Vlad Gheorghiu

Universal uncertainty relations.

Uncertainty relations are a distinctive characteristic of quantum theory that impose intrinsic limitations on the precision with which physical properties can be simultaneously determined. The modern work on uncertainty relations employs entropic measures to quantify the lack of knowledge associated with measuring noncommuting observables. However, there is no fundamental reason for using entropies as quantifiers; any functional relation that characterizes the uncertainty of the measurement outcomes defines an uncertainty relation. Starting from a very reasonable assumption of invariance under mere relabeling of the measurement outcomes, we show that Schur-concave functions are the most general uncertainty quantifiers. We then discover a fine-grained uncertainty relation that is given in terms of the majorization order between two probability vectors, significantly extending a majorization-based uncertainty relation first introduced in M. H. Partovi, Phys. Rev. A 84, 052117 (2011). Such a vector-type uncertainty relation generates an infinite family of distinct scalar uncertainty relations via the application of arbitrary uncertainty quantifiers. Our relation is therefore universal and captures the essence of uncertainty in quantum theory.

Quantum-error-correcting codes using qudit graph states

Graph states are generalized from qubits to collections of

Separable Operations on Pure States

n

Construction of equally entangled bases in arbitrary dimensions via quadratic Gauss sums and graph states

qudits of arbitrary dimension

Estimating the Cost of Generic Quantum Pre-image Attacks on SHA-2 and SHA-3

D

Standard form of qudit stabilizer groups

, and simple graphical methods are used to construct both additive and nonadditive quantum error correcting codes. Codes of distance 2 saturating the quantum Singleton bound for arbitrarily large

Location of quantum information in additive graph codes

n

Comparison of memory thresholds for planar qudit geometries

and

Consistent histories for tunneling molecules subject to collisional decoherence

D

Information-theoretic treatment of tripartite systems and quantum channels

are constructed using simple graphs, except when