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arXiv:1003.0484

Quantum dense coding without entanglement

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

Published Mar 2, 2010• 0 citations
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Abstract

We describe a quantum cryptography protocol with up to twenty four-dimensional ($\mathcal{D} =4$) 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.

DOI
10.48550/arxiv.1003.0484

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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.
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.
We firstly propose a simultaneous dense coding protocol with two-photon four-qubit cluster states in which two receivers can simultaneously get their respective classical information sent by a sender. Because each photon has two degrees of freedom, the protocol will achieve a high transmittance. The security of the simultaneous dense coding protocol has also been analyzed. Secondly, we investigate how to simultaneously teleport two different quantum states with polarization and path degree of freedom using cluster states to two receivers, respectively, and discuss its security. The preparation and transmission of two-photon four-qubit cluster states is less difficult than that of four-photon entangled states, and it has been experimentally generated with nearly perfect fidelity and high generation rate. Thus, our protocols are feasible with current quantum techniques.
We have implemented the 'six-state' quantum cryptography protocol using polarization-entangled photon pairs, in which the polarization of each photon of a pair is measured in one of three randomly chosen bases. For a given amount of eavesdropping, this protocol results in a larger error rate than in four- or two-state protocols, but reduces the number of key-producing events. We have experimentally investigated several incoherent eavesdropping strategies, and verified the predicted enhancement in error rate. However, we demonstrate that for low error rates, the efficiency for secret key generation is higher when using the four-state protocol.
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%.
We are introducing an efficient bidirectional quantum secure direct communication protocol that employs the four qubit cluster states, creating a novel quantum channel based on dense coding between the transmitter and receiver. By dense coding, after a conventional announcement, two legitimate users can simultaneously exchange their messages. Two safety checking measures are taken to ensure safe transmission. Information leaking is not an issue in this protocol, and it is secure against some well-known eavesdropping assaults. It is also accessible with cutting-edge technology.