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Complementarity of quantum discord and classically accessible information
The sum of the Holevo quantity (that bounds the capacity of quantum channels to transmit classical information about an observable) and the quantum discord (a measure of the quantumness of correlations of that observable) yields an observable-independent total given by the quantum mutual information. This split naturally delineates information about quantum systems accessible to observers - information that is redundantly transmitted by the environment - while showing that it is maximized for the quasi-classical pointer observable. Other observables are accessible only via correlations with the pointer observable. We also prove an anti-symmetry property relating accessible information and discord. It shows that information becomes objective - accessible to many observers - accessible as quantum information is relegated to correlations with the global environment, and, therefore, locally inaccessible. The resulting complementarity explains why, in a quantum Universe, we perceive objective classical reality while flagrantly quantum superpositions are out of reach.Keywords: States, Decoherence, Physical reality, Darwinism, Einselection, Mechanical descriptio
Universe's Primordial Quantum Memories
We provide a very general argument showing that the Universe must have kept
its quantum memories from an epoch much earlier than e-foldings before the
end of inflation. The point is that a generic system of enhanced memory storage
capacity exhibits a phenomenon of memory burden. Due to its universal nature
this effect must be applicable to de Sitter since the latter has a maximal
memory storage capacity thanks to its Gibbons-Hawking entropy. The primordial
information pattern encoded in de Sitter memory initially costs very little
energy. However, because of Gibbons-Hawking evaporation, the memory burden of
the pattern grows in time and increasingly back reacts on the evaporation
process. After a finite time the memory burden becomes unbearable and de Sitter
quantum breaks. If inflation ended not long before its quantum break-time, the
imprints of the primordial memory pattern can be observable. This provides a
qualitatively new type of window in the Universe's beginning, a sort of cosmic
quantum hair.Comment: 9 pages, 2 figure
Languages of Quantum Information Theory
This note will introduce some notation and definitions for information
theoretic quantities in the context of quantum systems, such as (conditional)
entropy and (conditional) mutual information. We will employ the natural
C*-algebra formalism, and it turns out that one has an allover dualism of
language: we can define everything for (compatible) observables, but also for
(compatible) C*-subalgebras. The two approaches are unified in the formalism of
quantum operations, and they are connected by a very satisfying inequality,
generalizing the well known Holevo bound. Then we turn to communication via
(discrete memoryless) quantum channels: we formulate the Fano inequality, bound
the capacity region of quantum multiway channels, and comment on the quantum
broadcast channel.Comment: 16 pages, REVTEX, typos corrected, references added and extende
Information capacity of quantum observable
In this paper we consider the classical capacities of quantum-classical
channels corresponding to measurement of observables. Special attention is paid
to the case of continuous observables. We give the formulas for unassisted and
entanglement-assisted classical capacities and consider some
explicitly solvable cases which give simple examples of entanglement-breaking
channels with We also elaborate on the ensemble-observable duality
to show that for the measurement channel is related to the
-quantity for the dual ensemble in the same way as is related to the
accessible information. This provides both accessible information and the
-quantity for the quantum ensembles dual to our examples.Comment: 13 pages. New section and references are added concerning the
ensemble-observable dualit
Coding theorems for hybrid channels. II
The present work continues investigation of the capacities of measurement
(quantum-classical) channels in the most general setting, initiated
in~\cite{HCT}. The proof of coding theorems is given for the classical capacity
and entanglement-assisted classical capacity of the measurement channel with
arbitrary output alphabet, without assuming that the channel is given by a
bounded operator-valued density.Comment: 15 pages, one figur
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