Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1411.1768 · European Journal of Physics

No-faster-than-light-signaling implies linear evolution. A re-derivation

Angelo Bassi, Kasra Hejazi

Published Aug 4, 2015• 40 citations
arXivHTMLPDF

Abstract

Abstract There is a growing interest, both from the theoretical as well as experimental side, to test the validity of the quantum superposition principle, and of theories which explicitly violate it by adding nonlinear terms to the Schrödinger equation. We review the original argument elaborated by Gisin (1989 Helv. Phys. Acta 62 363), which shows that the non-superluminal-signaling condition implies that the dynamics of the density matrix must be linear. This places very strong constraints on the permissible modifications of the Schrödinger equation, since they have to give rise, at the statistical level, to a linear evolution for the density matrix. The derivation is done in a heuristic way here and is appropriate for the students familiar with the textbook quantum mechanics and the language of density matrices.

DOI
10.1088/0143-0807/36/5/055027

Related papers

Nonlinearity without superluminality

Adrian Kent

Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signaling. As Czachor, Gisin, and Polchinski pointed out, this is not generally true of general nonlinear modifications of the Schr\"odinger equation. Excluding superluminal signaling has thus been taken to rule out most nonlinear versions of quantum theory. The no-superluminal-signaling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by nonrelativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localized pure states need not allow superluminal signaling, provided that the devices display the values of the states of entangled subsystems as defined in a nonstandard, although natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality.

arXiv:quant-ph/0204106•Physical Review A•Jul 18, 2005•65 citations

Wave Function Collapse and the No-Superluminal-Signaling Principle

Edward J. Gillis

The assumption that wave function collapse is a real occurrence has very interesting consequences - both experimental and theoretical. Besides predicting observable deviations from linear evolution, it implies that these deviations must originate in nondeterministic effects at the elementary level in order to prevent superluminal signaling, as demonstrated by Gisin. This lack of determinism implies that information cannot be instantiated in a reproducible form in isolated microsystems (as illustrated by the No-cloning theorem). By stipulating that information is a reproducible and referential property of physical systems, one can formulate the no-signaling principle in strictly physical terms as a prohibition of the acquisition of information about spacelike-separated occurrences. This formulation provides a new perspective on the relationship between relativity and spacetime structure, and it imposes tight constraints on the way in which collapse effects are induced. These constraints indicate that wave function collapse results from (presumably small) nondeterministic deviations from linear evolution associated with nonlocally entangling interactions. This hypothesis can be formalized in a stochastic collapse equation and used to assess the feasibility of testing for collapse effects.

arXiv:1501.03198•Jan 13, 2015•11 citations

Nonlinear, non-signaling Schrödinger equation

Tamás Geszti

A nonlinear extension of Schrödinger's wave equation is proposed that ensures non-signaling by keeping linear the evolution of \textit{coordinate-diagonal} elements of the density matrix. The equation contains a negative kinetic energy term that turns spreading of wave packets into its opposite: collapsing, as some effective mass $M$ grows beyond a universal critical mass, estimated to be about $μ= 2\cdot10^{-23}~$kg; then linear quantum kinetic energy gets negligible, which marks the quantum-classical border. Interference of large molecules is suggested for an experimental check of the proposed framework.

arXiv:2402.08757•Feb 13, 2024•0 citations

Nonlinearity without Superluminality. (arXiv:quant-ph/0204106v4 CROSS LISTED)

Adrian Kent

Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signalling. As Czachor, Gisin and Polchinski pointed out, this is not true for general nonlinear modifications of the Schroedinger equation. Excluding superluminal signalling has thus been taken to rule out most nonlinear versions of quantum theory. The no superluminal signalling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by non-relativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localised pure states need not allow superluminal signalling, provided that the devices display the values of the states of entangled subsystems as defined in a non-standard, but natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality.

•Jul 16, 2018•0 citations

Experimental Tests of the Projection Postulate

Edward J. Gillis

Bell [Helv. Phys.Act. 48 1975] described an idealized test of the projection postulate in order to illustrate the ambiguities in the experimental predictions of quantum theory. An approach to the implementation of such tests is outlined here, based on the interesting logical relationship between the projection postulate and the no-superluminal-signaling principle. Gisin's theorem [Helv. Phys. Act. 62 1989] shows that the no-signaling principle implies that any description of projection at the elementary level must be nondeterministic. The lack of determinism means that information cannot be instantiated in a reproducible and transmittable form in isolated microsystems. The implied limitation on information allows one to interpret the no-signaling principle in purely physical terms as a prohibition of superluminal information transmission. This prohibition, in turn, imposes tight constraints on the connection between projection and elementary processes, leading to a specific hypothesis about how projection effects originate. The hypothesis serves as the basis for the experimental proposal.

•Jan 13, 2015•0 citations

Uniqueness of the Equation for Quantum State Vector Collapse

Angelo Bassi, Detlef Dürr, Günter Hinrichs

The linearity of quantum mechanics leads, under the assumption that the wave function offers a complete description of reality, to grotesque situations famously known as Schrödinger's cat. Ways out are either adding elements of reality or replacing the linear evolution by a nonlinear one. Models of spontaneous wave function collapses took the latter path. The way such models are constructed leaves the question of whether such models are in some sense unique, i.e., whether the nonlinear equations replacing Schrödinger's equation are uniquely determined as collapse equations. Various people worked on identifying the class of nonlinear modifications of the Schrödinger equation, compatible with general physical requirements. Here we identify the most general class of continuous wave function evolutions under the assumption of no-faster-than-light signaling.

arXiv:1303.4284•Physical Review Letters•Nov 18, 2013•35 citations
Abstract There is a growing interest, both from the theoretical as well as experimental side, to test the validity of the quantum superposition principle, and of theories which explicitly violate it by adding nonlinear terms to the Schrödinger equation. We review the original argument elaborated by Gisin (1989 Helv. Phys. Acta 62 363), which shows that the non-superluminal-signaling condition implies that the dynamics of the density matrix must be linear. This places very strong constraints on the permissible modifications of the Schrödinger equation, since they have to give rise, at the statistical level, to a linear evolution for the density matrix. The derivation is done in a heuristic way here and is appropriate for the students familiar with the textbook quantum mechanics and the language of density matrices.
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signaling. As Czachor, Gisin, and Polchinski pointed out, this is not generally true of general nonlinear modifications of the Schr\"odinger equation. Excluding superluminal signaling has thus been taken to rule out most nonlinear versions of quantum theory. The no-superluminal-signaling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by nonrelativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localized pure states need not allow superluminal signaling, provided that the devices display the values of the states of entangled subsystems as defined in a nonstandard, although natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality.
The assumption that wave function collapse is a real occurrence has very interesting consequences - both experimental and theoretical. Besides predicting observable deviations from linear evolution, it implies that these deviations must originate in nondeterministic effects at the elementary level in order to prevent superluminal signaling, as demonstrated by Gisin. This lack of determinism implies that information cannot be instantiated in a reproducible form in isolated microsystems (as illustrated by the No-cloning theorem). By stipulating that information is a reproducible and referential property of physical systems, one can formulate the no-signaling principle in strictly physical terms as a prohibition of the acquisition of information about spacelike-separated occurrences. This formulation provides a new perspective on the relationship between relativity and spacetime structure, and it imposes tight constraints on the way in which collapse effects are induced. These constraints indicate that wave function collapse results from (presumably small) nondeterministic deviations from linear evolution associated with nonlocally entangling interactions. This hypothesis can be formalized in a stochastic collapse equation and used to assess the feasibility of testing for collapse effects.
A nonlinear extension of Schrödinger's wave equation is proposed that ensures non-signaling by keeping linear the evolution of \textit{coordinate-diagonal} elements of the density matrix. The equation contains a negative kinetic energy term that turns spreading of wave packets into its opposite: collapsing, as some effective mass MMM grows beyond a universal critical mass, estimated to be about μ=2⋅10−23 μ= 2\cdot10^{-23}~μ=2⋅10−23 kg; then linear quantum kinetic energy gets negligible, which marks the quantum-classical border. Interference of large molecules is suggested for an experimental check of the proposed framework.
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signalling. As Czachor, Gisin and Polchinski pointed out, this is not true for general nonlinear modifications of the Schroedinger equation. Excluding superluminal signalling has thus been taken to rule out most nonlinear versions of quantum theory. The no superluminal signalling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by non-relativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localised pure states need not allow superluminal signalling, provided that the devices display the values of the states of entangled subsystems as defined in a non-standard, but natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality.
Bell [Helv. Phys.Act. 48 1975] described an idealized test of the projection postulate in order to illustrate the ambiguities in the experimental predictions of quantum theory. An approach to the implementation of such tests is outlined here, based on the interesting logical relationship between the projection postulate and the no-superluminal-signaling principle. Gisin's theorem [Helv. Phys. Act. 62 1989] shows that the no-signaling principle implies that any description of projection at the elementary level must be nondeterministic. The lack of determinism means that information cannot be instantiated in a reproducible and transmittable form in isolated microsystems. The implied limitation on information allows one to interpret the no-signaling principle in purely physical terms as a prohibition of superluminal information transmission. This prohibition, in turn, imposes tight constraints on the connection between projection and elementary processes, leading to a specific hypothesis about how projection effects originate. The hypothesis serves as the basis for the experimental proposal.
The linearity of quantum mechanics leads, under the assumption that the wave function offers a complete description of reality, to grotesque situations famously known as Schrödinger's cat. Ways out are either adding elements of reality or replacing the linear evolution by a nonlinear one. Models of spontaneous wave function collapses took the latter path. The way such models are constructed leaves the question of whether such models are in some sense unique, i.e., whether the nonlinear equations replacing Schrödinger's equation are uniquely determined as collapse equations. Various people worked on identifying the class of nonlinear modifications of the Schrödinger equation, compatible with general physical requirements. Here we identify the most general class of continuous wave function evolutions under the assumption of no-faster-than-light signaling.