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DOI : 10.22661/AAPPSBL.2014.24.1.14
Optical Hybrid Quantum Teleportation
SHUNTARO TAKEDA AND AKIRA FURU
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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 KTiOPO4: 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

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[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).
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[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.

 
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