- Published 2003

We propose a linear optical scheme to transmit an unknown qubit robustly over bit-flip-error channel. To avoid the technical difficulty of the standard quantum error correction code, our scheme is based on the concept of errorrejection. The whole scheme is based on currently existing technology. An unknown qubit can be sent to a remote party robustly through a noisy channel if we use the quantum error correction code (QECC) [1–3], which plays a very important role in quantum computation and information [4]. The main idea there is first to encode the unknown qubit to an entangled state of many qubits and after the remote party receives this quantum code, he first decodes it and then obtains the original state faithfully. This is very different from the classical error correction since the unknown qubit in principle can not be copied [5] or observed exactly therefore the simple repetition code as used in classical coding is not applicable here. With the discovery of maximal polarization entangled state with the spontaneous parametric down conversion(SPDC) [6], linear optics method has been perhaps the most powerful tool for realizing the entanglement based quantum tasks. So far many of the tasks have been proposed or demonstrated with linear optics, such as quantum teleportation [7], universal ∗email: wang@qci.jst.go.jp 1 quantum cloning [8], quantum U-NOT operation [9], quantum entanglement concentration [10] and destructive quantum logic gate [11]. However, none of the quantum error correction code has been experimentally realized so far. Realizing either Shor’s 9-qubit code, Steane’s 7-qubit code or the 5-qubit code [3] is technically challenging by our current technology. All of them are based on the quantum entangled state with more than 5 qubits. This requires at least 3 pairs to be emitted by SPDC [6]. In a paper two years ago [13], the optical realization of quantum error rejection code over the bit-flip-error channel is considered. It was shown there [13] that the controlled-NOT operation in quantum error correction can be done probabilistically by a polarizing beam splitter and one can transfer a qubit robustly over a bit flip channel by teleportation. However, that scheme is based on the resource of three-photon GHZ state which is thought of as a type of impractical resource by our currently existing technology [13]. In particular, it was pointed in Ref. [13] that the post selection method given by [14,15] cannot be applied to the scheme proposed in [13]. In this letter, we propose a realization of quantum error rejection code over bit-flip-error channel with currently existing devices and resources in linear optics. To test the main points of the quantum error correction code we shall consider a simpler case here: transmitting an unknown qubit robustly over the bit flip channel using a smaller quantum code. We assume no phase flip noise for channel. Note that even in such a case there is no trivial way to complete the task: a repetition code is not allowed by the noncloning principle. To further simplify the experimental realization, instead of correcting the error, here we shall only reject the corrupted qubits by using an quantum error rejection code (QERC). Suppose Alice is given the following unknown qubit |u〉 = (cos(γ/2)|0〉+ e sin(γ/2)|1〉). (1) If the qubit is directly sent through the channel, the qubit state after passing through the bit flip channel will be ρa = (1− η)|u〉〈u|+ η|uf〉〈uf | (2) 2

@inproceedings{Xiangbin2003QuantumER,
title={Quantum error rejection code with spontaneous parametric down conversion},
author={Wang Xiang-bin},
year={2003}
}