A unitary t-design is a set of unitaries that is" evenly distributed" in the sense that the
average of any t-th order polynomial over the design equals the average over the entire …

We prove that magic states from the Clifford hierarchy give optimal solutions for tasks
involving nonlocality and entropic uncertainty with respect to Pauli measurements. For both …

Mutually unbiased bases (MUBs) are interesting for various reasons. The most attractive
example of (a complete set of) MUBs is the one constructed by Ivanović as well as Wootters …

We show that if a set of four mutually unbiased bases (MUBs) in $\newcommand
{\n}{\nu}\newcommand {\m}{\mu}\mathbb {C}^ 6$ exists and contains the identity, then any …

Stabilizer states are eigenvectors of maximal commuting sets of operators in a finite
Heisenberg group. States that are far from being stabilizer states include magic states in …

A Galois unitary is a generalization of the notion of anti-unitary operators. They act only on
those vectors in Hilbert space whose entries belong to some chosen number field. For …

Tomographic reconstruction of quantum states plays a fundamental role in benchmarking
quantum systems and retrieving information from quantum computers. Among the …

A conjecture connected with quantum physics led N. Katz to discover some amazing mixed
character sum identities over a field of q elements, where q is a power of a prime p> 3. His …

A conjecture connected with quantum physics led N. Katz to discover some amazing mixed
character sum identities over a field of q elements, where q is a power of a prime p> 3 p> 3 …

Finding four six-dimensional mutually unbiased bases (MUBs) is a long-standing open
problem in quantum information. By assuming that they exist and contain the identity matrix …