# Felix Huber

PhD studentRoom: B-111

Phone: +49 271 740 3716

## Preprints

See also arxiv

Felix Huber, Christopher Eltschka, Jens Siewert and Otfried Gühne
*
Bounds on absolutely maximally entangled states from shadow
inequalities, and the quantum MacWilliams identity
*

arXiv:1708.06298

A pure multipartite quantum state is called absolutely maximally entangled (AME), if all reductions obtained by tracing out at least half of its parties are maximally mixed. However, the existence of such states is in many cases unclear. With the help of the weight enumerator machinery known from quantum error correcting codes and the generalized shadow inequalities, we obtain new bounds on the existence of AME states in higher dimensions. To complete the treatment on the weight enumerator machinery, the quantum MacWilliams identity is derived in the Bloch representation.

## Publications

Nikolai Wyderka, Felix Huber and Otfried Gühne
*
Almost all four-particle pure states are determined by their two-body
marginals
*

Phys. Rev. A
*
96
*,
010102
(2017),
arXiv:1703.10950

We show that generic pure states (states drawn according to the Haar measure) of four particles of equal internal dimension are uniquely determined among all other pure states by their two-body marginals. In fact, certain subsets of three of the two-body marginals suffice for the characterization. We also discuss generalizations of the statement to pure states of more particles, showing that these are almost always determined among pure states by three of their $(n-2)$-body marginals. Finally, we present special families of symmetric pure four-particle states that share the same two-body marginals and are therefore undetermined. These are four-qubit Dicke states in superposition with generalized GHZ states.

Felix Huber, Otfried Gühne, Jens Siewert*Absolutely maximally entangled states of seven qubits do not exist*

Phys. Rev. Lett. *118*,
200502
(2017),
arXiv:1608.06228

Pure multiparticle quantum states are called absolutely maximally entangled if all reduced states obtained by tracing out at least half of the particles are maximally mixed. We provide a method to characterize these states for a general multiparticle system. With that, we prove that a seven-qubit state whose three-body marginals are all maximally mixed, or equivalently, a pure ((7,1,4))_2 quantum error correcting code, does not exist. Furthermore, we obtain an upper limit on the possible number of maximally mixed three-body marginals and identify the state saturating the bound. This solves the seven-particle problem as the last open case concerning maximally entangled states of qubits.

Felix Huber and Otfried Gühne*Characterizing Ground and Thermal States of Few-Body Hamiltonians*

Phys. Rev. Lett. *117*,
010403
(2016),
arXiv:1601.01630

The question whether a given quantum state is a ground or thermal state of a few-body Hamiltonian can be used to characterize the complexity of the state and is important for possible experimental implementations. We provide methods to characterize the states generated by two- and, more generally, k-body Hamiltonians as well as the convex hull of these sets. This leads to new insights into the question which states are uniquely determined by their marginals and to a generalization of the concept of entanglement. Finally, certification methods for quantum simulation can be derived.

## Miscellaneous

*QGeo*: a python toolkit to calculate various things in quantum information science / entanglement / information geometry, on (mostly) qubits.

link

*Table of AME states / perfect tensors.*

link