‘Nonlinear’ positive mappings for density matrices

✍ Scribed by Erwin Brüning; Francesco Petruccione

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 121 KB
• Volume: 42
• Category: Article
• ISSN: 1386-9477
• DOI: 10.1016/j.physe.2009.06.017

✦ Synopsis

In quantum physics one uses density matrices on separable Hilbert spaces for the mathematical description of states. Often it is important to know when the image of a density matrix under a mapping is again a density matrix. We propose some new classes of mappings which map the space of density matrices on one Hilbert space H into the space of density matrices on some other Hilbert space K where K ¼ H naturally is allowed. Such mappings may be 'linear' or 'nonlinear'. In the case of finite dimensional Hilbert spaces we find all mappings of this type.