Programmable discrimination with an error margin

Abstract

The problem of optimally discriminating between two completely unknown qubit states is generalized by allowing an error margin. It is visualized as a device-the programmable discriminator-with one data and two program ports, each fed with a number of identically prepared qubits-the data and the programs. The device aims at correctly identifying the data state with one of the two program states. This scheme has the unambiguous and the minimum error schemes as extremal cases, when the error margin is set to zero or it is sufficiently large, respectively. Analytical results are given in the two situations where the margin is imposed on the average error probability-weak condition-or it is imposed separately on the two probabilities of assigning the state of the data to the wrong program-strong condition. It is a general feature of our scheme that the success probability rises sharply as soon as a small error margin is allowed, thus providing a significant gain over the unambiguous scheme while still having high confidence results.

Optimal quantum operations at zero energy cost

“…A common example is that of stationary instruments with outcomes X = {succ, fail}. In this case, the stationarity condition (23) simply means that the probability of implementing the desired transformation M succ is the same at every time. Stationary two-outcome instruments can be used to describe tasks like probabilistic covariant cloning and probabilistic amplification, or more generally, any task where the goal is to probabilistically transform a set of states generated by time evolution.…”

“…For example, we will see that a beam of N atoms, each of them prepared in the superposition |S = (|E + |G )/ √ 2 of the ground state and the first excited state, can be probabilistically transformed at no energy cost into a stronger beam of N 2− atoms in a state that is nearly identical to the state of N 2− identical copies of |S , up to an exponentially small error. The ability to efficiently approximate forbidden transformations of coherence at zero energy cost is a new twist of the postselection approach widely applied in quantum information [19][20][21][22][23][24][25][26][27][28][29][30][31][32] and complements existing results on the resource theory of coherence [33? -38].…”

Success probabilities for universal unambiguous discriminators between unknown pure states

“…In this programmable quantum device, two possible states enter two program registers as "programs" respectively, and the data register is prepared with a third state (guaranteed to be one of the two possible states) which one wishes to identify. One amazing feature of this discriminator is that the states in the device can be unknown, which means no classical knowledge on the states is provided, and it is capable to distinguish any pair of states in this device.Later, the generalizations and the experimental realizations of programmable discriminators are introduced and widely discussed [8][9][10][11][12][13]. The problems with multiple copies in program and data registers or with high-dimensional states in the registers are considered.…”

“…Later, the generalizations and the experimental realizations of programmable discriminators are introduced and widely discussed [8][9][10][11][12][13]. The problems with multiple copies in program and data registers or with high-dimensional states in the registers are considered.…”

“…In most of these literatures, either the unambiguous discrimination or the minimum-error scheme is used, and quite recently, the two strategies are unified in Ref. [13] by introducing an error margin. With multi-copy and high-dimensional pure states in the * taozhousc@gmail.com registers, the optimal solution and success probability are hard to obtain.…”