Quantum parameter estimation has many applications, from gravitational wave detection to quantum key distribution. The most commonly used technique for this type of estimation is quantum filtering, using only past observations. We present the first experimental demonstration of quantum smoothing, a time-symmetric technique that uses past and future observations, for quantum parameter estimation...

The correspondence between exotic quantum holonomy, which occurs in families of Hermitian cycles, and exceptional points (EPs) for non-Hermitian quantum theory is examined in quantum kicked tops. Under a suitable condition, an explicit expression of the adiabatic parameter dependencies of quasienergies and stationary states, which exhibit anholonomies, is obtained. It is also shown that the qua...

The quantization of the continous cat maps on the torus has led to rather pathological quantum objects [6]. The non-generic behaviour of this model has led some to conclude that the Correspondence Principle fails in this case [2]. In this note we introduce the quantum sawtooth models, since this is the natural family to which the cat maps belong. Thus, a simple propagator depending on a paramet...

Quantum parameter estimation is central to many fields such as quantum computation, communications and metrology. Optimal estimation theory has been instrumental in achieving the best accuracy in quantum parameter estimation, which is possible when we have very precise knowledge of and control over the model. However, uncertainties in key parameters underlying the system are unavoidable and may...

We discuss a toy model for adiabatic quantum computation which displays some phenomenological properties expected in more realistic implementations. This model has two free parameters: the adiabatic evolution parameter s and the α parameter which emulates many-variables constrains in the classical computational problem. The proposed model presents, in the s − α plane, a line of first order quan...

We investigate two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gln and sln. We show that these quantum groups can be realized as Drinfel’d doubles of certain Hopf subalgebras with respect to Hopf pairings. Using the Hopf pairing, we construct a corresponding R-matrix. The quantum groups have a natural n-dimensional module V . The R-matrix enables...

We show that the XY quantum chain in a magnetic field is invariant under a two parameter deformation of the SU(1/1) superalgebra. One is led to an extension of the braid group and the Hecke algebra which reduce to the known ones when the two parameter coincide. The physical significance of the two parameters is discussed. CERN-TH.6299/91 October 1991 ∗Permanent address: Universität Bonn, Physik...

A statistical parameter estimation theory for quantum pure state models is presented. We rst investigate a general framework of the pure state estimation theory and derive quantum counterparts of the Fisher metric. Then we formulate a one parameter estimation theory, based on the symmetric logarithmic derivatives, and clarify the di erences between pure state models and strictly positive models.

A functional method is discussed, where the quantum fluctuations of a theory are controlled by a mass parameter and the evolution of the theory with this parameter is connected to its renormalization. It is found, in the framework of the gradient expansion, that the coupling constant of a N = 1 Wess-Zumino theory in 2+1 dimensions does not get quantum corrections.