On quantum states with a finite-dimensional approximation property
- URL: http://arxiv.org/abs/2103.09626v2
- Date: Thu, 18 Mar 2021 17:48:05 GMT
- Title: On quantum states with a finite-dimensional approximation property
- Authors: M.E.Shirokov
- Abstract summary: We consider a class of quantum states containing finite rank states containing infinite rank states with the sufficient rate decreasing of eigenvalues.
We show that this property implies finiteness of the entropy von Neumann entropy but unsolved the question concerning the converse implication.
We establish the uniform continuity of the above characteristics as functions of a channel w.r.t.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We consider a class (convex set) of quantum states containing all finite rank
states and infinite rank states with the sufficient rate of decreasing of
eigenvalues (in particular, all Gaussian states). Quantum states from this
class are characterized by the property (called the FA-property) that allows to
obtain several results concerning finite-dimensional approximation of basic
entropic and information characteristics of quantum systems and channels.
We obtain a simple sufficient condition of the FA-property. We show that this
property implies finiteness of the von Neumann entropy, but leave unsolved the
question concerning the converse implication.
We obtain uniform approximation results for characteristics depending on a
pair (channel, input state) and for characteristics depending on a pair
(channel, input ensemble). We establish the uniform continuity of the above
characteristics as functions of a channel w.r.t. the strong convergence
provided that the FA-property holds either for the input state or for the
average state of input ensemble.
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