Natural Quantum Operational Semantics with Predicates

Abstract

A general definition of a quantum predicate and quantum labelled transition systems for finite quantum computation systems is presented. The notion of a quantum predicate as a positive operator-valued measure is developed. The main results of this paper are a theorem about the existence of generalised predicates for quantum programs defined as completely positive maps and a theorem about the existence of a GSOS format for quantum labelled transition systems. The first theorem is a slight generalisation of D'Hondt and Panagaden's theorem about the quantum weakest precondition in terms of discrete support positive operator-valued measures.Keywords: quantum computation, predicate notion for quantum programs, quantum labelled transition systems.

Generalised quantum weakest preconditions

“…Especially important seems to be the question of providing interesting examples where previously known tools and results are not directly applicable. This will be a main topic of a forthcoming paper see also [32] for some preliminary results.…”

The Entanglement Level and the Detection of Quantum Data Transfer Correctness in Short Qutrit Spin Chains

“…Introducing a definition of the transfer protocol based on a Hamiltonian and a unitary operator allows to describe the transfer ( Fig. 1) as an algorithm (or structural quantum program [23], [16]). A very important issue is the use of γ condition as an invariant for the protocol.…”

“…The needed quantum state, for the spin chain with the number of nodes greater than two, we obtain by use of the partial trace operation. If ρ represents the state of the whole chain with N nodes then the state in the first (denoted as 1) and the last (described as N ) node we calculate as: Tr (2,3,...,i−k,...,N −2,N −1) (ρ) (23) where Tr (·) (ρ) is the partial trace operation.…”