L\"uders' and quantum Jeffrey's rules as entropic projections

We prove that the standard quantum mechanical description of a quantum state change due to measurement, given by Lueders' rules, is a special case of the constrained maximisation of a quantum relative entropy functional. This result is a quantum analogue of the derivation of the Bayes--Laplace rule as a special case of the constrained maximisation of relative entropy. The proof is provided for the Umegaki relative entropy of density operators over a Hilbert space as well as for the Araki relative entropy of normal states over a W*-algebra. We also introduce a quantum analogue of Jeffrey's rule, derive it in the same way as above, and discuss the meaning of these results for quantum bayesianism

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$_p$ spaces over semi-finite JBW-algebras, and noncommutative L$_p$ 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

Quantum collapse rules from the maximum relative entropy principle

We show that the von Neumann--Lueders collapse rules in quantum mechanics always select the unique state that maximises the quantum relative entropy with respect to the premeasurement state, subject to the constraint that the postmeasurement state has to be compatible with the knowledge gained in the measurement. This way we provide an information theoretic characterisation of quantum collapse rules by means of the maximum relative entropy principle.Comment: v2: some references added, improved presentation, result generalised to cover nonfaithful states; v3: cross-ref to arXiv:1408.3502 added, v4: some small corrections plus reference to a published version adde

Surface Structural Disordering in Graphite upon Lithium Intercalation/Deintercalation

We report on the origin of the surface structural disordering in graphite anodes induced by lithium intercalation and deintercalation processes. Average Raman spectra of graphitic anodes reveal that cycling at potentials that correspond to low lithium concentrations in LixC (0 \leq x < 0.16) is responsible for most of the structural damage observed at the graphite surface. The extent of surface structural disorder in graphite is significantly reduced for the anodes that were cycled at potentials where stage-1 and stage-2 compounds (x > 0.33) are present. Electrochemical impedance spectra show larger interfacial impedance for the electrodes that were fully delithiated during cycling as compared to electrodes that were cycled at lower potentials (U < 0.15 V vs. Li/Li+). Steep Li+ surface-bulk concentration gradients at the surface of graphite during early stages of intercalation processes, and the inherent increase of the LixC d-spacing tend to induce local stresses at the edges of graphene layers, and lead to the breakage of C-C bonds. The exposed graphite edge sites react with the electrolyte to (re)form the SEI layer, which leads to gradual degradation of the graphite anode, and causes reversible capacity loss in a lithium-ion battery.Comment: 12 pages, 5 figure