How device-independent approaches change the meaning of physical theory

Abstract

Dirac sought an interpretation of mathematical formalism in terms of physical entities and Einstein insisted that physics should describe "the real states of the real systems". While Bell inequalities put into question the reality of states, modern device-independent approaches do away with the idea of entities: physical theory may contain no physical systems. Focusing on the correlations between operationally defined inputs and outputs, device-independent methods promote a view more distant from the conventional one than Einstein's 'principle theories' were from 'constructive theories'. On the examples of indefinite causal orders and almost quantum correlations, we ask a puzzling question: if physical theory is not about systems, then what is it about? The answer given by the device-independent models is that physics is about languages. In moving away from the information-theoretic reconstructions of quantum theory, this answer marks a new conceptual development in the foundations of physics

Understanding quantum mechanics: a review and synthesis in precise language

“…The combination is complex in the sense that all the coefficients in its mathematical representation are complex numbers [197, § 2.2][232, pp. [16][17][18]. Strictly speaking the real numbers are a subset of the complex numbers, and this may explain why some authors [193] take mixed states to be a subset of superposition states.…”

“…Quantum mechanics uses agreed mathematical language to analyze phenomena. There is, however, no agreement on a corresponding non-mathematical language to describe such phenomena [10,[14][15][16][17][18][19]]. 3.…”

“…Given the potential need to modify pre-quantum mechanical concepts and word meanings, it is important to consider what these prejudices might be, and to make assumptions explicit [11, § VI] [29][30, pp. [16][17][18][31, pp. 6-8].…”

The effectiveness of mathematics in physics of the unknown

“…The box is unknown territory which, since it is assumed to be of interest for physical theory, is also a territory of science. The entire setup belongs within the boundaries of physics; at the same time, it opens a possibility to redefine these very boundaries [26]. This redefinition is achieved via the use of mathematics: particular mathematical constraints are applied in the general operational probabilistic framework, whose only elementary notions are the inputs and the outputs.…”

Decompositional Equivalence: A Fundamental Symmetry Underlying Quantum Theory

“…It is interesting, in this regard, that a view of systems as having only relative existence has recently emerged as a natural interpretative outcome of work in quantum cryptography, where the possibility that the device an observer thinks she is interacting with may not be the device that she is actually interacting with must be taken seriously. As Grinbaum (2015) puts it, "Device-independent methods convert the usually implicit trust of the observer (in, e.g. the identity of the system of interest or the experimental apparatus) into a theoretical problem.…”