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Optics Express

Efficient quantum key distribution against collective noise using polarization and transverse spatial mode of photons

Peng‐Liang Guo, Chen Dong, Yi He, Feng Jing, Wan‐Ting He, Bao‐Cang Ren, Chunyan Li, Fu‐Guo Deng

Published Jan 7, 2020• 24 citations
Publisher

Abstract

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.

DOI
10.1364/oe.374292

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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 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 propose a scheme for encoding logical qubits in a subspace protected against collective rotations around the propagation axis using the polarization and transverse spatial degrees of freedom of single photons. This encoding allows for quantum key distribution without the need of a shared reference frame. We present methods to generate entangled states of two logical qubits using present day down-conversion sources and linear optics, and show that the application of these entangled logical states to quantum information schemes allows for alignment-free tests of Bell's inequalities, quantum dense coding, and quantum teleportation.
The encoding in multiple degrees of freedom can effectively improve the performance of current quantum key distribution, but the collective channel noise reduces the security of these proposals. In this article, we propose a high capacity quantum key distribution with single-photon in polarization and spatial-mode degrees of freedom, and protect the quantum states against the general collective noise by error-rejection in two degrees of freedom and quantum channel multiplexing. The states transmission and measurements in the presented quantum key distribution can be realized deterministically. The security analysis under the intercept-measure-resend eavesdropping and controlled-NOT operation eavesdropping attacks is conducted to verify the security, and the secure key rate analysis proves the efficiency of our proposal. These advantages make our proposal useful in practical quantum communication under current experimental conditions.
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.
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.
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.