Английская Википедия:Entanglement depth
In quantum physics, entanglement depth characterizes the strength of multiparticle entanglement. An entanglement depth <math> k </math> means that the quantum state of a particle ensemble cannot be described under the assumption that particles interacted with each other only in groups having fewer than <math> k </math> particles. It has been used to characterize the quantum states created in experiments with cold gases.[1]
Definition
Entanglement depth appeared first in the context of cold gases, together with entanglement criteria that made it possible to bound it from below based on measured quantities.[2][3][4][5][6][7][8]
We will now present a general definition based on convex sets of quantum states. First, we will define <math>k</math>-producibility.[9] Let us consider a pure state that is the tensor product of multi-particle quantum states
<math> |\Psi\rangle=|\phi_1\rangle\otimes|\phi_2\rangle\otimes ... \otimes|\phi_n\rangle. </math>
The pure state <math>|\Psi\rangle</math> is said to be <math>k</math>-producible if all <math>\phi_i</math> are states of at most <math>k</math> particles. A mixed state is called <math>k</math>-producible, if it is a mixture of pure states that are all at most <math>k</math>-producible. The <math>k</math>-producible mixed states form a convex set.
A quantum state contains at least genuine multiparticle entanglement of <math>k+1</math> particles, if it is not <math>k</math>-producible.
Finally, a quantum state has an entanglement depth <math>k</math>, if it is <math>k</math>-producible, but not <math>(k-1)</math>-producible.
References
Шаблон:Reflist Шаблон:Quantum-stub