Related papers: The Bayes cost in the binary decision problem
The problem of quantum state discrimination between two wave functions of a particle in a square well potential is considered. The optimal minimum-error probability is known to be given by the Helstrom bound. A new strategy is introduced by…
The problem of quantum state discrimination between two wave functions of a particle in a square well potential is considered. The optimal minimum-error probability for the state discrimination is known to be given by the Helstrom bound. A…
Quantum state discrimination between two wave functions on a ring is considered. The optimal minimum-error probability is known to be given by the Helstrom bound. A new strategy is introduced by inserting instantaneously two impenetrable…
We consider the discrimination of two pure quantum states with three allowed outcomes: a correct guess, an incorrect guess, and a non-guess. To find an optimum measurement procedure, we define a tunable cost that penalizes the incorrect…
We investigate a state discrimination problem in operationally the most general framework to use a probability, including both classical, quantum theories, and more. In this wide framework, introducing closely related family of ensembles…
We derive a general lower bound on the minimum-error probability for {\it ambiguous discrimination} between arbitrary $m$ mixed quantum states with given prior probabilities. When $m=2$, this bound is precisely the well-known Helstrom…
For a binary system specified by the density operators r0 and r1 and by the prior probabilities q0 and q1, Helstrom's theory permits the evaluation of the optimal measurement operators and of the corresponding maximum correct detection…
Quantum state discrimination is a fundamental primitive in quantum information processing, underpinning tasks in quantum communication, sensing, and learning. We consider the general Bayes framework, as introduced by Helstrom, for state…
For a given ensemble of $N$ independent and identically prepared particles, we calculate the binary decision costs of different strategies for measurement of polarised spin 1/2 particles. The result proves that, for any given values of the…
The minimum error probability for distinguishing between two quantum states is bounded by the Helstrom limit, derived under the assumption that measurement strategies are restricted to positive operator-valued measurements. We explore…
A core problem in communications is the optimal discrimination of binary-phase-shift-keyed (BPSK) signals. A longstanding goal has been to reach the fundamental quantum limit, known as the Helstrom bound, for BPSK signals encoded in…
Discriminating between quantum states is a fundamental problem in quantum information protocols. The optimum approach saturates the Helstrom bound, which quantifies the unavoidable error probability of mistaking one state for another.…
We provide an operational reinterpretation of wave-particle complementarity in the low-gain Zou-Wang-Mandel (ZWM) induced-coherence interferometer. In the low gain limit, each photon pair is emitted by either one of two nonlinear crystals.…
Due to quantum noise fluctuations, the rate of error achievable in decision problems involving several possible configurations of a scattering system is subject to a fundamental limit known as the Helstrom bound. Here, we present a general…
We consider the problem of minimum-error quantum state discrimination for single-qubit mixed states. We present a method which uses the Helstrom conditions constructively and analytically; this algebraic approach is complementary to…
For the optimal success probability under minimum-error discrimination between $r\geq2$ arbitrary quantum states prepared with any a priori probabilities, we find new general analytical lower and upper bounds and specify the relations…
Multiple-copy state discrimination is a fundamental task in quantum information processing. If there are two, pure, non-orthogonal states then both local and collective schemes are known to reach the Helstrom bound, the maximum probability…
Determining the presence of a potential optical source in the interest region is important for an imaging system and can be achieved by using hypothesis testing. The previous studies assume that the potential source is completely…
The minimum-error probability of ambiguous discrimination for two quantum states is the well-known {\it Helstrom limit} presented in 1976. Since then, it has been thought of as an intractable problem to obtain the minimum-error probability…
Neural networks for semantic segmentation can be seen as statistical models that provide for each pixel of one image a probability distribution on predefined classes. The predicted class is then usually obtained by the maximum a-posteriori…