Minimum-error quantum state discrimination: Extremely tight upper and lower bounds with application in digital quantum communication

This paper proposes a class of tight upper and lower bounds for the optimal probability of correctly discriminating K quantum signals. The tightness of these bounds is shown analytically and numerically. These bounds are optimal for a binary quantum signal. The proposed upper bounds are based on a generalized trace distance measure between more than two quantum states. Also, we propose projector measurements that are good candidates for the near-optimal projector measurement. Also, an equivalent expression for the bounds is given based on the Gram matrix, which is more appropriate for numerical calculations, especially for digital quantum communication purposes, such as investigating the error probability of classical communication by using high-dimension quantum pulse position modulation signals.