NOON state

A NOON state is an entangled quantum mechanical many-body state. The term is commonly used, especially in quantum optics. Here, a NOON state a superposition state of photons that either all are in one or the other of two distinguishable sets of single-particle states. Photons, which are prepared in such a state, allow very precise ( for large ) phase measurements and have therefore been proposed for applications in quantum metrology and high-resolution lithography.

Definition

Mathematically NOON states as vectors in Hilbert space, the symmetric ( bosonic ) Fock space over two modes given. The state

Describes the superposition of the particles in the fashion, and no particles in mode and vice versa ( with relative phase). In practice, most photonic NOON states are considered, but each bosonic field can be prepared in a NOON state.

Applications

NOON states were examined in the context of applications of quantum metrology, as they allow it to perform with optical interferometers very accurate phase measurements. For example applies to the observable

That their expected value for a system in the NOON state from to change when the phase of the state from 0 to grow, that is, for large a very small phase already leads to a large change in the observables. For the inaccuracy (standard deviation ) of the measurements of the following applies:

This scaling with the number of particles is the best achievable with quantum mechanical behavior measurements and is also referred to as the Heisenberg limit. It represents a quadratic improvement over the standard quantum limit (), which describes the best achievable with independent (not entangled ) particle measurement.

NOON states are closely related to Schrodinger's cat states and Greenberger - Horne - Zeilinger states. As these are also the NOON states very fragile: even small uncontrolled interactions destroy the coherence of the superposition and result in a loss of the advantageous properties of the state ( decoherence ). This represents the practical benefits of NOON states for metrological purposes in many realistic situations in question.

Experimental generation

NOON states generated small in different experiments, for example with optical photons and with microwave photons.

History and terminology

NOON states were introduced by Barry Sanders in connection with the study of decoherence of Schrodinger cat states, and later rediscovered by Jonathan P. Dowling, who proposed it as the basis of quantum lithography. The English term " NOON state" was first described in an article by Lee, Kok and Dowling on quantum metrology, used (written as " n00n ", with zeroes instead of Os).

Credentials

• Quantum computer science
• Quantum mechanics