Scaling laws for precision in quantum interferometry and bifurcation landscape of optimal state

Phase precision in optimal 2-channel quantum interferometry is studied in the limit of large photon number $N\gg 1$, for losses occurring in either one or both channels. For losses in one channel an optimal state undergoes an intriguing sequence of local bifurcations as the losses or the number of photons increase. We further show that fixing the loss paramater determines a scale for quantum metrology -- a crossover value of the photon number $N_c$ beyond which the supra-classical precision is progressively lost. For large losses the optimal state also has a different structure from those considered previously.Comment: 4 pages, 3 figures, v3 is modified in response to referee comment

Multi-Partite Entanglement Inequalities via Spin Vector Geometry

We introduce inequalities for multi-partite entanglement, derived from the geometry of spin vectors. The criteria are constructed iteratively from cross and dot products between the spins of individual subsystems, each of which may have arbitrary dimension. For qubit ensembles the maximum violation for our inequalities is larger than that for the Mermin-Klyshko Bell inequalities, and the maximally violating states are different from Greenberger-Horne-Zeilinger states. Our inequalities are violated by certain bound entangled states for which no Bell-type violation has yet been found.Comment: 4 pages, 2 tables, 1 figure. A truncated version is published in Physical Review Letters, volume 95 issue 18, 180402 (October 2005

Preferred Measurements: Optimality and Stability in Quantum Parameter Estimation

We explore precision in a measurement process incorporating pure probe states, unitary dynamics and complete measurements via a simple formalism. The concept of `information complement' is introduced. It undermines measurement precision and its minimization reveals the system properties at an optimal point. Maximally precise measurements can exhibit independence from the true value of the estimated parameter, but demanding this severely restricts the type of viable probe and dynamics, including the requirement that the Hamiltonian be block-diagonal in a basis of preferred measurements. The curvature of the information complement near a globally optimal point provides a new quantification of measurement stability.Comment: 4 pages, 2 figures, in submission. Substantial Extension and replacement of arXiv:0902.3260v1 in response to Referees' remark

Local and Global Distinguishability in Quantum Interferometry

A statistical distinguishability based on relative entropy characterises the fitness of quantum states for phase estimation. This criterion is employed in the context of a Mach-Zehnder interferometer and used to interpolate between two regimes, of local and global phase distinguishability. The scaling of distinguishability in these regimes with photon number is explored for various quantum states. It emerges that local distinguishability is dependent on a discrepancy between quantum and classical rotational energy. Our analysis demonstrates that the Heisenberg limit is the true upper limit for local phase sensitivity. Only the `NOON' states share this bound, but other states exhibit a better trade-off when comparing local and global phase regimes.Comment: 4 pages, in submission, minor revision