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)