Related papers: Quantum inference of states and processes
Maximum likelihood principle is shown to be the best measure for relating the experimental data with the predictions of quantum theory.
Maximum likelihood estimation is applied to the determination of an unknown quantum measurement. The measuring apparatus performs measurements on many different quantum states and the positive operator-valued measures governing the…
New algorithm for quantum state estimation based on the maximum likelihood estimation is proposed. Existing techniques for state reconstruction based on the inversion of measured data are shown to be overestimated since they do not…
Even though measurement results obtained in the real world are generally both noisy and continuous, quantum measurement theory tends to emphasize the ideal limit of perfect precision and quantized measurement results. In this article, a…
Intrinsic randomness is generated when a quantum state is measured in any basis in which it is not diagonal. In an adversarial scenario, we quantify this randomness by the probability that a correlated eavesdropper could correctly guess the…
We propose an iterative algorithm for incomplete quantum process tomography, with the help of quantum state estimation, based on the combined principles of maximum-likelihood and maximum-entropy. The algorithm yields a unique estimator for…
We present a detailed account of quantum state estimation by joint maximization of the likelihood and the entropy. After establishing the algorithms for both perfect and imperfect measurements, we apply the procedure to data from simulated…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
We state a quantum version of Bayes's rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state…
Maximum-likelihood estimation is applied to identification of an unknown quantum mechanical process represented by a ``black box''. In contrast to linear reconstruction schemes the proposed approach always yields physically sensible…
We address quantum estimation in situations where one has at disposal data from the measurement of an incomplete set of observables and some a priori information on the state itself. By expressing the a priori information in terms of a bias…
We extend the concept of probabilistic unambiguous discrimination of quantum states to quantum state estimation. We consider a scenario where the measurement device can output either an estimate of the unknown input state or an inconclusive…
Quantum-limited amplifiers increase the amplitude of quantum signals at the price of introducing additional noise. Quantum purification protocols operate in the reverse way, by reducing the noise while attenuating the signal. Here we…
Knowing and guessing, these are two essential epistemological pillars in the theory of quantum-mechanical measurement. As formulated quantum mechanics is a statistical theory. In general, a priori unknown states can be completely determined…
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…
We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map…
For many-particle systems, quantum information in base n can be defined by partitioning the set of states according to the outcomes of n-ary (joint) observables. Thereby, k particles can carry k nits. With regards to the randomness of…
Assessment of practical quantum information processing (QIP) remains partial without understanding limits imposed by noise. Unfortunately, mere description of noise grows exponentially with system size, becoming cumbersome even for modest…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
We show that the Jaynes principle is indeed a proper inference scheme when applied to compound systems and will correctly produce the entangled maximum entropy states compatible with appropriate data. This is accomplished by including the…