We use classical mutual information to characterize two photons measured in three mutually unbiased bases. We theoretically and experimentally compare entangled and separable states and find a bound on the information capacity of the pair.
We encode mutually unbiased bases (MUBs) using the higher-dimensional orbital angular momentum (OAM) degree of freedom and illustrate how these states are encoded on a phase-only spatial light modulator (SLM). We perform ( d - 1)- mutual unbiased measurements in both a classical prepare and measure scheme and on entangled photon pairs for dimensions ranging from d = 2 to 5. The calculated average error rate, mutual information and secret key rate show an increase in information capacity as well as higher generation rates as the dimension increases.
We present an experimental study of higher-dimensional quantum key distribution protocols based on mutually unbiased bases, implemented by means of photons carrying orbital angular momentum. We perform (d+1) mutually unbiased measurements in a classically simulated prepare-and-measure scheme and on a pair of entangled photons for dimensions ranging from d=2 to 5. In our analysis, we pay attention to the detection efficiency and photon pair creation probability. As security measures, we determine from experimental data the average error rate, the mutual information shared between the sender and receiver, and the secret key generation rate per photon. We demonstrate that increasing the dimension leads to an increased information capacity as well as higher key generation rates per photon. However, we find that the benefit of increasing the dimension is limited by practical implementation considerations, which in our case results in deleterious effects observed beyond a dimension of d=4.
Measurements in mutually unbiased bases (MUBs) are integral to quantum science. An underlying principle of a set of MUBs is that a measurement in one such basis provides no information about a measurement in one of the others. This feature is especially relevant for quantum key distribution. We perform a complete set of mutually unbiased measurements for high-dimensional orbital angular momentum (OAM) states of light. For a two-photon entangled state we show that specific joint measurements provide the minimum number of experimental settings required to characterize the quantum state. From these measurements we reconstruct the density matrix describing the high-dimensional two-photon entangled state. The experimental procedure that we outline can be applied to many different multipartite and high-dimensional systems.