation [1]: the act of transferring
quantum information from a sender to a spatially
distant receiver without direct transmission of the physical
entity itself. Among various physical implementations
of quantum teleportation (e.g. trapped ions, atomic ensembles
and superconducting circuits), optical quantum
teleportation is the most promising candidate in terms of
applications to various quantum communication protocols.
It also opens a way to quantum logic gates for optical
quantum computers.

**Fig. 1:** Quantum teleportation of qubits (top) and CVs (bottom). In our hybrid teleportation
experiment, single-photon- based qubits are combined with CV quantum teleportation.

There are two complementary approaches to realize
optical quantum teleportation (Fig. 1). One is based on
quantum bits (qubits) in which the information is carried
by single photons; therefore, the basic techniques in
realization are single-photon generation, manipulation
and detection [1, 2]. The other is based on continuous
variables (CVs) in which the information is carried by the
amplitude and phase of optical waves [3-5]. In this case,
squeezing, modulation, and homodyne measurement
techniques play the central role. The conceptual difference
between these two approaches can be understood
by analogy with classical digital and analog signal processing.

Unfortunately, both approaches have drawbacks hindering
their direct applications to various teleportationbased
quantum information protocols due to experimental
inefficiencies and restrictions. The major drawbacks
of qubit teleportation are its low transfer efficiency and
the necessity of post-processing, whereas CV teleportation
would come with limited transfer fidelity (accuracy).
Recently, we succeeded in deterministically and unconditionally
teleporting photonic qubits by CV teleportation,
thereby overcoming the previous limitations in qubit
teleportation [6]. This "hybrid" experiment required
the combination of two conceptually different and previously
incompatible approaches. In this article, we start by
reviewing the basic concepts of teleportation, and then
explain the difference between the two approaches in
optical quantum teleportation. We then summarize our
recent accomplishment of combining both technologies
to realize the experiment of Ref. [6].

**Fig. 2:** Quantum teleportation circuit for qubits and CVs. The sender performs either photon
detection (qubit) or homodyne measurement (CV).

2. TWO APPROACHES IN QUANTUM
TELEPORTATION

A. Basic Concept

Let us first explain the basic concepts of quantum teleportation.
Quantum teleportation was first proposed for
qubits in 1993 [1], and later extended to CVs [3, 4]. The
procedure is the same for both schemes (Fig. 2). Here we
define the mode of the quantum state to be teleported as
mode 1. Quantum teleportation consists of the following
four steps:

(1) The sender and receiver share an ancillary entangled
state in mode 2 and 3 (EPR state).

(2) The sender performs a joint measurement on mode 1
and 2 (Bell-state measurement).

(3) The sender sends the measurement results to the receiver
as a classical message.

(4) The receiver performs a unitary operation on mode 3
based on the measurement results.

As a result, the quantum state in mode 1 is transferred to
mode 3 by means of the shared entanglement and clasical
communications. The nomenclature of "teleportation"
comes from the fact that the initial quantum state
in mode 1 inevitably vanishes, and the same quantum
state reappears in mode 3. In this way, quantum teleportation
evades violating the no-cloning theorem, which
prohibits making an exact copy of a quantum state.

B. Teleportation of Qubits

After the original proposal, Bouwmeester et al. reported
the first experimental realization of quantum teleportation
using single-photon-based qubits in 1997 [2].

Here, single photons which carry information are regarded
as one of the eigenstates of a photon number
operator where and are annihilation and
creation operators of quantized electromagnetic field.
The experiment of Ref. [2] used the polarization degree
of freedom of a single photon to encode a qubit:
. In this case, the
ancillary state in step (1) is polarization-entangled photons,

These states can be probabilistically created by parametric
down conversion (PDC), where a pump photon is
converted into two photons in a nonlinear crystal. The
Bell-state measurement in step (2) is performed using
a 50:50 beam splitter and photon detectors. Only when
the two detectors simultaneously detect photons, mode 3
becomes the same polarization qubit as ; in this case
the operation of step (4) is unnecessary.

However, this scheme involved two important drawbacks
in terms of applications. One is its low transfer efficiency
due to the intrinsically probabilistic nature of the PDC
and Bell-state measurement: this is estimated to be far
below 1%. Another is that this scheme requires postselection
of successful events by measuring the output qubits
after teleportation and discarding the unwanted events
[7]. The transferred qubits are destroyed in this process,
and thus cannot be used for further information processing.
This problem arises from the fact that the detectors
cannot detect the error of two pairs of photons occasionally
created in the PDC. Despite these inefficiencies, the
transfer fidelity of the post-selected successful events is
relatively high in this scheme.

C. Teleportation of Continuous-Variables

In 1998, Furusawa et al. demonstrated teleportation
using the amplitude and phase quadratures of a
light field, which is called CV quantum teleportation
[5]. Here, information is encoded in the quadratures,
corresponding to the operators and , in contrast to the photon numbers
used in qubit teleportation. The eigenstates of
serve as a continuous-variable basis to represent quantum
states in the infinite-dimensional Hilbert space:
Teleportation of such states requires
an ancillary EPR state entangled in quadrature basis:

The strength of CV teleportation is that an approximated
form of this EPR state can be prepared on-demand by squeezed light. The squeezed light is generated using
the same mechanism as PDC but with a strong pump.
Furthermore, complete Bell-state measurements can be
performed by two homodyne detectors each measuring and , followed by amplitude and phase modulations
for step (4). As a result, infinite-dimensional quantum
states are deterministically teleported from mode 1 to
mode 3, in contrast to the probabilistic scheme of qubit
teleportation.

The major drawback of CV teleportation is that the
transfer fidelity is limited due to the imperfect EPR state
generated from finitely-squeezed light. The fidelity approaches
unity in the limit of infinite squeezing, but this
would require infinite energy. Though efforts were made
to circumvent this drawback using higher squeezing levels,
transfer errors could not be eradicated.

Fig. 3: (a) Schematic diagram of hybrid quantum teleportation demonstrated by Takeda et al. [6]. (b), (c) Experimental results. The two-mode density
matrices are reconstructed both for the input and the output states in photon-number bases: Blue, red and green bars
correspond to the vacuum, qubit and two-photon components, respectively.

3. HYBRID QUANTUM TELEPORTATION

A. Proposal and Difficulties

As we have reviewed above, teleportation schemes of
qubits and CVs are technically different, and both have
fundamental deficiencies. In recent years, there has been
significant progress in combining both technologies with
a view to realizing hybrid protocols that overcome the current
limitations of optical quantum information processing
[8]. One of the most fundamental hybrid protocols is CV
quantum teleportation of photonic qubits. This protocol
enables deterministic teleportation of a qubit as opposed
to the probabilistic and inefficient scheme used thus far.
However, the experimental realization was too demanding
when the proposal was made around 2000 [9, 10].

There were three main reasons that made experimental
realization so demanding. First was that the high squeezing
levels required for the resource EPR state to teleport photonic qubits, which are highly non-classical states, was
beyond the technology of that time. Squeezing is typically
quantified by the reduction in noise level of the squeezed
quadrature below the shot noise level. The world record
for squeezing had been 6 dB [11], which was not enough
for such teleportation. We overcame this limitation by
finding a new nonlinear crystal periodically poled KTiOPO_{4}:
this produced 9 dB of squeezing in 2007 [12]. The
current world record for high-levelsqueezing is 13 dB,
reported with the same nonlinear medium [13].

Second is the bandwidth incompatibility. The typical
single-photon-based qubit has a broad bandwidth in frequency
domain because it is a wave packet, i.e., a pulse.
In contrast, a conventional CV teleportation device only
works for narrow frequency sidebands [5]. Therefore we
could not teleport a wave packet using the conventional
setup of CV teleportation. In order to overcome these
difficulties, we had to broaden the bandwidth of the CV
teleporter. We first broadened the bandwidth of the EPR
resource [14], and then used the broadband and highly
entangled EPR resource to teleport highly non-classical
wave packets of light in 2011 [15].

Third, we created a narrow-band qubit compatible with
the CV teleporter we had. Although the original proposals
of CV teleportation of qubits were for polarization
qubits [9, 10], we chose time-bin qubits. This consists of
two optical pulses separated temporally, and described
as a superposition of a photon in either pulse: The advantage of the time-bin qubit is that
it can be teleported using one CV teleporter, since the
two pulses have the same polarization, while polarization
qubit teleportation require two CV teleporters (one for
each polarization). We then developed generation and
characterization techniques for time-bin qubits with a
suitable frequency spectrum [16], which was a prerequisite
for teleportation. Now it is time for the hybrid quantum
teleportation.

B. Demonstration of Hybrid Teleportation

The combination of all state-of-the-art technologies
discussed above enabled our CV quantum teleportation
of time-bin qubits [6] (Fig. 3a). Our time-bin qubits
are conditionally created at a rate of ~5000 s^{-1}. The CV
teleporter always teleports these qubits on-demand, in
contrast to the former probabilistic scheme. In order to
verify the success of teleportation, we measure both the
input and output qubits, and then calculate the transfer
fidelity. We discovered a scheme to overcome the effects of finite squeezing levels by adjusting the gain in CV
teleportation. This allowed the qubit information to be
faithfully transferred [17]. This is another strength of the
hybrid teleportation scheme.

This hybrid technique enabled the realization of completely
deterministic quantum teleportation of photonic
qubits without post-selection. One of our experimental
results is given in Figs. 3b and 3c. The qubit components
(red bars) decrease from 69% in the input state to 42% at
the output. However, the output qubit components still
retain the original phase information of the superposition and at input, demonstrating that the
non-classical feature of the qubits are preserved during
the teleportation process. The overall transfer fidelity
ranged from 79 to 82 percent for four different qubits,
all of which exceed the classical limit of teleportation.
This quantitatively confirms our deterministic success.

This experiment required more than 500 mirrors and
beam splitters on an optical table of 4.2 m long and 1.5
m wide (Fig. 4). The beam power, pointing and optical
path length are both passively and actively stabilized
for better performance of the teleporter. In the future,
onchip integrated photonic circuits may improve the
performance as well as decrease the size and complexity
of our current experimental setup. See the online video
news for close-up views of our setup [18].

**Fig. 4:** Configuration of the teleportation experiment. Laser sources and non-linear optical
processes supply the qubit and the required entanglement. More than 500 mirrors and
beam splitters constitute the teleportation circuit.

4. CONCLUDING REMARKS

The development of hybrid technologies enabled us to
demonstrate deterministic teleportation of photonic
qubits for the first time. This is a decisive breakthrough
in the field of optical teleportation 16 years after the first
experimental realization. More advanced quantum communication
and computation protocols, impossible with
previous qubit teleportation, may be realized based on
this hybrid teleportation technology.
In addition to the hybrid teleportation experiment, we
are making headway in opening the doors to hybrid
quantum computing based on CV quantum teleportation.
As an example, we have succeeded in squeezing a
single photon by using a CV teleportation-based squeezer,
which is a typical CV quantum operation [19]. We
hope our work stimulates further development of hybrid
quantum information processing to overcome the current
limitations in both the qubit and CV regimes.

References

[1] C. H. Bennett et al., Physical Review Letters 70, 1895 (1993).

[2] D. Bouwmeester et al., Nature 390, 575 (1997).

[3] L. Vaidman, Physical Review A 49, 1473 (1994).

[4] S. L. Braunstein and H. J. Kimble, Physical Review Letters 80, 869 (1998).

[5] A. Furusawa et al., Science 282, 706 (1998).

[6] S. Takeda et al., Nature 500, 315 (2013).

[7] S. L. Braunstein and H. J. Kimble, Nature 394, 840 (1998).

[8] A. Furusawa and P. van Loock, Quantum Teleportation and Entanglement:
A Hybrid Approach to Optical Quantum Information Processing (Wiley,
New York, 2011).

[9] R. E. S. Polkinghorne and T. C. Ralph, Physical Review Letters 83, 2095
(1999).

[10] T. Ide et al., Physical Review A 65, 012313 (2001).

[11] E. S. Polzik et al., Applied Physics B 55, 279 (1992).

[12] Y. Takeno et al., Optics Express 15, 4321 (2007).

[13] T. Eberle et al., Physical Review Letters 104, 251102 (2010).

[14] N. Takei et al., Physical Review A 74, 060101(R) (2006).

[15] N. Lee et al.,
Science 332, 330 (2011).

[16] S. Takeda et al., Physical Review A 87, 043803 (2013).

[17] S. Takeda et al., Physical Review A 88, 042327 (2013).

[18] http://www.diginfo.tv/v/13-0068-f-en.php

[19] Y. Miwa et al., arXiv:1209.2804.

**Shuntaro Takeda** received his master's degree
in applied physics from the University of Tokyo in
2012. He is currently a PhD candidate in applied
physics at the University of Tokyo, and also a
research fellow of the Japan Society for the
Promotion of Science. His research field is optical
quantum information processing based on
continuous-variable quantum teleportation.

**Akira Furusawa** is a professor at the University
of Tokyo. He received his PhD from the University
of Tokyo in 1991. After working on the
experiment of continuous-variable quantum
teleportation at the California Institute of
Technology from 1996 to 1998, he joined the
University of Tokyo as an associate professor in
2000, and became a full professor in 2007.