Related papers: Sub-Planck phase-space structures and Heisenberg-l…
We propose a measurement-based quantum metrology protocol in a composite model, where the probe system (a spin ensemble) is coupled to an ancillary two-level system (qubit) with a general Heisenberg XXZ interaction. With an optimized and…
For the continuous Wigner function and for certain discrete Wigner functions, permuting the values of the Wigner function in accordance with a symplectic linear transformation is equivalent to performing a certain unitary transformation on…
We extend the notions of quantum harmonic analysis, as introduced in R. Werner's paper from 1984 (J. Math. Phys. 25(5)), to abelian phase spaces, by which we mean a locally compact abelian group endowed with a Heisenberg multiplier. In this…
Quantum metrology and quantum sensing aim to use quantum properties to enhance measurement precision beyond what could be classically achieved. Here, we demonstrate how the analysis of the phase space structure of the classical limit of…
We discuss the Heisenberg-Wigner phase-space formalism in quantum electrodynamics as well as scalar quantum electrodynamics with respect to transverse fields. In regard to the special characteristics of such field types we derive modified…
The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being…
We experimentally investigate the non-Gaussian features of the phase-randomized coherent states, a class of states exploited in communication channels and in decoy state-based quantum key distribution protocols. In particular, we…
In this work we study symplectic unitary representations for the Galilei group. As a consequence the Schr\"odinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and using…
The phase resolution of interferometers is limited by the so-called Heisenberg limit, which states that the optimum phase sensitivity is inversely proportional to the number of interfering particles N, a 1/sqrt{N} improvement over the…
States with a negative Wigner function, a significant subclass of nonclassical states, serve as a valuable resource for various quantum information processing tasks. Here, we provide a criterion for detecting such quantum states…
Quantum devices are preparing increasingly more complex entangled quantum states. How can one effectively study these states in light of their increasing dimensions? Phase spaces such as Wigner functions provide a suitable framework. We…
We examine the results of the paper "Precision metrology using weak measurements", [Zhang, Datta, and Walmsley, arXiv:1310.5302] from a quantum state discrimination point of view. The Heisenberg scaling of the photon number for the…
In order to quantize systems involving second-class constraints, one should use Dirac bracket instead of Poisson bracket. Furthermore, one can specify a star product in which the term linear in $\hbar$ is proportional to the Dirac bracket.…
We show that real polarization method can be effectively used to geometrically quantize physical systems with compact phase space, like the spin. Our method enables us to construct a wave function of a qubit in both position and momentum…
When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do…
We further elaborate on a phase-space picture for a system of $N$ qubits and explore the structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves satisfying certain additional properties and…
Parallel to the quantization of the complex plane, using the canonical coherent states of a right quaternionic Hilbert space, quaternion field of quaternionic quantum mechanics is quantized. Associated upper symbols, lower symbols and…
Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of…
A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of…
We propose a method using the dispersive interaction between atoms and a high quality cavity to realize the mesoscopic superposition of coherent states which would exhibit sub-Planck structures in phase space. In particular we focus on a…