Related papers: Uncertainty principle with quantum Fisher informat…
While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the…
Conventional quantum mechanics with a complex Hilbert space and the Born Rule is derived from five axioms describing properties of probability distributions for the outcome of measurements. Axioms I,II,III are common to quantum mechanics…
The uncertainty principle is an inherent characteristic of quantum mechanics. This principle can be formulated in various form. Fundamentally, this principle can be expressed in terms of the standard deviation of the measured observables.…
We have introduced a measure of Gaussian quantum correlations based on quantum Fisher information. For bipartite Gaussian states the minimum quantum Fisher information due to local unitary evolution on one of the parties reliably quantifies…
We develop a variational principle to determine the quantum controls and initial state which optimizes the quantum Fisher information, the quantity characterizing the precision in quantum metrology. When the set of available controls is…
Preconditioning with the quantum Fisher information matrix (QFIM) is a popular approach in quantum variational algorithms. Yet the QFIM is costly to obtain directly, usually requiring more state preparation than its classical counterpart:…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
Starting from the Hamilton-Jacobi equation describing a classical ensemble, one may infer a quantum dynamics using the principle of maximum uncertainty. That procedure requires an appropriate measure of uncertainty: Such a measure is…
Quantum metrology uses small changes in the output probabilities of a quantum measurement to estimate the magnitude of a weak interaction with the system. The sensitivity of this procedure depends on the relation between the input state,…
In quantum mechanics, measurements cause wavefunction collapse that yields precise outcomes, for non-commuting observables such as position and momentum Heisenberg's uncertainty principle limits the intrinsic precision of a state. Although…
Diffraction on the slit can be interpreted in accordance with the Heisenberg uncertainty principle. This elementary example hints at the importance of the information theory for the quantum physics. The role played by one particularly…
We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…
Within the framework of the new formalism of quantum theory - the quantum principle of least action - the initial state of the universe is determined, which is an analogue of the Hartle-Hawking no-boundary wave function. The quantum…
Uncertainty principle is the basis of quantum mechanics. It reflects the basic law of the movement of microscopic particles. Wigner-Yanase skew information, as a measure of quantum uncertainties, is used to characterize the intrinsic…
Informational dependence between statistical or quantum subsystems can be described with Fisher matrix or Fubini-Study metric obtained from variations of the sample/configuration space coordinates. Using these non-covariant objects as…
The quantum variables that can be accessed directly by experiments are described by observables. Therefore, physical parameters can only be evaluated indirectly, via estimations based on experimental measurement results. I show that the…
Uncertainty principle forbids one to determine which of the two paths a quantum system has travelled, unless interference between the alternatives had been destroyed by a measuring device, e.g., by a pointer. One can try to weaken the…
We consider the geometrization of quantum mechanics. We then focus on the pull-back of the Fubini-Study metric tensor field from the projective Hibert space to the orbits of the local unitary groups. An inner product on these tensor fields…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
Hypothesis testing is a fundamental issue in statistical inference and has been a crucial element in the development of information sciences. The Chernoff bound gives the minimal Bayesian error probability when discriminating two hypotheses…