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Quantum Information and Computation

Practical four-dimensional quantum key distribution without entanglement

W. T. Buttler, S. K. Lamoreaux, Justin R. Torgerson

Published Jan 1, 2012• 6 citations
Publisher

Abstract

We describe a four-dimensional ($\mathcal{D} = 4$) single-photon quantum cryptography protocol with up to twenty ($\mathcal{D} \times (2^2 + 1)$) possible states generated by a polarization-, phase- and time-encoding transmitter. This protocol can be experimentally realized with existing technology, drawing from time- and polarization-encoded systems. The protocol is error tolerant and has a maximum raw bit rate of two raw bits per detection, which when combined with state detection efficiency yields a qubit rate of up to one per transmission under ideal assumptions, or up to twice the raw bit rate of two-dimensional protocols such as the well-known BB84 protocol.

DOI
10.26421/qic12.1-2-1

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We describe a four-dimensional (D=4\mathcal{D} = 4D=4) single-photon quantum cryptography protocol with up to twenty (D×(22+1)\mathcal{D} \times (2^2 + 1)D×(22+1)) possible states generated by a polarization-, phase- and time-encoding transmitter. This protocol can be experimentally realized with existing technology, drawing from time- and polarization-encoded systems. The protocol is error tolerant and has a maximum raw bit rate of two raw bits per detection, which when combined with state detection efficiency yields a qubit rate of up to one per transmission under ideal assumptions, or up to twice the raw bit rate of two-dimensional protocols such as the well-known BB84 protocol.
We describe a quantum cryptography protocol with up to twenty four-dimensional (D=4\mathcal{D} =4D=4) states generated by a polarization-, phase- and time-encoding transmitter. This protocol can be experimentally realized with existing technology, drawing from time-encoded and polarization-encoded systems. The protocol is error tolerant and has a quantum bit-rate of 2 per transmission/detection, which when combined with state detection efficiency yields a qubit efficiency of up to 1 or double that of BB84-{\it like} protocols.
By realizing a quantum cryptography system based on polarization entangled photon pairs we establish highly secure keys, because a single photon source is approximated and the inherent randomness of quantum measurements is exploited. We implement a novel key distribution scheme using Wigner's inequality to test the security of the quantum channel, and, alternatively, realize a variant of the BB84 protocol. Our system has two completely independent users separated by 360 m, and generates raw keys at rates of 400-800 bits/s with bit error rates around 3%.
High-dimensional quantum key distribution (QKD) allows achievement of information-theoretic secure communications, providing high key-generation rates, which cannot, in principle, be obtained by QKD protocols with binary encoding. Nonetheless, the amount of experimental resources needed increases as the quantum states to be detected belong to a larger Hilbert space, thus raising the costs of practical high-dimensional systems. Here, we present an alternative scheme for fiber-based four-dimensional QKD, with time and phase encoding and one-decoy state technique. Quantum state transmission is tested over different channel lengths up to 145 km of standard single-mode fiber, evaluating the enhancement of the secret key rate in comparison to the three-state two-dimensional BB84 protocol, which is tested with the same experimental setup. Our scheme allows measurement of the four-dimensional states with a simplified and compact receiver, where only two single-photon detectors are necessary, thus making it a cost-effective solution for practical and fiber-based QKD.
High-dimensional encoding using higher degrees of freedom has become topical in quantum communication protocols. When taking advantage of entanglement correlations, the state space can be made even larger. Here, we exploit the entanglement between two dimensional space and polarization qubits, to realize a four-dimensional quantum key distribution protocol. This is achieved by using entangled states as a basis, analogous to the Bell basis, rather than typically encoding information on individual qubits. The encoding and decoding in the required complementary bases is achieved by manipulating the Pancharatnam-Berry phase with a single optical element: a q-plate. Our scheme shows a transmission fidelity of 0.98 and secret key rate of 0.9 bits per photon. While the use of only static elements is preferable, we show that the low secret key rate is a consequence of the filter based detection of the modes, rather than our choice of encoding modes.
In this paper, we introduce a new quantum key distribution protocol, which we refer to as polarization-phase (PoP) protocol. In this protocol, two degrees of photonic freedom of the same particle in a hybrid manner are used to encode the information in the format of two- or high-dimensional quantum states (qubits and qudits, respectively). Here, we only discuss the qubit version of the general PoP protocol (we refer to two-dimensional PoP (TD-PoP) protocol) as an interesting extension for the standard BB84 protocol. We investigate the performance of the TD-PoP protocol using infinite-key analysis against restricted individual attacks, i.e. the intercept-resend and photon number splitting attacks, in both ideal single-photon and Poisson (attenuated laser) sources. In addition, we demonstrate that this protocol, despite using two physical dimensions, is simple and fully has empirical implementation capability. Ability to extract two bits of information from each detection event, and increasing the sifting parameter, the secure key rate, and the likelihood of detection of an eavesdropper, are the advantages of the TD-PoP protocol compared to the standard polarization- or phase-encoded BB84 protocol.
Conventional quantum key distribution (QKD) typically uses binary encoding based on photon polarization or time-bin degrees of freedom and achieves a key capacity of at most one bit per photon. Under photon-starved conditions the rate of detection events is much lower than the photon generation rate, because of losses in long distance propagation and the relatively long recovery times of available single-photon detectors. Multi-bit encoding in the photon arrival times can be beneficial in such photon-starved situations. Recent security proofs indicate high-dimensional encoding in the photon arrival times is robust and can be implemented to yield high secure throughput. In this work we demonstrate entanglement-based QKD with high-dimensional encoding whose security against collective Gaussian attacks is provided by a high-visibility Franson interferometer. We achieve unprecedented key capacity and throughput for an entanglement-based QKD system because of four principal factors: Franson interferometry that does not degrade with loss; error correction coding that can tolerate high error rates; optimized time–energy entanglement generation; and highly efficient WSi superconducting nanowire single-photon detectors. The secure key capacity yields as much as 8.7 bits per coincidence. When optimized for throughput we observe a secure key rate of 2.7 Mbit s−1 after 20 km fiber transmission with a key capacity of 6.9 bits per photon coincidence. Our results demonstrate a viable approach to high-rate QKD using practical photonic entanglement and single-photon detection technologies.