It is conjecture that a particular kind of group-covariant SIC–POVM exists in arbitrary dimensions, providing numerical results up to dimension 45 to bolster this claim.Expand

The Heisenberg uncertainty principle bounds the uncertainties about the outcomes of two incompatible measurements on a quantum particle. This bound, however, changes if a memory device is involved… Expand

It is shown that the free energy of thermodynamics emerges naturally from the resource theory of energy-preserving transformations, provided that a sublinear amount of coherent superposition over energy levels is available, a situation analogous to the sub linear amount of classical communication required for entanglement dilution.Expand

In this hybrid classical-quantum version of the famous Slepian-Wolf problem, the smooth max entropy is found to govern the number of bits into which classical information can be compressed so that it can be reliably recovered from the compressed version and quantum side information.Expand

A special case for certain conjugate observables is proved by adapting a similar result found by Christandl and Winter pertaining to quantum channels, and possible applications to the decoupling of quantum systems and for security analysis in quantum cryptography are discussed.Expand

We show that optimal protocols for noisy channel coding of public or private information over either classical or quantum channels can be directly constructed from two more primitive… Expand

These protocols are distinct from previously known schemes in that they combine two practically relevant properties: they achieve the ultimate rate--defined with respect to a strong secrecy condition--and their complexity is essentially linear in the blocklength.Expand

An entropy measure for quantum systems is studied that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy, and is derived from the formulation as a semidefinite program.Expand

This work finds approximate and exact characterizations of this trade-off for various channels of interest, including dephasing, depolarizing and erasure channels, and develops several bounds that are valid for general quantum channels and can be computed for small instances.Expand

We prove a Gleason-type theorem for the quantum probability rule using frame functions defined on positive-operator-valued measures (POVMs), as opposed to the restricted class of orthogonal… Expand