Squashing model for detectors and applications to quantum-key-distribution protocols

Abstract

We develop a framework that allows a description of measurements in Hilbert spaces that are smaller than their natural representation. This description, which we call a "squashing model", consists of a squashing map that maps the input states of the measurement from the original Hilbert space to the smaller one, followed by a targeted prescribed measurement on the smaller Hilbert space. This framework has applications in quantum key distribution, but also in other cryptographic tasks, as it greatly simplifies the theoretical analysis under adversarial conditions.

Practical round-robin differential phase-shift quantum key distribution

“…A similar problem also exists for other QKD schemes [31]. The solution there is to apply the squashing model [32,33,34] to Bob's measurement. As a result, the signal Bob receives can be regarded as a qubit state in the security analysis.…”

Multi-partite squash operation and its application to device-independent quantum key distribution

“…As we have seen in the previous section, once the squash operation F is shown to exist for a practical detector ( | ) M r c , it serves as a very useful tool for analyzing protocols involving ( | ) M r c . At the present, however, F is shown to exist for a relatively limited class of detectors, e.g., the threshold detector of the BB84 type measurement [11,12,15], and of the six-state measurement with a passive basis choice [12], and a few others [14].…”

“…For example, Beaudry et al gave an explicit condition for the existence of a squash operation, and used it to show positive and negative results on the six-state protocol with threshold detectors [12]. Later their techniques were refined further and applied to other types of measurement devices [14]. In [15], one of the present authors discussed whether symmetries of a given detector can imply the existence of the squash operation corresponding to it, and also showed that the above result on the BB84 type measurement is valid even for multi-mode cases.…”

Detector-decoy quantum key distribution without monitoring signal disturbance

“…Yet in practice, this assumption cannot be satisfied due to the fact that weak laser pulses are usually used as the source, which occasionally include more than one photon, and that the eavesdropper may intercept and send multiphotons to the receiver. Therefore, for qubit-based quantum communication protocols [1][2][3][4][5][6][18][19][20][21][22], the decoy state method [4,5] has solved the multiphoton problems at the source with great enhancements, while squash models [23][24][25][26] are proposed to solve problems at the detector. In the RRDPS-QKD protocol [10], a practical vulnerability lies in that Bob's measurement device requires experimentally challenging detectors that are able to discriminate between single photons from two or more photons, i.e., photon number resolving detectors.…”