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

Physics

On the Alleged Locality in the Schrödinger Picture. Comment on Vedral, V. Locality in the Schrödinger Picture of Quantum Mechanics. Physics 2024, 6, 793–800

Charles Alexandre Bédard

Published Apr 9, 2025• 0 citations
Publisher

Abstract

In his recent paper, Vlatko Vedral claims that the Schrödinger picture can describe quantum systems as locally as the Heisenberg picture, relying on a product notation for the density matrix. Here, I refute that claim. I show that the so-called ‘local factors’ in the product notation do not correspond to individual systems and therefore fail to satisfy Einsteinian locality. Furthermore, the product notation does not track where local gates are applied. Finally, I expose internal inconsistencies in the argument: if, as is also stated, the Schrödinger-picture locality ultimately depends on the explicit bookkeeping of all operations, then the explanatory power of the product notation is de facto undermined.

DOI
10.3390/physics7020011

Related papers

On the Alleged Locality in the Schrödinger Picture

Charles Alexandre Bédard

Vedral claims that the Schrödinger picture can describe quantum systems as locally as the Heisenberg picture, relying on a product notation for the density matrix. Here, I refute that claim. I show that the so-called `local factors' in the product notation do not correspond to individual systems and therefore fail to satisfy Einsteinian locality. Furthermore, the product notation does not track where local gates are applied. Finally, I expose internal inconsistencies in the argument: if, as is also stated, Schrödinger-picture locality ultimately depends on explicit bookkeeping of all operations, then the explanatory power of the product notation is de facto undermined.

arXiv:2502.12991•Feb 18, 2025•0 citations

The Heisenberg picture

Dževad Belkić

In this chapter, the authors describe the Heisenberg picture of quantum mechanics by formally accomplishing a time-dependent transformation of state vectors and operators of the Schrodinger picture. Any new picture of quantum mechanics will be acceptable, if the Schrodinger state vectors and operators are subjected to a transformation, which does not alter: the spectrum of the eigenvalues of the operators and the scalar product of an arbitrary state vector with the eigenstate vectors. These two conditions are easily fulfilled by means of the unitary transformations. The authors show that a unitary operator represents an isomorph mapping of a certain unitary vector space onto itself. Since the physical quantities measured in the experiment are, in fact, a measure of the scalar product, as implied by the definition of the probability W through the scalar product in, it is clear that the predictions based upon the new, Heisenberg picture must be identical to those obtained in the Schrodinger picture.

CRC Press eBooks•Jan 15, 2020•0 citations

Realism and the Inequivalence of the Two Quantum Pictures

Charles Alexandre Bédard

Abstract The standard claim that the Schrödinger and Heisenberg pictures of quantum mechanics are equivalent rests on the fact that they yield identical empirical predictions. This equivalence therefore assumes the instrumentalist worldview in which theories serve only as tools for prediction. Under scientific realism, by contrast, theories aim to describe reality. Whereas the Schrödinger picture posits a time-evolving wave function, the Heisenberg picture posits so-called descriptors, time-evolving generators of the algebra of observables. These two structures are non-isomorphic: descriptors surject onto but do not reduce to the Schrödinger state. Hence, under realism, the pictures are inequivalent. The chapter argues that this inequivalence marks an opening toward a richer, separable ontology for quantum theory. On explanatory grounds, descriptors provide genuinely local accounts of superdense coding, teleportation, branching, and Bell inequality violations—phenomena that the Schrödinger framework does not explain fully locally.

arXiv:2510.02138•Aug 26, 2026•0 citations

Comment on an alleged refutation of non-locality

R. L. Schafir

A recent claim (Deutsch and Hayden (2000)), that non-locality can be refuted by considering the evolution of the system in the Heisenberg picture, is denied. What they demonstrated was not the falsity of non-locality but the no-superluminal-signalling principle.

arXiv:quant-ph/0201065•Jan 16, 2002•1 citation

Interpolating between the gauge and Schrödinger pictures of quantum dynamics

Sayak Guha Roy, Kevin Slagle

Although spatial locality is explicit in the Heisenberg picture of quantum dynamics, spatial locality is not explicit in the Schrödinger picture equations of motion. The gauge picture is a modification of Schrödinger’s picture such that locality is explicit in the equations of motion. In order to achieve this explicit locality, the gauge picture utilizes (1) a distinct wavefunction associated with each patch of space, and (2) time-dependent unitary connections to relate the Hilbert spaces associated with nearby patches. In this work, we show that by adding an additional spatially-local term to the gauge picture equations of motion, we can effectively interpolate between the gauge and Schrödinger pictures, such that when this additional term has a large coefficient, all of the gauge picture wavefunctions approach the Schrödginer picture wavefunction (and the connections approach the identity).

arXiv:2307.02369•SciPost Physics Core•Nov 24, 2023•0 citations

Locality in the Schrödinger Picture of Quantum Mechanics

Vlatko Vedral

This paper explains how the so-called Einstein locality is to be understood in the Schrödinger picture of quantum mechanics. This notion is fully compatible with the Bell non-locality exhibited by entangled states. Contrary to the belief that quantum mechanics is incomplete, it is, As a matter of fact, its overcompleteness, as exemplified by the different pictures of quantum physics, that points to the same underlying reality.

Physics•May 19, 2024•1 citation
In his recent paper, Vlatko Vedral claims that the Schrödinger picture can describe quantum systems as locally as the Heisenberg picture, relying on a product notation for the density matrix. Here, I refute that claim. I show that the so-called ‘local factors’ in the product notation do not correspond to individual systems and therefore fail to satisfy Einsteinian locality. Furthermore, the product notation does not track where local gates are applied. Finally, I expose internal inconsistencies in the argument: if, as is also stated, the Schrödinger-picture locality ultimately depends on the explicit bookkeeping of all operations, then the explanatory power of the product notation is de facto undermined.
Vedral claims that the Schrödinger picture can describe quantum systems as locally as the Heisenberg picture, relying on a product notation for the density matrix. Here, I refute that claim. I show that the so-called `local factors' in the product notation do not correspond to individual systems and therefore fail to satisfy Einsteinian locality. Furthermore, the product notation does not track where local gates are applied. Finally, I expose internal inconsistencies in the argument: if, as is also stated, Schrödinger-picture locality ultimately depends on explicit bookkeeping of all operations, then the explanatory power of the product notation is de facto undermined.
In this chapter, the authors describe the Heisenberg picture of quantum mechanics by formally accomplishing a time-dependent transformation of state vectors and operators of the Schrodinger picture. Any new picture of quantum mechanics will be acceptable, if the Schrodinger state vectors and operators are subjected to a transformation, which does not alter: the spectrum of the eigenvalues of the operators and the scalar product of an arbitrary state vector with the eigenstate vectors. These two conditions are easily fulfilled by means of the unitary transformations. The authors show that a unitary operator represents an isomorph mapping of a certain unitary vector space onto itself. Since the physical quantities measured in the experiment are, in fact, a measure of the scalar product, as implied by the definition of the probability W through the scalar product in, it is clear that the predictions based upon the new, Heisenberg picture must be identical to those obtained in the Schrodinger picture.
Abstract The standard claim that the Schrödinger and Heisenberg pictures of quantum mechanics are equivalent rests on the fact that they yield identical empirical predictions. This equivalence therefore assumes the instrumentalist worldview in which theories serve only as tools for prediction. Under scientific realism, by contrast, theories aim to describe reality. Whereas the Schrödinger picture posits a time-evolving wave function, the Heisenberg picture posits so-called descriptors, time-evolving generators of the algebra of observables. These two structures are non-isomorphic: descriptors surject onto but do not reduce to the Schrödinger state. Hence, under realism, the pictures are inequivalent. The chapter argues that this inequivalence marks an opening toward a richer, separable ontology for quantum theory. On explanatory grounds, descriptors provide genuinely local accounts of superdense coding, teleportation, branching, and Bell inequality violations—phenomena that the Schrödinger framework does not explain fully locally.
Although spatial locality is explicit in the Heisenberg picture of quantum dynamics, spatial locality is not explicit in the Schrödinger picture equations of motion. The gauge picture is a modification of Schrödinger’s picture such that locality is explicit in the equations of motion. In order to achieve this explicit locality, the gauge picture utilizes (1) a distinct wavefunction associated with each patch of space, and (2) time-dependent unitary connections to relate the Hilbert spaces associated with nearby patches. In this work, we show that by adding an additional spatially-local term to the gauge picture equations of motion, we can effectively interpolate between the gauge and Schrödinger pictures, such that when this additional term has a large coefficient, all of the gauge picture wavefunctions approach the Schrödginer picture wavefunction (and the connections approach the identity).