Accessible Information Without Disturbing Partially Known Quantum States on a von Neumann Algebra

Kuramochi, Yui

doi:10.1007/s10773-018-3749-8

Cited by 4 publications

(2 citation statements)

References 25 publications

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“…The following theorem, which is immediate from Corollary 1 of Ref. 19, is an operator algebraic version of the quantum no-broadcasting theorem and will play an important role in the proof of the main result. (i) Λ is broadcastable in the sense of algebraic tensor product.…”

Section: E No-broadcasting Theoremmentioning

confidence: 99%

Entanglement-breaking channels with general outcome operator algebras

Kuramochi

2018

Journal of Mathematical Physics

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A unit-preserving and completely positive linear map, or a channel, Λ :is a separable state for any C * -algebra B and any state ω on the injective C * -tensor product A in ⊗B. In this paper, we establish the equivalence of the following conditions for a channel Λ with a quantum input space and with a general outcome C * -algebra, generalizing known results in finite dimensions: (i) Λ is EB; (ii) Λ has a measurementprepare form (Holevo form); (iii) n copies of Λ are compatible for all 2 ≤ n < ∞;(iv) countably infinite copies of Λ are compatible. By using this equivalence, we also show that the set of randomization-equivalence classes of normal EB channels with a fixed input von Neumann algebra is upper and lower Dedekind-closed, i.e. the supremum or infimum of any randomization-increasing or decreasing net of EB channels is also EB. As an example, we construct an injective normal EB channel with an arbitrary outcome operator algebra M acting on an infinite-dimensional separable Hilbert space by using the coherent states and the Bargmann measure.

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Section: E No-broadcasting Theoremmentioning

confidence: 99%

Entanglement-breaking channels with general outcome operator algebras

Kuramochi

2018

Journal of Mathematical Physics

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“…To establish the lower Dedekind-closedness of CH QC (L(H in )), we use an operator algebraic version of the quantum no-broadcasting theorem. 25…”

Section: Lemma 7 Ch(l(h In )) Is An Upper Dcpomentioning

confidence: 99%

Directed-completeness of quantum statistical experiments in the randomization order

Kuramochi

2018

Preprint

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A parametrized family of normal states on a von Neumann algebra is called a statistical experiment, which generalizes the corresponding concepts in classical statistics and finite-dimensional quantum systems. We introduce randomization preorder and equivalence relations for statistical experiments with a fixed parameter set and for normal channels with a fixed input space by post-processing completely positive channels. In this paper, we prove that the set of equivalence classes of statistical experiments or those of normal channels is an upper and lower directed-complete partially ordered set with respect to the randomization order, i.e. any increasing or decreasing net of statistical experiments or channels has its supremum or infimum in the randomization order. We also show that if the outcome space of each statistical experiment or channel of a randomization-monotone net is commutative, the outcome space of the supremum or infimum can also be taken to be commutative.We consider two examples of homogeneous Markov processes of channels on infinitedimensional separable Hilbert spaces, namely block-diagonalization with irrational translation and ideal quantum linear amplifier channels, and explicitly derive their infima. Throughout the paper, the concept of channel conjugation is used to obtain results for decreasing channels from those for increasing channels.

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