We are using this wiki-page to collect questions and comments for our informal discussion on "Open problems & questions in entanglement physics" on Thursday, December 9th.

Everybody is welcome to contribute to this list, such as to extend/correct/clarify it.

Entanglement as a way to understand quantum systems

How useful is entanglement in classifying quantum states?

Is entanglement more useful than correlation functions in understanding quantum systems?

Is there a sharper measure than the entanglement entropy to

characterize the "complexity" of a problem

characterize the computational cost associated with finding the ground state

Is there an entanglement measure that would indicate whether a system has a sign-problem in QMC?
(There will be no general answer to this, but has anyone thought about this connection?)

Can we think of tensor network states as a new representation of quantum mechanics?

Given the ground state wave-function of a chiral topologically ordered state (such as a Fractional Quantum Hall state), how much information about the phase of matter (such as it's excitations, fusion rules, braiding etc.) can one extract from the entanglement spectrum of this wave-function?

Is the AdS/CFT - MERA correspondence just analogy? Or speculation? Or is there any quantitative relationship? What does the network mean in terms of AdS?

Tensor networks states and algorithms

Which problems have been solved / are within reach to be solved using tensor network algorithms?

Which open problems are best solved with QMC versus DMRG versus PEPS versus MERA (etc)?

What interesting problems seem to be "ripe" for our current techniques?

What interesting problems seem too hard for the current techniques?

Can we directly represent any arbitrary continuous system with tensor network-like states?

What are the current capabilities of dynamical methods for (1) spectral functions and related equilibrium quantities; (2) non-equilibrium systems?

Is there any relation between the sign problem and difficulty of simulating with a tensor network state?

Why and how do PEPS/MERA favor ground states with low entanglement? Does that mean that if one state has slightly lower energy than the other one but significantly higher entanglement (but still area law), I would obtain the latter one as my final variationally optimized answer (at least for a range of bond dimensions)?

What is the exact correspondence between PEPS and slave-particle construction of topologically ordered states? Can one read off the full PSG from a PEPS wave-function?

What is the connection, if any, between MPS/PEPS and slave-particle (Gutzwiller) constructions of gapless quantum states?

Is MERA optimal? In other words, can MERA represent any quantum state that can be represented by others with the same network structure and dimension but without isometricity?

Is tensor optimization for a given network structure a fundamental problem from computational point of view? NP-hard? When is it? Always? Never?

Highlights / developments from the recent literature
(which you feel might have been overlooked by the broader community) Please only mention work by OTHER people (and list your name)

"Open problems & questions in entanglement physics" on Thursday, December 9th.Everybody is welcome to contribute to this list, such as to extend/correct/clarify it.

Entanglement as a way to understand quantum systems(There will be no general answer to this, but has anyone thought about this connection?)

Tensor networks states and algorithmsHighlights / developments from the recent literature(which you feel might have been overlooked by the broader community)

Please only mention work by OTHER people (and list your name)