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Journal of Experimental and Theoretical Physics

Practical implementation of multilevel quantum cryptography

S. P. Kulik, Gleb Maslennikov, Ekaterina V. Moreva

Published May 1, 2006• 4 citations
Publisher

Abstract

The physical principles of a quantum key distribution protocol using four-level optical systems are discussed. Quantum information is encoded into polarization states created by frequency-nondegenerate spontaneous parametric down-conversion in collinear geometry. In the scheme under analysis, the required nonorthogonal states are generated in a single nonlinear crystal. All states in the selected basis are measured deterministically. The results of initial experiments on transformation of the basis polarization states of a four-level optical system are discussed.

DOI
10.1134/s1063776106050037

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The physical principles of a quantum key distribution protocol using four-level optical systems are discussed. Quantum information is encoded into polarization states created by frequency-nondegenerate spontaneous parametric down-conversion in collinear geometry. In the scheme under analysis, the required nonorthogonal states are generated in a single nonlinear crystal. All states in the selected basis are measured deterministically. The results of initial experiments on transformation of the basis polarization states of a four-level optical system are discussed.
We discuss a procedure of measurement of an arbitrary quantum state of an optical system in Hilbert space with the dimension d=4. Such states can be realized using a collinear frequency-nondegenerate regime of spontaneous parametric down-conversion. The method has been tested for a number of polarization states of a biphoton field. A high accuracy of the reconstruction of the states (above 99%) indicates that the procedures proposed for reconstructing the quantum state of the system are adequate.
We discuss the proof-of-principle demonstration of the extended deterministic Quantum Key Distribution (QKD) protocol based on ququarts. The experimental realization is based on the polarization degrees of freedom of two-mode biphotons, making the process of state preparation, transformation and measurement rather simple. The scheme uses only single nonlinear crystal for biphoton generation and linear optical elements for their following transformation and can be used as a base for further practical applications.
Quantum techniques for key distribution---the classically impossible task of distributing secret information over an insecure channel whose transmissions are subject to inspection by an eavesdropper, between parties who share no secret initially---have been proposed using (a) four nonorthogonally polarized single-photon states or low-intensity light pulses, and (b) polarization-entangled or spacetime-entangled two-photon states. Here we show that in principle any two nonorthogonal quantum states suffice, and describe a practical interferometric realization using low-intensity coherent light pulses.
We report on the engineering, preparation, and utilization of polarization entangled-photon states in the telecommunications window of 1.5 µm for secure quantum key distribution. Traditionally, such sources have been based on the use of the process of spontaneous parametric down conversion (SPDC) when nonlinear crystal is pumped by a continuous wave (cw) or a pulsed laser. The pump photon disintegrates spontaneously giving birth to two twin photons that are strongly correlated in frequency, polarization and wave vector (direction of propagation). Photon entanglement results from the fact that the possible values of correlated parameters of twin photons are made indistinguishable from each other either at the generation or at the single-photon detection stage. This leads to non-classical interference effects.
The use of quantum bits (qubits) in cryptography holds the promise of secure cryptographic quantum key distribution schemes. It is based usually on single-photon polarization states. Unfortunately, the implemented ``qubits'' in the usual weak pulse experiments are not true two-level systems, and quantum key distribution based on these imperfect qubits is totally insecure in the presence of high (realistic) loss rate. In this work, we investigate another potential implementation: qubits generated using a process of parametric downconversion. We find that, to first (two-photon) and second (four-photon) order in the parametric downconversion small parameter, this implementation of quantum key distribution is equivalent to the theoretical version. Once realistic measurements are taken into account, quantum key distribution based on parametric downconversion suffers also from sensitivity to extremely high (nonrealistic) losses. By choosing the small parameter of the process according to the loss rates, both implementations of quantum key distribution can in principle become secure against the attack studied in this paper. However, adjusting the small parameter to the required levels seems to be impractical in the weak pulse process. On the other hand, this can easily be done in the parametric downconversion process, making it a much more promising implementation.