Reference-frame-independent quantum key distribution

We describe a quantum key distribution protocol based on pairs of entangled qubits that generates a secure key between two partners in an environment of unknown and slowly varying reference frame. A direction of particle delivery is required, but the phases between the computational basis states need not be known or fixed. The protocol can simplify the operation of existing setups and has immediate applications to emerging scenarios such as earth-to-satellite links and the use of integrated photonic waveguides. We compute the asymptotic secret key rate for a two-qubit source, which coincides with the rate of the six-state protocol for white noise. We give the generalization of the protocol to higher-dimensional systems and detail a scheme for physical implementation in the three-dimensional qutrit case.

Figure 1

Two meaningful scenarios for reference frame independent QKD. (a) Polarization encoding in earth-to-satellite quantum communication. Here the circular polarization states are stable, but the linear states can vary with the rotation of the satellite. (b) Path encoding in chip-to-chip quantum communication. While the path information is stable, the unpredictable wavelength-scale changes in relative path length amount to a varying reference frame. This may occur between chips communicating through free space, or between chips connected by optical fibres.

Figure 2

Integrated photonic components for measurement in the qutrit version of reference-frame-independent QKD. (a) The state-splitter chip takes an arbitrary qutrit input state and splits it into a superposition of two probabilistic copies. The reflectivity of directional couplers (DC) can be set to select the relative probability of the copy. Two directional couplers implement a Mach Zender interferometer (MZ) with internal phase such that a photon exits from the path opposite to the one in which it entered. (b) A qutrit Hadamard chip takes a particular equal superposition basis and rotates to the computational basis in preparation for measurement. (c) Three state-splitter chips are used to make a superposition of four probabilistic copies of the incoming states. One probabilistic copy is immediately measured in the computational basis while the other three are fed into different Hadamard chips before measurement.