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 error rejection. The whole scheme is based on currently existing technology.
An optical scheme for the error-free transfer of quantum information through a noisy quantum channel is proposed. The scheme is inspired by quantum error-correction schemes, but it avoids the currently unfeasible requirement for a controlled-NOT operation between single photons. The quantum communication scheme presented here rejects bit-flip errors instead of correcting them and combines quantum-measurement properties of three-particle entangled states with properties of the quantum teleportation protocol.
An optical scheme for the reliable transfer of quantum information through a noisy quantum channel is proposed. The scheme is inspired by quantum error-correction protocols, but it avoids the currently infeasible requirement for a controlled-NOT operation between single photons. The quantum communication scheme presented here rejects single bit-flip errors instead of correcting them and combines quantum-measurement properties of three-particle entangled (GHZ) states with properties of quantum teleportation.
The natural choice of physical qubit for quantum communication is the photon: a photon can be transmitted quickly from the sender to a distant receiver and the technology for creating, manipulating, distributing, and measuring light pulses is well established. Many of these classical techniques can also be employed for quantum communication protocols. We will therefore focus our attention on optical setups for quantum communication. We will study a number of optical setups in the next few sections and use the conventions introduced in Chapter 4 to analyze them. In particular, we will assume that the qubits are encoded in the degrees of freedom of a single photon. Some of the main technical challenges in quantum communication arise from this need to work with single photon pulses. For instance, photons do not interact with each other in vacuum or linear media, and interactions between two photons in non-linear optical media are relatively small, so that realizing entangling two photon gates via coherent interactions is a challenging task. The quantum communication schemes discussed here circumvent this technical problem to a large extent. They only use non-linear optical materials for parametric down-conversion to create Bell-pairs of photons and then exploit standard linear optical devices and photo-detectors to manipulate them. No further non-linear entangling gates are required. Parametric down-conversion In non-linear optical media a single photon can be down-converted into a pair of photons. In this coherent process the incoming photon is destroyed and two photons of lower energy are created.
We propose a scheme for quantum error correction using robust continuous variable probe modes, rather than fragile ancilla qubits, to detect errors without destroying data qubits. The use of such probe modes reduces the required number of expensive qubits in error correction and allows efficient encoding, error detection, and error correction. Moreover, the elimination of the need for direct qubit interactions significantly simplifies the construction of quantum circuits. We will illustrate how the approach implements three existing quantum error correcting codes: the three-qubit bit-flip (phase-flip) code, the Shor code, and an erasure code.
We propose a linear-optical implementation of a hyperentanglement-assisted quantum error-correcting code. The code is hyperentanglement assisted because the shared entanglement resource is a photonic state hyperentangled in polarization and orbital angular momentum. It is possible to encode, decode, and diagnose channel errors using linear-optical techniques. The code corrects for polarization ``flip'' errors and is thus suitable only for a proof-of-principle experiment. The encoding and decoding circuits use a Knill-Laflamme-Milburn-like scheme for transforming polarization and orbital angular momentum photonic qubits. A numerical optimization algorithm finds a unit-fidelity encoding circuit that requires only three ancilla modes and has success probability equal to 0.0097.