Detecting Bias in Randomness by PT-Symmetric Quantum State Discrimination

Random number generators are used in computing, security, and cryptographic applications. The random number outputs retaining the entropy without bias is critical for the integrity of the random number generator and the relying applications. $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics provides a mechanism to improve the detection of the bias in randomness since it can convert two non-orthogonal quantum states into orthogonal ones. We propose a new randomness bias detection and quantification method by using $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics. Previous studies show that, if the bias amount is a priori known, its presence can be detected by, in principle, a single measurement in $\mathcal{P}\mathcal{T}$-symmetric system. Taking advantage of an additional degree of freedom provided by $\mathcal{P}\mathcal{T}$ symmetry, we extend this approach to the case when the bias amount is not a priori known. We provide an algorithm and the analysis using $\mathcal{P}\mathcal{T}$ symmetry for randomness bias detection and quantification.