Modeling light entangled in polarization and frequency: case study in quantum cryptography

摘要

With the recognition of a logical gap between experiments and equations of quantum mechanics conies: (1) a chance to clarify such purely mathematical entities as probabilities, density operators, and partial traces—separated out from the choices and judgments necessary to apply them to describing experiments with devices, and (2) an added freedom to invent equations by which to model devices, stemming from the corresponding freedom in interpreting how these equations connect to experiments. Here I apply a few of these clarifications and freedoms to model polarization-entangled light pulses called for in quantum key distribution (QKD). Available light pulses are entangled not only in polarization but also in frequency. Although absent from the simplified models that initiated QKD, the degree of frequency entanglement of polarization-entangled light pulses is shown to affect the amount of key that can be distilled from raw light signals, in one case by a factor of 4/3. Open questions remain, because QKD brings concepts of quantum decision theory, such as measures of distinguisha-bility, mostly worked out in the context of finite-dimensional vector spaces, into contact with infinite-dimensional Hilbert spaces needed to give expression to optical frequency spectra.