Quantum nondemolition measurement

Quantum nondemolition (QND) measurement is a measurement of a quantum system, which preserves the integrity of the system and the value of the measured observable. This allows exactly the same system to be measured repeatedly.

The term nondemolition does not imply that the wave function fails to collapse. In fact, QND measurement is best thought of as the ideal quantum projective measurement.

For example, most devices capable of detecting a single particle and measuring its position destroy the particle in the measurement process. Less dramatically, the measurement may simply perturb the particle so that it is not in the measured eigenstate even immediately after the measurement.

A perfect QND measurement of a particle's position, in contrast, would leave the particle in its measured position. QND measurements are extremely difficult to carry out experimentally.

Technical definition

Consider a full Von Neumann measurement by giving a quantum description to both the system $|\psi\rang$ and the measuring apparatus $|A\rang$. Suppose the dynamics can be described by a Hamiltonian of the form

$H = H_{\rm self}+H_{\rm int} \, ,$

where H_self is the self-interaction of the system and H_int is the coupling between the system and the measuring apparatus. Generally, the H_int term is modeled as "turning on" for only a brief time and yielding the ideal (weak) Von Neumann measurement:

$|\psi\rang |A\rang \rightarrow \sum_n c_n |\psi_n\rang |A_n\rang$

This measurement is a QND measurement if

$[H_{\rm self} \, , \, H_{\rm int}]=0 .$

Description from the literature

A. Lupascu et al.^[1]:

In quantum mechanics, the process of measurement is a subtle interplay between extraction of information and disturbance of the state of the quantum system. A quantum non-demolition (QND) measurement minimizes this disturbance by using a particular system—detector interaction that preserves the eigenstates of a suitable operator of the quantum system. This leads to an ideal projective measurement.

References

1. ^ Lupascu, A.; et al. (2007). "Quantum non-demolition measurement of a superconducting two-level system". Nature Physics 3 (2): 119–125. arXiv:cond-mat/0611505. Bibcode 2007NatPh...3..119L. doi:10.1038/nphys509. http://www.nature.com/nphys/journal/v3/n2/full/nphys509.html. 

External links

• Physicsworld article
• Measuring quantum information without destroying it
• Counting photons without destroying them