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Given a local Hamiltonian, how difficult is it to determine the entanglement structure of its ground state? We show that this problem is computationally intractable even if one is only trying to decide if the ground state is volume-law vs near area-law entangled.
A continuity property of the entropy density for spin lattice systems
M. Fannes · 1973
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Quantum data processing and error correction
Benjamin Schumacher and M. A. Nielsen · 1996
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Comparing entropies in statistical zero knowledge with applications to the structure of szk
Oded Goldreich and Salil Vadhan · 1999
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Distillation and bound entanglement
Pawel Horodecki and Ryszard Horodecki · 2001
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The asymptotic entanglement cost of preparing a quantum state
Patrick M Hayden, Michal Horodecki, and Barbara M Terhal · 2001
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Entanglement of formation and concurrence
William K. Wootters · 2001
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The uniqueness theorem for entanglement measures
Matthew J. Donald, Michał Horodecki, and Oliver Rudolph · 2002
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Classical and Quantum Computation
A. Yu. Kitaev, A. H. Shen, and M. N. Vyalyi · 2002
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A complete problem for statistical zero knowledge
Amit Sahai and Salil Vadhan · 2003
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Distillation of secret key and entanglement from quantum states
Igor Devetak and Andreas Winter · 2005
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The structure of bipartite quantum states-insights from group theory and cryptography
Matthias Christandl · 2006
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Holographic derivation of entanglement entropy from the anti–de sitter space/conformal field theory correspondence
Shinsei Ryu and Tadashi Takayanagi · 2006
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A sharp continuity estimate for the von Neumann entropy
Koenraad M R Audenaert · 2007
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An area law for one-dimensional quantum systems
Matthew B Hastings · 2007
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Adiabatic quantum computation is equivalent to standard quantum computation
Dorit Aharonov, Wim Van Dam, Julia Kempe, Zeph Landau, Seth Lloyd, and Oded Regev · 2008
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Quantum expanders: Motivation and constructions
Avraham Ben-Aroya, Oded Schwartz, and Amnon Ta-Shma · 2008
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Computational difficulty of finding matrix product ground states
Norbert Schuch, Ignacio Cirac, and Frank Verstraete · 2008
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The power of quantum systems on a line
Dorit Aharonov, Daniel Gottesman, Sandy Irani, and Julia Kempe · 2009
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Quantum entanglement
Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, and Karol Horodecki · 2009
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On lattices, learning with errors, random linear codes, and cryptography
Oded Regev · 2009
Cited alongside, same era.
Efficient quantum state tomography
Marcus Cramer, Martin B Plenio, Steven T Flammia, Rolando Somma, David Gross, Stephen D Bartlett, Olivier Landon-Cardinal, David Poulin, and Yi-Kai Liu · 2010
Cited alongside, same era.
Pseudorandom quantum states
Zhengfeng Ji, Yi-Kai Liu, and Fang Song · 2018
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Approximate low-weight check codes and circuit lower bounds for noisy ground states
Chinmay Nirkhe, Umesh Vazirani, and Henry Yuen · 2018
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Computational pseudorandomness, the wormhole growth paradox, and constraints on the ads/cft duality
Adam Bouland, Bill Fefferman, and Umesh Vazirani · 2019
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(Pseudo) random quantum states with binary phase
Zvika Brakerski and Omri Shmueli · 2019
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Undecidability of the spectral gap in one dimension
Johannes Bausch, Toby S Cubitt, Angelo Lucia, and David Perez-Garcia · 2020
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Robustness of the learning with errors assumption
Shafi Goldwasser, Yael Tauman Kalai, Chris Peikert, and Vinod Vaikuntanathan · 2010
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Better key sizes (and attacks) for lwe-based encryption
Richard Lindner and Chris Peikert · 2011
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Pseudorandomness
Salil Vadhan · 2012
Cited alongside, same era.
Undecidability of the spectral gap
Toby S Cubitt, David Perez-Garcia, and Michael M Wolf · 2015
Cited alongside, same era.
A polynomial time algorithm for the ground state of one-dimensional gapped local Hamiltonians
Zeph Landau, Umesh Vazirani, and Thomas Vidick · 2015
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A decade of lattice cryptography
Chris Peikert · 2016
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Alexandru Gheorghiu and Matty J Hoban · 2020
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An area law for 2d frustration-free spin systems
Anurag Anshu, Itai Arad, and David Gosset · 2022
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Provably efficient machine learning for quantum many-body problems
Hsin-Yuan Huang, Richard Kueng, Giacomo Torlai, Victor V Albert, and John Preskill · 2022
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Efficient certifiable randomness from a single quantum device, 2022
Urmila Mahadev, Umesh Vazirani, and Thomas Vidick · 2022
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A survey on the complexity of learning quantum states
Anurag Anshu and Srinivasan Arunachalam · 2023
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Unitary complexity and the uhlmann transformation problem
John Bostanci, Yuval Efron, Tony Metger, Alexander Poremba, Luowen Qian, and Henry Yuen · 2023
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Mark Zhandry · 2023
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