Quantum Coin Method for Numerical Integration

A Numerical Integration Method by Using Generalized Series of Functions

Convergence of product integration method applied for numerical solution of linear weakly singular Volterra systems

We develop and apply the product integration method to a large class of linear weakly singular Volterra systems. We show that under certain sufficient conditions this method converges. Numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.

Relativistic quantum coin tossing

A relativistic quantum information exchange protocol is proposed allowing two distant users to realize “coin tossing” procedure. The protocol is based on the point that in relativistic quantum theory reliable distinguishing between the two orthogonal states generally requires a finite time depending on the structure of these states. PACS numbers: 03.67.-a, 03.65.Bz, 42.50Dv The coin tossing pro...

Experimental quantum coin tossing.

In this Letter we present the first implementation of a quantum coin-tossing protocol. This protocol belongs to a class of "two-party" cryptographic problems, where the communication partners distrust each other. As with a number of such two-party protocols, the best implementation of the quantum coin tossing requires qutrits, resulting in a higher security than using qubits. In this way, we ha...

Quantum Counterfeit Coin Problems

The counterfeit coin problem requires us to find all false coins from a given bunch of coins using a balance scale. We assume that the balance scale gives us only “balanced” or “tilted” information and that we know the number k of false coins in advance. The balance scale can be modeled by a certain type of oracle and its query complexity is a measure for the cost of weighing algorithms (the nu...