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Full-Text Articles in Physics
Quark And Gluon Entanglement In The Proton On The Light Cone At Intermediate X, Adrian Dumitru, Eric Kolbusz
Quark And Gluon Entanglement In The Proton On The Light Cone At Intermediate X, Adrian Dumitru, Eric Kolbusz
Publications and Research
In QCD with $N_c$ colors the antisymmetric valence quark color space singlet state $\sim \epsilon_{i_1\cdots i_{N_c}} |i_1,\cdots, i_{N_c}\rangle$ of the proton corresponds to the reduced density matrix $\rho_{ij}=(1/N_c) \delta_{ij}$ for a single color degree of freedom. Its degenerate spectrum of eigenvalues, $\lambda_i=1/N_c$, the purity $\tr \rho^2 = 1/N_c$, and the von Neumann entropy $S_\mathrm{vN}=\log(N_c)$ all indicate maximal entanglement of color. On the other hand, for $N_c\to\infty$ the spatial wave function of the proton factorizes into valence quark wave functions determined by a mean field [E. Witten, Nucl. Phys. B160, 57 (1979)] where there is no entanglement of spatial degrees of …
Extractable Entanglement From A Euclidean Hourglass, Takanori Anegawa, Norihiro Iizuka, Daniel Kabat
Extractable Entanglement From A Euclidean Hourglass, Takanori Anegawa, Norihiro Iizuka, Daniel Kabat
Publications and Research
We previously proposed that entanglement across a planar surface can be obtained from the partition function on a Euclidean hourglass geometry. Here we extend the prescription to spherical entangling surfaces in conformal field theory. We use the prescription to evaluate log terms in the entropy of a conformal field theory in two dimensions, a conformally coupled scalar in four dimensions, and a Maxwell field in four dimensions. For Maxwell we reproduce the extractable entropy obtained by Soni and Trivedi. We take this as evidence that the hourglass prescription provides a Euclidean technique for evaluating extractable entropy in quantum field theory.
Defining Entanglement Without Tensor Factoring: A Euclidean Hourglass Prescription, Takanori Anegawa, Norihiro Iizuka, Daniel Kabat
Defining Entanglement Without Tensor Factoring: A Euclidean Hourglass Prescription, Takanori Anegawa, Norihiro Iizuka, Daniel Kabat
Publications and Research
We consider entanglement across a planar boundary in flat space. Entanglement entropy is usually thought of as the von Neumann entropy of a reduced density matrix, but it can also be thought of as half the von Neumann entropy of a product of reduced density matrices on the left and right. The latter form allows a natural regulator in which two cones are smoothed into a Euclidean hourglass geometry. Since there is no need to tensor factor the Hilbert space, the regulated entropy is manifestly gauge invariant and has a manifest state-counting interpretation. We explore this prescription for scalar fields, …