Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Grover Search and the No-Signaling Principle

Journal Article · · Physical Review Letters
 [1];  [2];  [3]
  1. California Institute of Technology (CalTech), Pasadena, CA (United States); Caltech
  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)
+ Show Author Affiliations
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.
Research Organization:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Organization:
Gordon and Betty Moore Foundation; National Science Foundation (NSF); USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Grant/Contract Number:
SC0011632
OSTI ID:
1600495
Alternate ID(s):
OSTI ID: 1324491
Journal Information:
Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 12 Vol. 117; ISSN 0031-9007; ISSN PRLTAO
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (33)

Elements of Information Theory book January 1991
Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren book January 1931
Violations of the Born rule in cool state-dependent horizons journal January 2016
Black holes: complementarity or firewalls? journal February 2013
Quantum computation vs. firewalls journal June 2013
Aspects of the Papadodimas-Raju proposal for the black hole interior journal November 2014
Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group journal March 2006
Simulation of Topological Field Theories¶by Quantum Computers journal June 2002
NP is as easy as detecting unique solutions journal January 1986
Weinberg's non-linear quantum mechanics and supraluminal communications journal January 1990
Computers with Closed Timelike Curves Can Solve Hard Problems Efficiently journal January 2003
The black hole final state journal February 2004
Comment on "The black hole final state" journal March 2004
Nonlinear quantum search using the Gross–Pitaevskii equation journal June 2013
Quantum computing, postselection, and probabilistic polynomial-time journal August 2005
Closed timelike curves make quantum and classical computing equivalent journal October 2008
Systems of Self-Gravitating Particles in General Relativity and the Concept of an Equation of State journal November 1969
Grover’s quantum searching algorithm is optimal journal October 1999
Information processing in generalized probabilistic theories journal March 2007
Quantum search with general nonlinearities journal January 2014
Optimal state discrimination and unstructured search in nonlinear quantum mechanics journal February 2016
Quantum mechanics near closed timelike lines journal November 1991
State-dependent bulk-boundary maps and black hole complementarity journal April 2014
Can Closed Timelike Curves or Nonlinear Quantum Mechanics Improve Quantum State Discrimination or Help Solve Hard Problems? journal October 2009
No-Signaling Principle Can Determine Optimal Quantum State Discrimination journal October 2011
Better Late than Never: Information Retrieval from Black Holes journal March 2013
Weinberg’s nonlinear quantum mechanics and the Einstein-Podolsky-Rosen paradox journal January 1991
Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels journal March 1993
Nonlinear Quantum Mechanics Implies Polynomial-Time Solution for NP -Complete and # P Problems journal November 1998
Jerusalem lectures on black holes and quantum information journal February 2016
Quantum Algorithms for Quantum Field Theories journal May 2012
Strengths and Weaknesses of Quantum Computing journal October 1997
Guest Column: NP-complete problems and physical reality journal March 2005

Cited By (3)

Fast optimization algorithms and the cosmological constant journal November 2017
Branches of the black hole wave function need not contain firewalls journal June 2018
Any modification of the Born rule leads to a violation of the purification and local tomography principles journal November 2018

Similar Records

Fast optimization algorithms and the cosmological constant
Journal Article · Sun Nov 12 19:00:00 EST 2017 · Physical Review D · OSTI ID:1420107
Quantum multi-programming for Grover’s search
Journal Article · Tue Jan 17 19:00:00 EST 2023 · Quantum Information Processing · OSTI ID:1924191
Grover-algorithm-like operator using only single-qubit gates
Journal Article · Thu Sep 15 00:00:00 EDT 2005 · Physical Review. A · OSTI ID:20718505

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
79 ASTRONOMY AND ASTROPHYSICS