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arXiv:0808.0042 · Physical Review A

Efficient quantum key distribution over a collective noise channel

Xihan Li, Fu‐Guo Deng, Hong-Yu Zhou

Published Aug 13, 2008• 386 citations
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Abstract

We present two efficient quantum key distribution schemes over two different collective-noise channels. The accepted hypothesis of collective noise is that photons travel inside a time window small compared to the variation of noise. Noiseless subspaces are made up of two Bell states and the spatial degree of freedom is introduced to form two nonorthogonal bases. Although these protocols resort to entangled states for encoding the key bit, the receiver is only required to perform single-particle product measurements and there is no basis mismatch. Moreover, the detection is passive as the receiver does not switch his measurements between two conjugate measurement bases to get the key.

DOI
10.1103/physreva.78.022321

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We present two efficient quantum key distribution schemes over two different collective-noise channels. The accepted hypothesis of collective noise is that photons travel inside a time window small compared to the variation of noise. Noiseless subspaces are made up of two Bell states and the spatial degree of freedom is introduced to form two nonorthogonal bases. Although these protocols resort to entangled states for encoding the key bit, the receiver is only required to perform single-particle product measurements and there is no basis mismatch. Moreover, the detection is passive as the receiver does not switch his measurements between two conjugate measurement bases to get the key.
Based on the quantum key distribution protocol [X. H. Li, F. G. Deng and H. Y. Zhou, Phys. Rev. A78 (2008) 022321], we proposed two efficient fault-tolerant quantum secret sharing schemes over two collective-noise channels, in which the sharers can establish a key with the sender only if all the sharers collaborate together. Noiseless subspaces are composed of two Bell states based on the hypothesis of collective noise and the spatial degree of freedom is introduced to insure the security. Although entangled states are used to encode the key bits, the sharers are only required to perform single-particle product operations or single-particle product measurement, making the schemes convenient with current technique. As there is no basis mismatch during the measurement, almost all of the samples can be used to share the key.
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.
Channel noise is the main issue which reduces the efficiency of quantum communication. Here we present an efficient scheme for quantum key distribution against collective-rotation channel noise using polarization and transverse spatial mode of photons. Exploiting the two single-photon Bell states and two-photon hyperentangled Bell states in the polarization and the transverse spatial mode degrees of freedom (DOFs), the mutually unbiased bases can be encoded for logical qubits against the collective-rotation noise. Our scheme shows noiseless subspaces can be made up of two DOFs of two photons instead of multiple photons, which will reduce the resources required for noiseless subspaces and depress the photonic loss sensitivity. Moreover, the two single-photon Bell states and two-photon hyperentangled Bell states are symmetrical to the two photons, which means the relative order of the two photons is not required in our scheme, so the receiver only needs to measure the state of each photon, which makes our protocol easy to execute in experiment than the previous works.
Decoherence-free subspace (DFS) is a valid solution to realize quantum communication over a collective noise channel, and has been widely studied. Generally speaking, replacing a qubit with a DFS state will cause the reduction of communication efficiency. However, in this letter, it is shown that some kinds of noises may not lower the transmission rate of quantum key distribution. To illustrate it, we propose two quantum key distribution protocols based on Bell states. Here, two nonorthogonal and unbiased sets in a DFS are constructed by linear combination of particles at different positions. Since n−1n-1n−1 classical bits are distributed by using 2n2n2n qubits in our protocols, the transmission rate is close to that of noiseless BB84 protocol. Furthermore, when considering the cost of transmitting classical bits, the efficiencies of these protocols are even higher than that of BB84 protocol.
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 robust quantum key distribution protocols against two kinds of collective noise, following some ideas in quantum dense coding. Three-qubit entangled states are used as quantum information carriers, two of which form the logical qubit, which is invariant with a special type of collective noise. The information is encoded on logical qubits with four unitary operations, which can be read out faithfully with Bell-state analysis on two physical qubits and a single-photon measurement on the other physical qubit, not three-photon joint measurements. Two bits of information are exchanged faithfully and securely by transmitting two physical qubits through a noisy channel. When the losses in the noisy channel is low, these protocols can be used to transmit a secret message directly in principle.