Entanglement in Phase Space

Bingsheng Lin, Jian Xu, Taihua Heng

We study the entanglement entropy of harmonic oscillators in non-commutative phase space (NCPS). We propose a new definition of quantum Rényi entropy based on Wigner functions in NCPS. Using the Rényi entropy, we calculate the entanglement entropy of the ground state of the 2D isotropic harmonic oscillators. We find that for some values of the non-commutative parameters, the harmonic oscillators can be entangled in NCPS. This is a new entanglement-like effect caused by the non-commutativity of the phase space.

Vatsal Dwivedi, Victor Chua

Abstract The study of quantum entanglement involves the choice of an entanglement cut, often corresponding to a partitioning of the system in position space. We generalize these partitions to a family of entanglement cuts corresponding to arbitrary directions in the classical phase space. For one dimensional free fermionic many-body wavefunctions, we analytically compute the full entanglement spectra for a family of entanglement cuts corresponding to a rotation in the classical phase space. These cuts continuously interpolate between the commonly studied position- and momentum-space cuts, as well as provide an implementation of the inversion symmetry smoothly connected to identity. The inversion symmetry of the wavefunctions is reflected in the chiral symmetry of the phase space entanglement spectra, and we use the associated chiral invariant to classify the inversion symmetric fermionic many-body wavefunctions.

Garay, Linda Bertel

Vatsal Dwivedi, Victor Chua

The study of quantum entanglement involves the choice of an entanglement cut, often corresponding to a partitioning of the system in posit ion space. We generalize these partitions to a family of entanglement cuts corresponding to arbitrary directions in the classical phase space. For one dimensional free fermionic many-body wavefunctions, we analytically compute the full entanglement spectra for a family of entanglement cuts corresponding to a rotation in the classical phase space. These cuts continuously interpolate between the commonly studied position- and momentum-space cuts, as well as provide an implementation of the inversion symmetry smoothly connected to identity. The inversion symmetry of the wavefunctions is reflected in the chiral symmetry of the phase space entanglement spectra, and we use the associated chiral invariant to classify the inversion symmetric fermionic many-body wavefunctions.

Liesel K. Hill