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Title: Grover Search and the No-Signaling Principle

Abstract

Two of the prime properties of quantum physics are the no-signaling principle and the Grover search lower bound. That is, despite admitting stronger-than-classical correlations, quantum mechanics does not imply superluminal signaling, and despite a form of exponential parallelism, quantum mechanics does not imply polynomial-time brute force solution of NP-complete problems. Herein, we investigate the degree to which these two properties are connected. We explore four classes of deviations from quantum mechanics, for which we draw inspiration from the literature on the black hole information paradox. We show that in these models, the physical resources required to send a superluminal signal scale polynomially with the resources needed to speed up Grover’s algorithm. Hence the no-signaling principle is equivalent to the inability to solve NP-hard problems efficiently by brute force within the classes of theories analyzed.

Authors:
 [1];  [2];  [3]
+ Show Author Affiliations
  1. California Institute of Technology (CalTech), Pasadena, CA (United States)
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
  3. National Inst. of Standards and Technology (NIST), Gaithersburg, MD (United States); Univ. of Maryland, College Park, MD (United States)
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); Gordon and Betty Moore Foundation
OSTI Identifier:
1600495
Alternate Identifier(s):
OSTI ID: 1324491
Grant/Contract Number:  
SC0011632; PHY-1125565; GBMF-12500028
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 117; Journal Issue: 12; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 79 ASTRONOMY AND ASTROPHYSICS

Citation Formats

Bao, Ning, Bouland, Adam, and Jordan, Stephen P. Grover Search and the No-Signaling Principle. United States: N. p., 2016. Web. doi:10.1103/PhysRevLett.117.120501.
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Bao, Ning, Bouland, Adam, & Jordan, Stephen P. Grover Search and the No-Signaling Principle. United States. https://doi.org/10.1103/PhysRevLett.117.120501
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Bao, Ning, Bouland, Adam, and Jordan, Stephen P. Wed . "Grover Search and the No-Signaling Principle". United States. https://doi.org/10.1103/PhysRevLett.117.120501. https://www.osti.gov/servlets/purl/1600495.
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@article{osti_1600495,
title = {Grover Search and the No-Signaling Principle},
author = {Bao, Ning and Bouland, Adam and Jordan, Stephen P.},
abstractNote = {Two of the prime properties of quantum physics are the no-signaling principle and the Grover search lower bound. That is, despite admitting stronger-than-classical correlations, quantum mechanics does not imply superluminal signaling, and despite a form of exponential parallelism, quantum mechanics does not imply polynomial-time brute force solution of NP-complete problems. Herein, we investigate the degree to which these two properties are connected. We explore four classes of deviations from quantum mechanics, for which we draw inspiration from the literature on the black hole information paradox. We show that in these models, the physical resources required to send a superluminal signal scale polynomially with the resources needed to speed up Grover’s algorithm. Hence the no-signaling principle is equivalent to the inability to solve NP-hard problems efficiently by brute force within the classes of theories analyzed.},
doi = {10.1103/PhysRevLett.117.120501},
journal = {Physical Review Letters},
number = 12,
volume = 117,
place = {United States},
year = {Wed Sep 14 00:00:00 EDT 2016},
month = {Wed Sep 14 00:00:00 EDT 2016}
}
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https://doi.org/10.1103/PhysRevLett.117.120501
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