On Schmidt Decomposition: Approach Based on Correlation Operator as Bipartite Entanglement Entity

Abstract

An elaborated review with proofs of Schmidt canonical decomposition of any bipartite state vector is approached through general subsystem basis expansion. The upgraded forms of Schmidt decomposition in terms of correlation operator and twin observables are presented in detail. The discussion is extended to distant measurement, Einstein–Podolsky–Rosen states and Schrödinger's steering. All claims and proofs are given in standard form unlike in the previous articles of the author where all results were obtained utilizing the very rarely used antilinear Hilbert–Schmidt maps of one subsystem state space into the other. For practical reasons the formalism of partial traces with their rules and reduced density operators together with correlation operator are used. Quanta 2018; 7: 19–39.