Page curves and typical entanglement in linear optics

Journal Article · Tue May 23 00:00:00 EDT 2023 · Quantum

DOI:https://doi.org/10.22331/q-2023-05-23-1017· OSTI ID:2420922

Iosue, Joseph T. ^[1]; Ehrenberg, Adam ^[2]; Hangleiter, Dominik ^[3]; Deshpande, Abhinav ^[4]; Gorshkov, Alexey V. ^[2]

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1. Univ. of Maryland, College Park, MD (United States). Joint Quantum Institute and Joint Center for Quantum Information and Computer Science; Univ. of Maryland, College Park, MD (United States)
2. Univ. of Maryland, College Park, MD (United States). Joint Quantum Institute and Joint Center for Quantum Information and Computer Science
3. Univ. of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science and Joint Quantum Institute
4. California Institute of Technology (CalTech), Pasadena, CA (United States)

Bosonic Gaussian states are a special class of quantum states in an infinite dimensional Hilbert space that are relevant to universal continuous-variable quantum computation as well as to near-term quantum sampling tasks such as Gaussian Boson Sampling. In this work, we study entanglement within a set of squeezed modes that have been evolved by a random linear optical unitary. We first derive formulas that are asymptotically exact in the number of modes for the Rényi-2 Page curve (the average Rényi-2 entropy of a subsystem of a pure bosonic Gaussian state) and the corresponding Page correction (the average information of the subsystem) in certain squeezing regimes. We then prove various results on the typicality of entanglement as measured by the Rényi-2 entropy by studying its variance. Using the aforementioned results for the Rényi-2 entropy, we upper and lower bound the von Neumann entropy Page curve and prove certain regimes of entanglement typicality as measured by the von Neumann entropy. Our main proofs make use of a symmetry property obeyed by the average and the variance of the entropy that dramatically simplifies the averaging over unitaries. In this light, we propose future research directions where this symmetry might also be exploited. We conclude by discussing potential applications of our results and their generalizations to Gaussian Boson Sampling and to illuminating the relationship between entanglement and computational complexity.

• Research Organization: Univ. of Maryland, College Park, MD (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: SC0019040; SC0020312
• OSTI ID: 2420922
• Journal Information: Quantum, Journal Name: Quantum Vol. 7; ISSN 2521-327X
• Publisher: Quantum Science Open Community
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Physics