Variations on the Choi-Jamiolkowski isomorphism
arXiv:2211.16533 · doi:10.1088/1751-8121/ad5394
Abstract
We address various aspects of a widely used tool in quantum information theory: the Choi-Jamiolkowski isomorphism [A. Jamiolkowski, Rep. Math. Phys., 3, 275 (1972)]. We review different versions of the isomorphism, their properties and propose a unified description that combines them all. To this end, we identify the physical reason for the appearance of the (basis-dependent) operation of transposition in the isomorphism as used in Choi's theorem [M.-D. Choi, Lin. Alg. Appl., 10, 285 (1975)]. This requires a careful distinction between Jordan algebras and the different C*-algebras they arise from, which are distinguished by their order of composition. Physically, the latter encodes a choice of time orientation in the respective algebras, which relates to a number of recent results, including a characterisation of quantum from more general non-signalling bipartite correlations [M. Frembs and A. Döring, arXiv:2204.11471] and a classification of bipartite entanglement [M. Frembs, arXiv:2207.00024].
12 pages, comments welcome
References in corpus (8)
- Entanglement detection
- Fault-Tolerant Postselected Quantum Computation: Schemes
- Quantum operations with indefinite time direction
- Symmetries of quantum evolutions
- Error-disturbance relations in mixed states
- Choi matrices revisited
- Bipartite entanglement and the arrow of time
- Two New Complete Invariants of von Neumann Algebras