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Quantum Pseudoentanglement

Authors Scott Aaronson, Adam Bouland, Bill Fefferman, Soumik Ghosh, Umesh Vazirani, Chenyi Zhang, Zixin Zhou

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Author Details

Scott Aaronson
  • Department of Computer Science, University of Texas at Austin, TX, USA
Adam Bouland
  • Department of Computer Science, Stanford University, CA, USA
Bill Fefferman
  • Department of Computer Science, University of Chicago, IL, USA
Soumik Ghosh
  • Department of Computer Science, University of Chicago, IL, USA
Umesh Vazirani
  • Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, USA
Chenyi Zhang
  • Department of Computer Science, Stanford University, CA, USA
Zixin Zhou
  • Department of Computer Science, Stanford University, CA, USA

Funding

B.F. and S.G. acknowledge support from AFOSR (FA9550-21-1-0008). This material is based upon work partially supported by the National Science Foundation under Grant CCF-2044923 (CAREER) and by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers (Q-NEXT). This research was also supported in part by the National Science Foundation under Grant No. NSF PHY-1748958. A.B. and B.F. were supported in part by the DOE QuantISED grant DE-SC0020360. A.B. and C.Z. were supported in part by the AFOSR under grant FA9550-21-1-0392. A.B. was supported in part by the U.S. DOE Office of Science under Award Number DE-SC0020266. U.V. acknowledges the Vannevar Bush faculty fellowship N00014-17-1-3025, and was supported by DOE NQISRC QSA grant FP00010905, QSA grant FP00010905, and NSF QLCI Grant No. 2016245. Z.Z. was supported in part by a Stanford School of Engineering Fellowship. S.A is supported by a Vannevar Bush Fellowship from the US Department of Defense, the Berkeley NSF-QLCI CIQC Center, a Simons Investigator Award, and the Simons "It from Qubit" collaboration.

Acknowledgements

We thank Jordan Docter, Tudor Giurgica-Tiron, Nick Hunter-Jones, and Wilson Nguyen for helpful discussions.

Cite AsGet BibTex

Scott Aaronson, Adam Bouland, Bill Fefferman, Soumik Ghosh, Umesh Vazirani, Chenyi Zhang, and Zixin Zhou. Quantum Pseudoentanglement. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 2:1-2:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ITCS.2024.2

Abstract

Entanglement is a quantum resource, in some ways analogous to randomness in classical computation. Inspired by recent work of Gheorghiu and Hoban, we define the notion of "pseudoentanglement", a property exhibited by ensembles of efficiently constructible quantum states which are indistinguishable from quantum states with maximal entanglement. Our construction relies on the notion of quantum pseudorandom states - first defined by Ji, Liu and Song - which are efficiently constructible states indistinguishable from (maximally entangled) Haar-random states. Specifically, we give a construction of pseudoentangled states with entanglement entropy arbitrarily close to log n across every cut, a tight bound providing an exponential separation between computational vs information theoretic quantum pseudorandomness. We discuss applications of this result to Matrix Product State testing, entanglement distillation, and the complexity of the AdS/CFT correspondence. As compared with a previous version of this manuscript (arXiv:2211.00747v1) this version introduces a new pseudorandom state construction, has a simpler proof of correctness, and achieves a technically stronger result of low entanglement across all cuts simultaneously.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum computation theory
  • Theory of computation → Pseudorandomness and derandomization
  • Theory of computation → Quantum complexity theory
Keywords
  • Quantum computing
  • Quantum complexity theory
  • entanglement

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