In quantum optics and quantum information, a Dicke state is a quantum state defined by Robert H. Dicke in connection to spontaneous radiation processes taking place in an ensemble of two-state atoms.
A Dicke state is the simultaneous eigenstate of the angular momentum operators
They are highly entangled, and in quantum metrology they lead to the maximal Heisenberg scaling of the precision of parameter estimation.
particles as the simultaneous eigenstates of the angular momentum operators
is a label used to distinguish several states orthogonal to each other, for which the two eigenvalues are the same.
The entanglement properties of symmetric Dicke states have been studied extensively.
particles can easily be mapped to symmetric Dicke states of
i.e., the case of non-symmetric Dicke states in multi-qubit systems is more complicated.
label to dinstinguish several eigenstates with the same eigenvalues orthogonal to each other.
[5] In an experiment, determining the fidelity with respect to pure quantum states is not an easy task in general.
However, for states in the symmetric (bosonic subspace) the necessary measuement effort increases only polynomially with the number of particles.
local measurement settings, which is known from the theory of Permutationally invariant quantum state tomography.
It is also a valid bound for measuring the fidelity with respect to symmetric Dicke states.
For the 4-qubit case, 7 local measurement settings is sufficient,[6][7] while for the 6-qubit case 21 local measuementy settings is sufficient.
[8][9][7] When a Dicke states has been prepared in an experiment, it is important to verify that the state has been prepared with a good quality.
Apart from obtaining the fidelity, a usual goal is to show that the quantum state was highly entangled.
the fidelity with respect to W-states holds then the quantum state is genuine multipartite entangled.
This means that all the particles are entangled with each other, and the quantum state cannot be put together with entangled quantum states of smaller units by trivial operations such as making a tensor product and mixing.
, which can make experiments with large systems difficult.
, which makes experiments for detecting genuine multipartite entanglement feasible even for a large
Unlike in the case of GHZ states, the entanglement of Dicke states can be detected by measuring collective observables.
[12][13] Finally, there are efficient methods to detect multipartite entanglement of noisey Dicke states based on their density matrix.
denotes the quantum Fisher information characterizing how well the state
in the unitary dynamics For separable states the bound discovered by Pezze and Smerzi [15] holds, which is relevant for linear interferometers, a very large class of interferometers used in experiments.
Greenberger-Horne-Zeilinger (GHZ) states also saturate this relation.
have been created in a four and a six-qubit photonic experiment in which genuine four- and six-paricle entanglement, respectively, has been demonstrated.
[6][8][9] They have also been prepared in a Bose-Einstein condensate with thousands of atoms.
[19][20] Dicke states have also been used for quantum metrology in cold gasses[19] and photonic systems.
[21] In these experiments it has been demonstrated that the experimentally created Dicke states outperform separable states in metrology.
[12][22][23] Bipartite entanglement and Einstein-Podolsky-Rosen (EPR) steering has been detected in Dicke states of an ensemble of thousands of cold atoms.