Abstract
In the device-independent framework we use “boxes” to describe the physical devices, or resources, of interest. A box, formally modelled as a conditional probability distribution (recall Sect. 3.1), is always defined with respect to a specific task or protocol.
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Notes
- 1.
Interestingly, if one considers protocols with more than two parties in which the devices can only be used in specific space-time coordinates and merely assumes that the box modelling the devices respects relativistic causality (in the sense that it cannot lead to casual loops) then the conditions defining the box are different than the non-signalling ones [1]. This acts as another example for how the specific use of the devices effects the mathematical model of the box.
- 2.
One can rightfully say that this property of boxes, among several other properties, renders them an “unphysical description” of real systems and resources. With this respect, the formalism of the so called “generalised probabilistic theories” [2, 3] is a more appropriate mathematical setting to discuss physical theories which extend, or abstract, quantum physics. In contrast, boxes are merely a simplified mathematical model sufficient for certain analyses.
- 3.
- 4.
These two extreme cases are easy to understand. When the box employs a classical strategy the adversary can simply hold a copy of A. When the box employs the optimal quantum strategy the used state is the maximally entangled state. Then, due to monogamy of entanglement, the adversary is completely decoupled from the Alice and Bob’s state. For more details see Sect. 4.2.
- 5.
That is, instead of assuming that we know just the winning probability of the single-round box in a specific game, we assume we know its winning probabilities in several different games. In the context of single-round boxes this is a stronger assumption regarding the device. However, in actual application this is not an issue, as will be mentioned later on.
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Arnon-Friedman, R. (2020). Single-Round Box. In: Device-Independent Quantum Information Processing. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-60231-4_5
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