Quantum Encodings in Spin Systems and Harmonic Oscillators

We show that higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation. Whereas qubit-based quantum computation is adequate for analyses of quantum vs classical computation, in practice qubits are often realized in higher-dimensional systems by truncating all but two levels, thereby reducing the size of the precious Hilbert space. We develop natural qudit gates for universal quantum computation, and exploit the entire accessible Hilbert space. Mathematically, we give representations of the generalized Pauli group for qudits in coupled spin systems and harmonic oscillators, and include analyses of the qubit and the infinite-dimensional limits.Comment: 4 pages, published versio

Inequivalent classes of closed three-level systems

We show here that the $\Lambda$ and V configurations of three-level atomic systems, while they have recently been shown to be equivalent for many important physical quantities when driven with classical fields [M. B. Plenio, Phys. Rev. A \textbf{62}, 015802 (2000)], are no longer equivalent when coupled via a quantum field. We analyze the physical origin of such behavior and show how the equivalence between these two configurations emerges in the semiclassical limit.Comment: 4 pages, 1 figure. To appear as Brief Report in Physical Review

State-independent preparation uncertainty relations

The standard state-dependent Heisenberg-Robertson uncertainly-relation lower bound fails to capture the quintessential incompatibility of observables as the bound can be zero for some states. To remedy this problem, we establish a class of tight (i.e., inequalities are saturated)variance-based sum-uncertainty relations derived from the Lie algebraic properties of observables and show that our lower bounds depend only on the irreducible representation assumed carried by the Hilbert space of state of the system. We illustrate our result for the cases of the Weyl-Heisenberg algebra, special unitary algebras up to rank 4, and any semisimple compact algebra. We also prove the usefulness of our results by extending a known variance-based entanglement detection criterion.Comment: 7 pages, 1 figur