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arXiv:0801.0256 · Quantum Information and Computation

Passively self-error-rejecting qubit transmission over a collective-noise channel

Fu‐Guo Deng, Xihan Li, Hong-Yu Zhou

Published Nov 1, 2011• 15 citations
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Abstract

We propose a passively self-error-rejecting single-qubit transmission scheme for an arbitrary polarization state of a single qubit over a collective-noise channel, without resorting to additional qubits and entanglement. By splitting a single qubit into some wavepackets with some Mach-Zehnder interferometers, we can obtain an uncorrupted state with a success probability approaching 100% via postselection in different time bins, independent of the parameters of collective noise. It is simpler and more flexible than the schemes utilizing decoherence-free subspace and those with additional qubits. One can directly apply this scheme to almost all quantum communication protocols based on single photons or entangled photon systems against a collective noise.

DOI
10.26421/qic11.11-12-2

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We propose a passively self-error-rejecting single-qubit transmission scheme for an arbitrary polarization state of a single qubit over a collective-noise channel, without resorting to additional qubits and entanglement. By splitting a single qubit into some wavepackets with some Mach-Zehnder interferometers, we can obtain an uncorrupted state with a success probability approaching 100% via postselection in different time bins, independent of the parameters of collective noise. It is simpler and more flexible than the schemes utilizing decoherence-free subspace and those with additional qubits. One can directly apply this scheme to almost all quantum communication protocols based on single photons or entangled photon systems against a collective noise.
We present a faithful qubit transmission scheme with linear optics against collective noise, not resorting to ancillary qubits. Its setup is composed of three unbalanced polarization interferometers, based on a polarizing beam splitter, a beam splitter, and a half wave plate, which makes this scheme more feasible than others with present technology. The fidelity of successful transmission is 1, independent of the parameters of the collective noise, and the success probability for obtaining an uncorrupted state can be improved to 100% with some time delayers. Moreover, this scheme has some good applications in one-way quantum communication for rejecting the errors caused by the collective noise in quantum channel.
Faithful transmission of quantum information over noisy channel is an essential requisite for quantum communication and distributed quantum computing. Here we experimentally demonstrate a noise-rejecting scheme for single-photon qubits transmission, resorting to neither ancillary photons nor globally entangled resources. Employing the unbalanced polarization interferometer, the polarization qubits are transformed to time-bin degrees of freedom. Meanwhile, the deterministic transmission of quantum states with high fidelity can be achieved. We find that the immunity of time-bin encoded qubits against collective noise paves the way to practical quantum error-correction and rejection in long-distance quantum communication.
Quantum communication utilizes the quantum state as information carrier. The transmission of quantum states is therefore a precondition for various quantum communication protocols. Photons play a central role in quantum communication since they are fast, cheap, easy to control and interact weakly with the environment. However, the widely used polarization degree of freedom of photons is vulnerable to the noise during the transmission. In this article, we review two main methods to deal with the channel noise, i.e., the quantum error rejection scheme and fault tolerant quantum communication. To transmit an arbitrary single-photon state, Li and Deng proposed two faithful state transmission schemes only by resorting to passive linear optics. The success probability can be (2N+1-1)/2N+1 by introducing a wave splitter composed of N unbalance interferometers. Compared with other quantum error rejection schemes, these two scheme are practical both in maneuverability and resource consumption. They are not only suitable for single-photon pure state transmission but also able to be used for transmitting mixed state, which makes them useful for one-way quantum communication. The success probability of error rejection is usually less than 100% since some error cases are rejected. To realize complete fault tolerant quantum communication, decoherence free subspace can be used to encode quantum information. In 2008, Li et al. proposed two efficient quantum key distribution schemes over two different collective-noise channels. The noiseless subspaces are made up of two Bell states and the spatial degree of freedom is introduced to form two nonorthogonal bases. Although entangled states are employed, only single-photon measurements are required to read the information. Later, the scheme is generalized to an efficient one which transmits n-1 bits information via n Einstein-Podolsky-Rosen pairs and many fault tolerant quantum communication schemes were proposed. We compare the practicality of different anti-noise schemes based on maneuverability and resource consumption and a perspective of these two research directions is given in the last section.
We propose a distribution scheme of polarization states of a single photon over collective-noise channel assisted with one additional photon in a fixed polarization state. Although the present scheme does not encode the polarization state of a photon to an entangled state of two photons in the decoherence-free subspace, the state is protected against collective noise and extracted by a measurement based on the parity check and the post-selection. This scheme will easily be applied to many quantum communication protocols based on qubits.
We propose a distribution scheme of polarization states of a single photon over a collective-noise channel. By adding one extra photon with a fixed polarization, we can protect the state against collective noise via a parity-check measurement and postselection. While the scheme succeeds only probabilistically, it is simpler and more flexible than the schemes utilizing decoherence-free subspace. An application to the Bennett-Brassard 1984 protocol through a collective-noise channel, which is robust to the Trojan horse attack, is also given.
Here, we experimentally demonstrate a faithful single-photon qubits transmission using error-rejecting coding, resorting to neither ancillary photons nor entangled photon resources. Using unbalanced polarization interferometer, the polarization qubits are transferred into the state on time-bin degree of freedom. Additionally, the deterministic transmission of single photon quantum states can be achieved with high fidelity. The immunity of time-bin encoded qubits against collective noise paves the way to practical quantum error-correction and error-rejection in quantum information science.