Information theory approach to quantum non-demolition measurements

Paul Busch, PEKKA J. LAHTI

Abstract The theory of unsharp quantum measurements is reviewed as a generalization of the von Neumann‐Lüders measurement theory and applied to measurements of continuous quantities. A generalized notion of repeatability is proposed which is applicable even to intrinsically unsharp continuous observables. As an illustration a precise formulation of a quantum non‐demolition (QND) measurement performed on a harmonic oscillator is given.

Stephen D. Bartlett, Geoff J. Pryde, Jeremy L. O’Brien +2 more

K. -E. Hellwig

C. S. Unnikrishnan

This is a limited overview of quantum non-demolition (QND) measurements, with brief discussions of illustrative examples meant to clarify the essential features. In a QND measurement, the predictability of a subsequent value of a precisely measured observable is maintained and any random back-action from uncertainty introduced into a noncommuting observable is avoided. The fundamental ideas, relevant theory and the conditions and scope for applicability are discussed with some examples. Precision measurements have indeed gained from developing QND measurements. Some implementations in quantum optics, gravitational wave detectors and spin-magnetometry are discussed.

K. -E. Hellwig

Adrian Lupaşcu, Shiro Saito, Thomas Picot +5 more

We present experiments that address the issue of measurement of superconducting qubits. A quantum non‐demolition (QND) type of readout is used to implement a projective measurement, which is an important component of many protocols in quantum information. The state of a persistent current qubit is measured using a driven non‐linear resonator, based on DC‐SQUID whose Josephson inductance is qubit‐state dependent. When properly optimized, the readout is efficient and projective. We discuss the relation between the concept of QND detection and the observed projective character of the measurement.