Quantum error correction for continuously detected errors

We show that quantum feedback control can be used as a quantum error correction process for errors induced by weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per physical qubit, quantum feedback can act to perfectly protect a stabilizer codespace. Using the stabilizer formalism we derive an explicit scheme, involving feedback and an additional constant Hamiltonian, to protect an ($n-1$)-qubit logical state encoded in $n$ physical qubits. This works for both Poisson (jump) and white-noise (diffusion) measurement processes. In addition, universal quantum computation is possible in this scheme. As an example, we show that detected-spontaneous emission error correction with a driving Hamiltonian can greatly reduce the amount of redundancy required to protect a state from that which has been previously postulated [e.g., Alber \emph{et al.}, Phys. Rev. Lett. 86, 4402 (2001)].Comment: 11 pages, 1 figure; minor correction

Selective linear or quadratic optomechanical coupling via measurement

The ability to engineer both linear and non-linear coupling with a mechanical resonator is an important goal for the preparation and investigation of macroscopic mechanical quantum behavior. In this work, a measurement based scheme is presented where linear or square mechanical displacement coupling can be achieved using the optomechanical interaction linearly proportional to the mechanical position. The resulting square displacement measurement strength is compared to that attainable in the dispersive case using the direct interaction to the mechanical displacement squared. An experimental protocol and parameter set are discussed for the generation and observation of non-Gaussian states of motion of the mechanical element.Comment: 7 pages, 2 figures, (accepted in Physical Review X

Modal dynamics for positive operator measures

The modal interpretation of quantum mechanics allows one to keep the standard classical definition of realism intact. That is, variables have a definite status for all time and a measurement only tells us which value it had. However, at present modal dynamics are only applicable to situations that are described in the orthodox theory by projective measures. In this paper we extend modal dynamics to include positive operator measures (POMs). That is, for example, rather than using a complete set of orthogonal projectors, we can use an overcomplete set of nonorthogonal projectors. We derive the conditions under which Bell's stochastic modal dynamics for projective measures reduce to deterministic dynamics, showing (incidentally) that Brown and Hiley's generalization of Bohmian mechanics [quant-ph/0005026, (2000)] cannot be thus derived. We then show how {\em deterministic} dynamics for positive operators can also be derived. As a simple case, we consider a Harmonic oscillator, and the overcomplete set of coherent state projectors (i.e. the Husimi POM). We show that the modal dynamics for this POM in the classical limit correspond to the classical dynamics, even for the nonclassical number state $\ket{n}$. This is in contrast to the Bohmian dynamics, which for energy eigenstates, the dynamics are always non-classical.Comment: 14 page

Nontrivial quantum effects in biology: A skeptical physicists' view

Invited contribution to "Quantum Aspects of Life", D. Abbott Ed. (World Scientific, Singapore, 2007).Comment: 15 pages, minor typographical errors correcte