On the Csorgo-Révész increments of finite dimensional Gaussian random fields

In this paper, we establish some limit theorems on the combined Csorgo-Révész increments with moduli of continuity for finite dimensional Gaussian random fields under mild conditions, via estimating upper bounds of large deviation probabilities on suprema of the finite dimensional Gaussian random fields.Csorgo-Révész increment; Gaussian process; random field; modulus of continuity; quasi-increasing; regularly varying function; large deviation probability.

Single-Copy Certification of Two-Qubit Gates without Entanglement

A quantum state transformation can be generally approximated by single- and two-qubit gates. This, however, does not hold with noisy intermediate-scale quantum technologies due to the errors appearing in the gate operations, where errors of two-qubit gates such as controlled-NOT and SWAP operations are dominated. In this work, we present a cost efficient single-copy certification for a realization of a two-qubit gate in the presence of depolarization noise, where it is aimed to identify if the realization is noise-free, or not. It is shown that entangled resources such as entangled states and a joint measurement are not necessary for the purpose, i.e., a noise-free two-qubit gate is not needed to certify an implementation of a two-qubit gate. A proof-of-principle demonstration is presented with photonic qubits.Comment: 8 pages. arXiv admin note: text overlap with arXiv:1812.0208