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Quantum Information and Computation

Quantum key distribution: defeating collective noise without reducing efficiency

Song Lin, Gongde Guo, Fei Gao, Xiao-Fen Liu

Published Jul 1, 2014• 12 citations
Publisher

Abstract

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 $n-1$ classical bits are distributed by using $2n$ 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.

DOI
10.26421/qic14.9-10-9

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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 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.
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.
We introduce a new quantum communication protocol for the transmission of quantum information under collective noise. Our protocol utilizes a decoherence-free subspace in such a way that an optimal asymptotic transmission rate is achieved, while at the same time encoding and decoding operations can be efficiently implemented. The encoding and decoding circuit requires a number of elementary gates that scale linearly with the number of transmitted qudits, mmm. The logical depth of our encoding and decoding operations is constant and depends only on the channel in question. For channels described by an arbitrary discrete group GGG, i.e.~with a discrete number, ∣G∣\lvert G\rvert∣G∣, of possible noise operators, perfect transmission at a rate m/(m+r)m/(m+r)m/(m+r) is achieved with an overhead that scales at most as O(dr)\mathcal{O}(d^r)O(dr) where the number of auxiliary qudits, rrr, depends solely on the group in question. Moreover, this overhead is independent of the number of transmitted qudits, mmm. For certain groups, e.g.~cyclic groups, we find that the overhead scales only linearly with the number of group elements ∣G∣|G|∣G∣.
Countering channel noise is an urgent problem to achieve safe and efficient quantum communication. In order to solve this problem, a quantum key distribution (QKD) scheme based on quantum error-avoiding code (QEAC) in decoherence-free subspace (DFS) is proposed. Firstly, we use group theory to design a simple method for constructing QEAC based on the DFS, which is a better solution to overcome quantum channel noise. Secondly, the constructed QEAC is applied in the construction of the QKD scheme for error avoidance. The idea of QEAC for quantum key distribution can effectively overcome the noise in the channel without complicated systems. The proposed method of constructing a QKD scheme for quantum secure communication skillfully utilizes DFS for analysis and research, and improves the quantum bit efficiency and security of quantum key distribution.
We introduce a new quantum communication protocol for the transmission of quantum information under collective noise. Our protocol utilizes a decoherence-free subspace in such a way that an optimal asymptotic transmission rate is achieved, while at the same time encoding and decoding operations can be efficiently implemented. The encoding and decoding circuit requires a number of elementary gates that scale linearly with the number of transmitted qudits, m. The logical depth of our encoding and decoding operations is constant and depends only on the channel in question. For channels described by an arbitrary discrete group G, i.e. with a discrete number, |G|, of possible noise operators, perfect transmission at a rate m/(m+r) is achieved with an overhead that scales at most as O(dr)\mathcal{O}(d^r)O(dr) where the number of auxiliary qudits, r, depends solely on the group in question. Moreover, this overhead is independent of the number of transmitted qudits, m. For certain groups, e.g. cyclic groups, we find that the overhead scales only linearly with the number of group elements |G|.