Jump to content

Pusey–Barrett–Rudolph theorem: Difference between revisions

Add links
From Wikipedia, the free encyclopedia
Browse history interactively
← Previous editNext edit →
Content deleted Content added
VisualWikitext
OAbot (talk | contribs)
Bots
439,234 edits
m Open access bot: add arxiv identifier to citation with #oabot.
Oxysh (talk | contribs)
28 edits
→Theorem: More description of the theorem in the opening section, including comparison to Bell and Kochen–Specker theorems. Added a "See also" section. Moved Valentini quote to introductory section. Removed mention of theorem being known as "Pusey's theorem": I can only find one instance of this online in a blog and not in any published articles; as a scientific work I think proper accreditation to all authors should be encouraged.
Line 1: Line 1:
The '''PBR theorem''' is a [[no-go theorem]] concerning certain realist or [[Hidden-variable theory|hidden variable interpretations]] of quantum mechanics concerning the meaning of [[quantum state]]s due to Matthew Pusey, Jonathan Barrett, and [[Terry Rudolph]], (for whom the theorem is named).
The '''PBR theorem<ref name="NatPhys2012" />''' is a [[no-go theorem]] in [[quantum foundations]] due to Matthew Pusey, Jonathan Barrett, and [[Terry Rudolph]] (for whom the theorem is named). It has particular significance for how one may interpret the nature of the [[quantum state]].

With respect to certain realist [[Hidden-variable theory|hidden variable theories]] that attempt to explain the predictions of [[quantum mechanics]], the theorem rules that pure quantum states must be "ontic" in the sense that they correspond directly to states of reality, rather than "epistemic" in the sense that they represents probabilistic or incomplete states of knowledge about reality.

The PBR theorem may also be compared with other no-go theorems like [[Bell's theorem]] and the [[Kochen–Specker theorem|Bell–Kochen–Specker theorem]], which, respectively, rule out the possibility of explaining the predictions of quantum mechanics with local hidden variable theories and noncontextual hidden variable theories. Similarly, the PBR theorem could be said to rule out ''preparation independent'' hidden variable theories, in which quantum states that are prepared independently have independent hidden variable descriptions.

This result was cited by theoretical physicist [[Antony Valentini]] as "the most important general theorem relating to the foundations of quantum mechanics since [[Bell's theorem]]".<ref>{{cite journal|last=Reich|first=Eugenie Samuel|date=17 November 2011|title=Quantum theorem shakes foundations|url=http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392|journal=Nature|doi=10.1038/nature.2011.9392|accessdate=20 November 2011}}</ref>


== Theorem ==
== Theorem ==
This theorem, first published as an [[arXiv]] preprint<ref>{{cite arXiv |last1= Pusey |first1=Matthew F. |last2=Barrett |first2=Jonathan |last3=Rudolph |first3=Terry |eprint=1111.3328v1 |class=quant-ph |year=2011 |title=The quantum state cannot be interpreted statistically}}</ref> and subsequently in ''[[Nature Physics]]''<ref name="NatPhys2012">{{cite journal | last1 = Pusey | first1 = M. F. | last2 = Barrett | first2 = J. | last3 = Rudolph | first3 = T. | year = 2012 | title = On the reality of the quantum state | url = | journal = Nature Physics | volume = 8 | issue = 6| pages = 475–478 | doi = 10.1038/nphys2309 | arxiv = 1111.3328 | bibcode = 2012NatPh...8..476P }}</ref>, concerns the interpretational status of pure quantum states. Under the classification of hidden variable models of Harrigan and Spekkens,<ref>{{Cite journal|last=Harrigan|first=Nicholas|last2=Spekkens|first2=Robert W.|date=2010|title=Einstein, Incompleteness, and the Epistemic View of Quantum States|url=http://link.springer.com/10.1007/s10701-009-9347-0|journal=Foundations of Physics|language=en|volume=40|issue=2|pages=125–157|arxiv=0706.2661|doi=10.1007/s10701-009-9347-0|issn=0015-9018|via=}}</ref> the interpretation of the quantum wavefunction <math>|\psi\rangle</math>can be categorized as either ''ψ''-ontic if "every complete physical state ontic state in the theory is consistent with only one pure quantum state" and ''ψ-''epistemic "if there exist ontic states that are consistent with more than one pure quantum state." The PBR theorem shows that within this hidden variable model, either the quantum state <math>|\psi\rangle</math>is ''ψ''-ontic, or else all quantum states, including non-[[quantum entanglement|entangled]] ones, can communicate by [[action at a distance (physics)|action at a distance]]. This result has been referred to as Pusey's theorem or the PBR theorem, and has been cited by theoretical physicist [[Antony Valentini]] as "the most important general theorem relating to the foundations of quantum mechanics since [[Bell's theorem]]".<ref>{{cite journal | last = Reich | first = Eugenie Samuel | title = Quantum theorem shakes foundations | url = http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392 | journal = Nature | date= 17 November 2011 |doi=10.1038/nature.2011.9392 |accessdate=20 November 2011}}</ref>
This theorem, which first appeared as an [[arXiv]] preprint<ref>{{cite arXiv |last1= Pusey |first1=Matthew F. |last2=Barrett |first2=Jonathan |last3=Rudolph |first3=Terry |eprint=1111.3328v1 |class=quant-ph |year=2011 |title=The quantum state cannot be interpreted statistically}}</ref> and was subsequently published in ''[[Nature Physics]]''<ref name="NatPhys2012">{{cite journal | last1 = Pusey | first1 = M. F. | last2 = Barrett | first2 = J. | last3 = Rudolph | first3 = T. | year = 2012 | title = On the reality of the quantum state | url = | journal = Nature Physics | volume = 8 | issue = 6| pages = 475–478 | doi = 10.1038/nphys2309 | arxiv = 1111.3328 | bibcode = 2012NatPh...8..476P }}</ref>, concerns the interpretational status of pure quantum states. Under the classification of hidden variable models of Harrigan and Spekkens,<ref>{{Cite journal|last=Harrigan|first=Nicholas|last2=Spekkens|first2=Robert W.|date=2010|title=Einstein, Incompleteness, and the Epistemic View of Quantum States|url=http://link.springer.com/10.1007/s10701-009-9347-0|journal=Foundations of Physics|language=en|volume=40|issue=2|pages=125–157|arxiv=0706.2661|doi=10.1007/s10701-009-9347-0|issn=0015-9018|via=}}</ref> the interpretation of the quantum wavefunction <math>|\psi\rangle</math>can be categorized as either ''ψ''-ontic if "every complete physical state ontic state in the theory is consistent with only one pure quantum state" and ''ψ-''epistemic "if there exist ontic states that are consistent with more than one pure quantum state." The PBR theorem proves that either the quantum state <math>|\psi\rangle</math>is ''ψ''-ontic, or else non-[[quantum entanglement|entangled]] quantum states violate the assumption of preparation independence, which would entail [[action at a distance (physics)|action at a distance]].


{{Quote|text=In conclusion, we have presented a [[no-go theorem]], which - modulo assumptions - shows that models in which the quantum state is interpreted as mere [[quantum information|information]] about an objective physical state of a system cannot reproduce the predictions of quantum theory. The result is in the same spirit as Bell’s theorem, which states that no local theory can reproduce the predictions of quantum theory.|author=Matthew F. Pusey, Jonathan Barrett, and Terry Rudolph|source="On the reality of the quantum state", ''Nature Physics'' '''8''', 475-478 (2012)}}
{{Quote|text=In conclusion, we have presented a [[no-go theorem]], which - modulo assumptions - shows that models in which the quantum state is interpreted as mere [[quantum information|information]] about an objective physical state of a system cannot reproduce the predictions of quantum theory. The result is in the same spirit as Bell’s theorem, which states that no local theory can reproduce the predictions of quantum theory.|author=Matthew F. Pusey, Jonathan Barrett, and Terry Rudolph|source="On the reality of the quantum state", ''Nature Physics'' '''8''', 475-478 (2012)}}

==See also==

* [[Quantum foundations]]
* [[Bell's theorem]]
* [[Kochen–Specker theorem]]


==References==
==References==

Revision as of 17:35, 26 July 2019

The PBR theorem[1] is a no-go theorem in quantum foundations due to Matthew Pusey, Jonathan Barrett, and Terry Rudolph (for whom the theorem is named). It has particular significance for how one may interpret the nature of the quantum state.

With respect to certain realist hidden variable theories that attempt to explain the predictions of quantum mechanics, the theorem rules that pure quantum states must be "ontic" in the sense that they correspond directly to states of reality, rather than "epistemic" in the sense that they represents probabilistic or incomplete states of knowledge about reality.

The PBR theorem may also be compared with other no-go theorems like Bell's theorem and the Bell–Kochen–Specker theorem, which, respectively, rule out the possibility of explaining the predictions of quantum mechanics with local hidden variable theories and noncontextual hidden variable theories. Similarly, the PBR theorem could be said to rule out preparation independent hidden variable theories, in which quantum states that are prepared independently have independent hidden variable descriptions.

This result was cited by theoretical physicist Antony Valentini as "the most important general theorem relating to the foundations of quantum mechanics since Bell's theorem".[2]

Theorem

This theorem, which first appeared as an arXiv preprint[3] and was subsequently published in Nature Physics[1], concerns the interpretational status of pure quantum states. Under the classification of hidden variable models of Harrigan and Spekkens,[4] the interpretation of the quantum wavefunction can be categorized as either ψ-ontic if "every complete physical state ontic state in the theory is consistent with only one pure quantum state" and ψ-epistemic "if there exist ontic states that are consistent with more than one pure quantum state." The PBR theorem proves that either the quantum state is ψ-ontic, or else non-entangled quantum states violate the assumption of preparation independence, which would entail action at a distance.

In conclusion, we have presented a no-go theorem, which - modulo assumptions - shows that models in which the quantum state is interpreted as mere information about an objective physical state of a system cannot reproduce the predictions of quantum theory. The result is in the same spirit as Bell’s theorem, which states that no local theory can reproduce the predictions of quantum theory.

— Matthew F. Pusey, Jonathan Barrett, and Terry Rudolph, "On the reality of the quantum state", Nature Physics 8, 475-478 (2012)

See also

References

  1. ^ a b Pusey, M. F.; Barrett, J.; Rudolph, T. (2012). "On the reality of the quantum state". Nature Physics. 8 (6): 475–478. arXiv:1111.3328. Bibcode:2012NatPh...8..476P. doi:10.1038/nphys2309.
  2. ^ Reich, Eugenie Samuel (17 November 2011). "Quantum theorem shakes foundations". Nature. doi:10.1038/nature.2011.9392. Retrieved 20 November 2011.
  3. ^ Pusey, Matthew F.; Barrett, Jonathan; Rudolph, Terry (2011). "The quantum state cannot be interpreted statistically". arXiv:1111.3328v1 [quant-ph].
  4. ^ Harrigan, Nicholas; Spekkens, Robert W. (2010). "Einstein, Incompleteness, and the Epistemic View of Quantum States". Foundations of Physics. 40 (2): 125–157. arXiv:0706.2661. doi:10.1007/s10701-009-9347-0. ISSN 0015-9018.
Retrieved from "https://en.wikipedia.org/enwiki/w/index.php?title=Pusey–Barrett–Rudolph_theorem&oldid=907994496"