Pusey–Barrett–Rudolph theorem

<h2 id="theorem">Theorem</h2>
<p>This theorem, which first appeared as an <a href="/facts/ArXiv/H6EtgnBe">arXiv</a> preprint<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> and was subsequently published in <i><a href="/facts/Nature_Physics/yNqfp2IJ">Nature Physics</a></i>,<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a> concerns the interpretational status of pure quantum states. Under the classification of hidden variable models of Harrigan and Spekkens,<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> the interpretation of the quantum wavefunction 
  
    
      
        
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        ψ
        ⟩
      
    
    {\displaystyle |\psi \rangle }
  
 can be categorized as either <i>ψ</i>-ontic if "every complete physical state or ontic state in the theory is consistent with only one pure quantum state" and <i>ψ-</i>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 
  
    
      
        
          |
        
        ψ
        ⟩
      
    
    {\displaystyle |\psi \rangle }
  
 is <i>ψ</i>-ontic, or else non-<a href="/facts/Quantum_entanglement/afzslwN0">entangled</a> quantum states violate the assumption of preparation independence, which would entail <a href="/facts/Action_at_a_distance_(physics)/RcnpWomY">action at a distance</a>. 
</p>
<blockquote><p>In conclusion, we have presented a <a href="/facts/No-go_theorem/FcIHLN2u">no-go theorem</a>, which—modulo assumptions—shows that models in which the quantum state is interpreted as mere <a href="/facts/Quantum_information/Bl9QIvHj">information</a> 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.</p>— Matthew F. Pusey, Jonathan Barrett, and Terry Rudolph, "On the reality of the quantum state", <i>Nature Physics</i> 8, 475-478 (2012)</blockquote>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Quantum_foundations/ALdNv2sn">Quantum foundations</a></li>
<li><a href="/facts/Bell%27s_theorem/lg1V6kpk">Bell's theorem</a></li>
<li><a href="/facts/Kochen%E2%80%93Specker_theorem/I3NzBK3F">Kochen–Specker theorem</a></li></ul>

<h2 id="external-links">External links</h2>
<ul><li>David Wallace (18 November 2011). <a href="http://blogs.discovermagazine.com/cosmicvariance/2011/11/18/guest-post-david-wallace-on-the-physicality-of-the-quantum-state/">"Guest Post: David Wallace on the Physicality of the Quantum State"</a>. <i>Discover Magazine (blog)</i>. Kalmbach Publishing Co. Retrieved 20 November 2011.</li>
<li><a href="http://science.slashdot.org/story/11/11/18/1742222/study-says-quantum-wavefunction-is-a-real-physical-object">"Study Says Quantum Wavefunction Is a Real Physical Object"</a>. <i>Slashdot</i>. 18 November 2011. Retrieved 20 November 2011.</li>
<li>Matt Leifer (20 November 2011). <a href="http://mattleifer.info/2011/11/20/can-the-quantum-state-be-interpreted-statistically/">"Can the quantum state be interpreted statistically?"</a>. <i>Mathematics — Physics — Quantum Theory blog</i>. Retrieved 24 November 2011.</li>
<li>Leifer, Matt (2014). "Is the quantum state real? An extended review of ψ-ontology theorems". <i>Quanta</i>. 3 (1): 67–155. <a href="/facts/ArXiv_(identifier)/H6EtgnBe">arXiv</a>:<a href="https://arxiv.org/abs/1409.1570">1409.1570</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.12743%2Fquanta.v3i1.22">10.12743/quanta.v3i1.22</a>. <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/1314-7374">1314-7374</a>. <a href="/facts/S2CID_(identifier)/ldJsHa2Y">S2CID</a> <a href="https://api.semanticscholar.org/CorpusID:119295895">119295895</a>.</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>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. S2CID 14618942. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Reich, Eugenie Samuel (17 November 2011). "Quantum theorem shakes foundations". Nature. doi:10.1038/nature.2011.9392. S2CID 211836537. Retrieved 20 November 2011. <a href="http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392" target="_blank">http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Pusey, Matthew F.; Barrett, Jonathan; Rudolph, Terry (2011). "The quantum state cannot be interpreted statistically". arXiv:1111.3328v1 [quant-ph]. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>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. S2CID 14618942. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>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. Bibcode:2010FoPh...40..125H. doi:10.1007/s10701-009-9347-0. ISSN 0015-9018. S2CID 32755624. <a href="/wiki/Robert_Spekkens" target="_blank">/wiki/Robert_Spekkens</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
</ol>

Pusey–Barrett–Rudolph theorem open-in-new

Pusey–Barrett–Rudolph theorem