Is Quantum Mechanics An Island In Theoryspace?

Abstract

This recreational paper investigates what happens if we change quantum mechanics in several ways. The main results are as follows. First, if we replace the 2-norm by some other p-norm, then there are no nontrivial norm-preserving linear maps. Second, if we relax the demand that norm be preserved, we end up with a theory that allows rapid solution of PP-complete problems (as well as superluminal signalling). And third, if we restrict amplitudes to be real, we run into a difficulty much simpler than the usual one based on parameter-counting of mixed states.

9 pages, minor corrections

References in corpus (5)

• Quantum Theory of Probability and Decisions
• Quantum Theory From Five Reasonable Axioms
• Unknown Quantum States: The Quantum de Finetti Representation
• Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems
• Environment - Assisted Invariance, Causality, and Probabilities in Quantum Physics

Cited by in corpus (14)

• The measurement postulates of quantum mechanics are operationally redundant
• Almost quantum theory
• Limits on Efficient Computation in the Physical World
• Triple Interference, Non-linear Talbot Effect and Gravitization of the Quantum
• Informal Resource Letter - Nonlinear quantum mechanics on arXiv up to August 2004
• Complex and Unpredictable Cardano
• Advantage of Quantum Theory Over Non-classical Models of Communication
• Quantum Computing and Hidden Variables II: The Complexity of Sampling Histories
• Born's rule from almost nothing
• An atomic test of higher-order interference
• The Born rule
• No-signaling non-unitary modification of quantum dynamics within a deterministic model of quantization
• Probability in two deterministic universes
• BQP_p = PP for integer p > 2