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In this review, we discuss a relation between quantum communication complexity and a long-standing debate in quantum foundation concerning the interpretation of the quantum state. Is the quantum state a physical element of reality as originally interpreted by Schrödinger? Or is it an abstract mathematical object containing statistical information about the outcome of measurements as interpreted by Born? Although these questions sound philosophical and pointless, they can be made precise in the framework of what we call classical theories of quantum processes, which are a reword of quantum phenomena in the language of classical probability theory. In 2012, Pusey, Barrett and Rudolph (PBR) proved, under an assumption of preparation independence, a theorem supporting the original interpretation of Schrödinger in the classical framework. The PBR theorem has attracted considerable interest revitalizing the debate and motivating other proofs with alternative hypotheses. Recently, we showed that these questions are related to a practical problem in quantum communication complexity, namely, quantifying the minimal amount of classical communication required in the classical simulation of a two-party quantum communication process. In particular, we argued that the statement of the PBR theorem can be proved if the classical communication cost of simulating the communication of n qubits grows more than exponentially in n. Our argument is based on an assumption that we call probability equipartition property. This property is somehow weaker than the preparation independence property used in the PBR theorem, as the former can be justified by the latter and the asymptotic equipartition property of independent stochastic sources. The probability equipartition property is a general and natural hypothesis that can be assumed even if the preparation independence hypothesis is dropped. In this review, we further develop our argument into the form of a theorem.

In classical physics there was a clear understanding of what physical space and time are: physical space is the theatre of the collection of all events that are actual at a certain moment of time, and physical time is the parametrization of the flow of time. 3-dimensional space and 1-dimensional time have been substituted by 4-dimensional time-space in relativity theory. But if reality is the 4-dimensional time-space manifold of relativity theory, what is then the meaning of ‘change in time’? We investigate this problem of relativity theory by following an operational approach originally elaborated for quantum mechanics. We show that the contradiction between a geometric view and process view of reality is due to a misconception in the interpretation of relativity theory. We argue that it is not time which is space-like, with the inevitable paradoxical situation of a block universe as result, but on the contrary, it is space which is time-like. This ‘dynamic’, ‘time-like’ conception of space answers the question of the meaning of ‘change in time’ within the 4-dimensional reality of relativity theory, and puts forward a new view on other aspects of the theory.

The concept of time in the ‘clockwork’ Newtonian world was irrelevant; and has generally been ignored until recently by several generations of physicists since the implementation of quantum mechanics. We will set aside the utility of time as a property relating to physical calculations of events relating to a metrics line element or as an aspect of the transformation of a particles motion/interaction in a coordinate system or in relation to thermodynamics etc., i.e. we will discard all the usual uses of time as a concept used to circularly define physical parameters in terms of other physical parameters; concentrating instead on time as an aspect of the fundamental cosmic topology of our virtual reality especially as it inseparably relates to the nature and role of the observer in natural science.