Mixed-state twin observables

Abstract

Twin observables, i.e. opposite subsystem observables A+ and A- that are indistinguishable in measurement in a given mixed or pure state W, are investigated in detail algebraicly and geometrically. It is shown that there is a far-reaching correspondence between the detectable (in W) spectral entities of the two operators. Twin observables are state-dependently quantum-logically equivalent, and direct subsystem measurement of one of them ipso facto gives rise to the indirect (i.e. distant) measurement of the other. Existence of nontrivial twins requires singularity of W. Systems in thermodynamic equilibrium do not admit subsystem twins. These observables may enable one to simplify the matrix representing W.

13 pages

References in corpus (1)

• Experimental quantum teleportation

Cited by in corpus (6)

• On Mutual Information in Multipartite Quantum States and Equality in Strong Subadditivity of Entropy
• Complete "Born's rule" from "environment-assisted invariance" in terms of pure-state twin unitaries
• Chains of Quasi-Classical Informations for Bipartite Correlations and the Role of Twin Observables
• The role of coherence entropy of physical twin observables in entanglement
• Hermitian Schmidt Decomposition and Twin Observables of Bipartite Mixed States
• Necesary and sufficient range-dimension conditions for bipartite quantum correlations