139 research outputs found
Postquantum Br\`{e}gman relative entropies and nonlinear resource theories
We introduce the family of postquantum Br\`{e}gman relative entropies, based
on nonlinear embeddings into reflexive Banach spaces (with examples given by
reflexive noncommutative Orlicz spaces over semi-finite W*-algebras,
nonassociative L spaces over semi-finite JBW-algebras, and noncommutative
L spaces over arbitrary W*-algebras). This allows us to define a class of
geometric categories for nonlinear postquantum inference theory (providing an
extension of Chencov's approach to foundations of statistical inference), with
constrained maximisations of Br\`{e}gman relative entropies as morphisms and
nonlinear images of closed convex sets as objects. Further generalisation to a
framework for nonlinear convex operational theories is developed using a larger
class of morphisms, determined by Br\`{e}gman nonexpansive operations (which
provide a well-behaved family of Mielnik's nonlinear transmitters). As an
application, we derive a range of nonlinear postquantum resource theories
determined in terms of this class of operations.Comment: v2: several corrections and improvements, including an extension to
the postquantum (generally) and JBW-algebraic (specifically) cases, a section
on nonlinear resource theories, and more informative paper's titl
From Quantum Source Compression to Quantum Thermodynamics
This thesis addresses problems in the field of quantum information theory.
The first part of the thesis is opened with concrete definitions of general
quantum source models and their compression, and each subsequent chapter
addresses the compression of a specific source model as a special case of the
initially defined general models. First, we find the optimal compression rate
of a general mixed state source which includes as special cases all the
previously studied models such as Schumacher's pure and ensemble sources and
other mixed state ensemble models. For an interpolation between the visible and
blind Schumacher's ensemble model, we find the optimal compression rate region
for the entanglement and quantum rates. Later, we study the classical-quantum
variation of the celebrated Slepian-Wolf problem and the ensemble model of
quantum state redistribution for which we find the optimal compression rate
considering per-copy fidelity and single-letter achievable and converse bounds
matching up to continuity of functions which appear in the corresponding
bounds.
The second part of the thesis revolves around information theoretical
perspective of quantum thermodynamics. We start with a resource theory point of
view of a quantum system with multiple non-commuting charges. Subsequently, we
apply this resource theory framework to study a traditional thermodynamics
setup with multiple non-commuting conserved quantities consisting of a main
system, a thermal bath and batteries to store various conserved quantities of
the system. We state the laws of the thermodynamics for this system, and show
that a purely quantum effect happens in some transformations of the system,
that is, some transformations are feasible only if there are quantum
correlations between the final state of the system and the thermal bath.Comment: PhD thesis, 176 page
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