TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.6.3.063
TI  - Entanglement classification via operator size
PY  - 2023/09/15
UR  - https://www.scipost.org/SciPostPhysCore.6.3.063
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 6
IS  - 3
SP  - 063
A1  - Wu, Qi-Feng
AB  - In this work, multipartite entanglement is classified by polynomials. I show that the operator size is closely related to the entanglement structure. Given a generic quantum state, I define a series of subspaces generated by operators of different sizes acting on it. The information about the entanglement is encoded into these subspaces. With the dimension of these subspaces as coefficients, I define a polynomial which I call the entanglement polynomial. The entanglement polynomial induces a homomorphism from quantum states to polynomials. It implies that we can characterize and find the building blocks of entanglement by polynomial factorization. Two states share the same entanglement polynomial if they are equivalent under the stochastic local operations and classical communication. To calculate the entanglement polynomial practically, I construct a series of states, called renormalized states, whose ranks are related to the coefficients of the entanglement polynomial.
ER  -

@Article{10.21468/SciPostPhysCore.6.3.063,
	title={{Entanglement classification via operator size}},
	author={Qi-Feng Wu},
	journal={SciPost Phys. Core},
	volume={6},
	pages={063},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.6.3.063},
	url={https://scipost.org/10.21468/SciPostPhysCore.6.3.063},
}