Todd Tilma

Entanglement is not a critical resource for quantum metrology

We investigate high-precision measurements beyond the standard quantum limit, utilizing nonclassical states. Although entanglement was considered a resource for achieving the Heisenberg limit in measurements, we show that any advantage expected from using entanglement is dependent on the measurement in question. We investigate several measurement scenarios and illustrate the role of entanglement as a resource for quantum high-precision measurement. In particular, we demonstrate that there is a regime wherein entanglement not only does not help, but prevents the achievement of the fundamental limit.

Towards a complete and continuous Wigner function for an ensemble of spins or qubits

We present a new quasi-probability distribution function for ensembles of spin-half particles or qubits that has many properties in common with Wigners original function for systems of continuous variables. We show that this function provides clear and intuitive graphical representation of a wide variety of states, including Fock states, spin-coherent states, squeezed states, superpositions and statistical mixtures. Unlike previous attempts to represent ensembles of spins/qubits, this distribution is capable of simultaneously representing several angular momentum shells.

SU(N)-symmetric quasi-probability distribution functions

We present a set of N-dimensional functions, based on generalized SU(N)-symmetric coherent states, that represent finite-dimensional Wigner, Q- and P-functions. We then show the fundamental properties of these functions and discuss their usefulness for analyzing N-dimensional pure and mixed quantum states.