Complete extension: the non-signaling analog of quantum purification
arXiv:1810.02222 · doi:10.22331/q-2023-11-03-1159
Abstract
Deriving quantum mechanics from information-theoretic postulates is a recent research direction taken, in part, with the view of finding a beyond-quantum theory; once the postulates are clear, we can consider modifications to them. A key postulate is the purification postulate, which we propose to replace by a more generally applicable postulate that we call the complete extension postulate (CEP), i.e., the existence of an extension of a physical system from which one can generate any other extension. This new concept leads to a plethora of open questions and research directions in the study of general theories satisfying the CEP (which may include a theory that hyper-decoheres to quantum theory). For example, we show that the CEP implies the impossibility of bit-commitment. This is exemplified by a case study of the theory of non-signalling behaviors which we show satisfies the CEP. We moreover show that in certain cases the complete extension will not be pure, highlighting the key divergence from the purification postulate.
29 + 42 pages, 9 figures and 2 tables
References in corpus (29)
- Device-independent security of quantum cryptography against collective attacks
- Characterizing quantum theory in terms of information-theoretic constraints
- A derivation of quantum theory from physical requirements
- Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
- Higher-order interference and single-system postulates characterizing quantum theory
- Disintegration and Bayesian Inversion via String Diagrams
- Quartic quantum theory: an extension of the standard quantum mechanics
- Ultimate data hiding in quantum mechanics and beyond
- The measurement postulates of quantum mechanics are operationally redundant
- Reconstructing quantum theory from diagrammatic postulates
- Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction
- Ruling out higher-order interference from purity principles
- Conditions on the existence of maximally incompatible two-outcome measurements in General Probabilistic Theory
- Categorical Probabilistic Theories
- Quantum theory from rules on information acquisition
- Fermionization and boundary states in 1+1 dimensions
- Oracles and query lower bounds in generalised probabilistic theories
- Structure of Optimal State Discrimination in Generalized Probabilistic Theories
- Leaks: quantum, classical, intermediate, and more
- How to make unforgeable money in generalised probabilistic theories
- Simple proof of the impossibility of bit-commitment in generalised probabilistic theories using cone programming
- An effect-theoretic reconstruction of quantum theory
- Two Roads to Classicality
- Nonclassicality without entanglement enables bit commitment
- Solute particle near a nanopore: influence of size and surface properties on the solvent-mediated forces
- Does Probability become Fuzzy in Small Regions of Spacetime?
- On the impossibility of coin-flipping in generalized probabilistic theories via discretizations of semi-infinite programs
- Derivation of quantum theory with superselection rules
- A computer scientist's reconstruction of quantum theory