Testing axioms for quantum theory on probabilistic toy-theories

Abstract

Abstract. In Ref.[1] one of the authors proposed postulates for axiomatizing Quantum Mechanics as a fair operational framework, namely regarding the theory as a set of rules that allow the experimenter to predict future events on the basis of suitable tests, having local control and low experimental complexity. In addition to causality, the following postulates have been considered: PFAITH (existence of a pure preparationally faithful state), and FAITHE (existence of a faithful effect). These postulates have exhibited an unexpected theoretical power, excluding all known nonquantum probabilistic theories. Later in Ref.[2] in addition to causality and PFAITH, local discriminability and PURIFY (purifiability of all states) have been postulated, narrowing the probabilistic theory to something very close to Quantum Mechanics. In the present paper we test the above postulates on some nonquantum probabilistic models. The first model, the two-box world is an extension of the Popescu-Rohrlich model [3], which achieves the greatest violation of the CHSH inequality compatible with the no-signaling principle. The second model the two-clock world is actually a full class of models, all having a disk as convex set of states for the local system. One of them corresponds to the the two-rebit world, namely qubits with real Hilbert space. The third model-the spin-factor-is a sort of n-dimensional generalization of the clock. Finally the last model is the classical probabilistic theory. We see how each model violates some of the proposed postulates, when and how teleportation can be achieved, and we analyze other interesting connections between these postulate violations, along with deep relations between the local and the non-local structures of the probabilistic theory.

Physics as Information Processing

“…Here I just mention that Postulates P1, P2 and P4 correspond to Causality, Local-Discriminability, and Atomicity of Evolution of Ref. P3 synthesizes the parallelism and reversibility of quantum computation, and is the most "quantum" postulate, in the sense that all postulates apart from P3 are satisfied by classical theory (P3 is not satisfied by PR boxes [20]). P3 is the purification postulate of Ref.…”

Information Theoretic Characterization of Physical Theories with Projective State Space

“…The works previously cited together with many others [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] contributed to define and consolidate a framework to model physical theories compatibly with the abandonment of determinism and with the assumption that physical laws are intrinsically random. This framework is currently known as probabilistic theories framework and constitutes a starting point to investigate the foundations of quantum theory and possible alternative or deeper theories.…”

No-Hypersignaling Principle

“…As such, this theory (and other analogous theories) would go undetected in any test involving only space-like correlations, despite displaying the anomalous effect of hypersignaling. On the technical side, our model is closely related to the standard implementation [15][16][17] of Popescu-Rohrlich [5] superquantum non-signaling space-like correlations (or "PRboxes," for short). However, while the PR-box model theory relies on entangled states to outperform quantum space-like correlations, our hypersignaling model relies on entangled measurements to outperform quantum timelike correlations.…”

“…The elementary system here is the same as that used to reproduce PR correlations in Refs. [15][16][17]. The states and effects of the elementary system are vectors in R 3 Due to self-consistency and the requirement that non-trivial reversible dynamics exist, however, bipartite states and effects cannot be chosen arbitrarily.…”

“…PR Model: this is the theory used to model PRboxes [15][16][17]. It contains all possible extremal bipartite states, including the eight entangled ones (i.e.…”