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arXiv:quant-ph/0406100 · Physical Review A

Fault tolerant quantum key distribution protocol with collective random unitary noise

Xiang‐Bin Wang

Published Nov 23, 2005• 69 citations
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Abstract

We propose an easy implementable prepare-and-measure protocol for robust quantum key distribution with photon polarization. The protocol is fault tolerant against collective random unitary channel noise. The protocol does not need any collective quantum measurement or quantum memory. A security proof and a specific linear optical realization using spontaneous parametric down conversion are given.

DOI
10.1103/physreva.72.050304

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We propose an easy implementable prepare-and-measure protocol for robust quantum key distribution with photon polarization. The protocol is fault tolerant against collective random unitary channel noise. The protocol does not need any collective quantum measurement or quantum memory. A security proof and a specific linear optical realization using spontaneous parametric down conversion are given.
We propose easy implementable protocols for robust quantum key distribution with the collective dephasing channel or collective rotating channel. In these protocols, Bob only takes passive photon detection to measure the polarization qubits in the random bases. The source for the protocol with collective rotating channel is made by type 2 spontaneous parametric down conversion with random unitary rotation and phase shifter, no quantum disentangler is required. A simple proof for unconditionally security is shown.
We experimentally implement a fault-tolerant quantum key distribution protocol with two photons in a decoherence-free subspace [Phys. Rev. A 72, 050304(R) (2005)]. It is demonstrated that our protocol can yield a good key rate even with a large bit-flip error rate caused by collective rotation, while the usual realization of the Bennett-Brassard 1984 protocol cannot produce any secure final key given the same channel. Since the experiment is performed in polarization space and does not need the calibration of a reference frame, important applications in free-space quantum communication are expected. Moreover, our method can also be used to robustly transmit an arbitrary two-level quantum state in a type of decoherence-free subspace.
Quantum key distribution (QKD) has been proved unconditionally secure. But noise and imperfection of realistic devices are major difficulties for implementing quantum key distribution. Particularly, the birefringence in optical fiber corresponds to an insuppressible collective unitary transformation on the polarization space. Obviously does not change the permutation symmetry of multiphoton state. By encoding on three 3-photon states with different permutation symmetries, we propose a novel polarization-based protocol, which is robust against an arbitrary degree of collective noise. A clear characteristic of this protocol is that entanglement is absent in principle.
We present two polarization-based protocols for quantum key distribution. The protocols encode key bits in noiseless subspaces or subsystems and so can function over a quantum channel subjected to an arbitrary degree of collective noise, as occurs, for instance, due to rotation of polarizations in an optical fiber. These protocols can be implemented using only entangled photon-pair sources, single-photon rotations, and single-photon detectors. Thus, our proposals offer practical and realistic alternatives to existing schemes for quantum key distribution over optical fibers without resorting to interferometry or two-way quantum communication, thereby circumventing, respectively, the need for high precision timing and the threat of Trojan horse attacks.
We present two quantum key distribution (QKD) schemes over a collective-noise channel. Each logical qubit, composed of two physical qubits with a decoherence-free subspace, is immune to a collective noise and can carry one bit of information in theory. Although the receiver should prepare entangled two-photon quantum systems, he can read out the information encoded by the sender with two unitary operations on two photons, resorting to only two single-photon measurements, not Bell-state measurements, which makes these protocols simpler than others in experiment. These two QKD protocols are deterministic, not random, which makes the classical information exchanged be reduced largely. Also, they have a high intrinsic efficiency.