Optimal programmable unambiguous discriminator between two unknown latitudinal states

Abstract

Two unknown states can be unambiguously distinguished by a universal programmable discriminator, which has been widely discussed in previous works and the optimal solution has also been obtained. In this paper, we investigate the programmable unambiguous discriminator between two unknown "latitudinal" states, which lie in a subspace of the total state space. By equivalence of unknown pure states to known average mixed states, the optimal solution for this problem is systematically derived, and the analytical success probabilities for the optimal unambiguous discrimination are obtained. It is beyond one's expectation that the optimal setting for the programmable unambiguous discrimination between two unknown "latitudinal" states is the same as that for the universal ones. The results in this work can be used for the realization of the programmable discriminator in laboratory.

The universal unambiguous discriminator between two unknown qudit states

“…Later, the cases where a certain number of copies in the registers are provided were discussed in refs. [23][24][25][26][27][28][29][30][31][32], which is the generalization of unambiguous discrimination discussed in refs. [22].…”

“…By equivalence of unknown pure states to known mixed states and with the Jordan-basis method, the unambiguous discrimination for the high-dimensional state in the registers with n A = n B = n C = 1 was discussed in refs. [28,29].…”

Optimal quantum state identification with qudit-encoded unknown states

“…In quantum state identification [1][2][3][4][5][6][7][8][9][10][11][12][13][14] the task is to identify the state of a quantum system, prepared with certain prior probability in a definite state out of a finite set of possible states, where some or all of the states are unknown. The unknown states are encoded into different reference copies, which together have been introduced as the program register in a programmable machine [1] for identifying the state of the probe, carrying the data.…”

“…A variant of the state identification problem, where for d = 2 one of the two pure states is known and the other is unknown, has also been studied [5]. In addition, for two unknown qubit states the case where some classical knowledge is available has been treated [10,11], and a modified identification strategy with a fixed error rate has been investigated [12].…”