R EFLECTIONS ON THE PBR T HEOREM : R EALITY C RITERIA & P - PowerPoint PPT Presentation

R EFLECTIONS ON THE PBR T HEOREM : R EALITY C RITERIA & P REPARATION I NDEPENDENCE Shane Mansfield QPL 2014

The Quantum State ψ — Real or Phenomenal? • Assume some space Λ of ontic states • Preparation of quantum states ψ , φ 2 H induce probability distributions µ ψ , µ φ over Λ , etc. µ φ µ ψ • If distributions can overlap ! ψ -epistemic • If distributions never overlap ! Each λ 2 Λ encodes a unique quantum state, so ψ -ontic Harrigan & Spekkens, arXiv:0706.2661 [quant-ph]

The Quantum State ψ — Real or Phenomenal? • Assume some space Λ of ontic states • Preparation of quantum states ψ , φ 2 H induce probability distributions µ ψ , µ φ over Λ , etc. µ φ µ ψ • If distributions can overlap ! ψ -epistemic • If distributions never overlap ! Each λ 2 Λ encodes a unique quantum state, so ψ -ontic Harrigan & Spekkens, arXiv:0706.2661 [quant-ph]

The PBR Theorem* The following assumptions 1. systems have an objective physical state 2. quantum predictions are correct 3. preparation independence imply ψ -ontic. λ A λ B preparation preparation device device p A p B *Pusey, Barrett & Rudolph, arXiv:1111.3328 [quant-ph]

The PBR Theorem* The following assumptions 1. systems have an objective physical state 2. quantum predictions are correct 3. preparation independence imply ψ -ontic . µ φ µ ψ *Pusey, Barrett & Rudolph, arXiv:1111.3328 [quant-ph]

Preparation Independence λ A λ B preparation preparation device device p A p B µ ( λ A , λ B | p A , p B ) = µ ( λ A | p A ) ⇥ µ ( λ B | p B ) Causes for suspicion: • Bell’s Theorem becomes trivial (Proceedings) • Gives rise to alarmingly strong No-Go results* • Motivated by local causality (on shaky ground since Bell) *Schlosshauer & Fine, arXiv:1306.5805 [quant-ph]

Comparison with Bell Locality o A o B measurement measurement device device m A m B λ p ( o A , o B | m A , m B , λ ) = p ( o A | m A , λ ) ⇥ p ( o A | m B , λ ) Ruled out by Bell’s Theorem

Comparison with Bell Locality o A o B measurement measurement device device m A m B p ( o A , o B | m A , m B , λ ) = p ( o A | m A , λ ) ⇥ p ( o A | m B , λ ) Ruled out by Bell’s Theorem

No-signalling o A o B measurement measurement device device m A m B p ( o A | m A , m B ) = p ( o A | m A ) p ( o B | m A , m B ) = p ( o B | m B )

An Alternative to Preparation Independence No-preparation-signalling λ A λ B preparation preparation device device p A p B µ ( λ A | p A , p B ) = µ ( λ A | p A ) µ ( λ B | p A , p B ) = µ ( λ B | p B ) • Preparation Independence = ) No-preparation-signalling

Escaping PBR’s Conclusion • Replace prep. independence with no-preparation-signalling • Detailed discussion of where PBR argument breaks down (Proceedings) • A ψ -epistemic model realising PBR statistics: 8 1 / if λ 2 { ( λ δ , λ 0 ) , ( λ δ , λ + ) , ( λ 0 , λ δ ) , ( λ + , λ δ ) } 4 > < ξ 1 ( λ ) : = 1 if λ = ( λ + , λ + ) > 0 otherwise : Define µ 00 , µ 0 + , µ + 0 , µ ++ by the table below and measurement response functions as on the right 8 1 / if λ 2 { ( λ δ , λ 0 ) , ( λ δ , λ + ) , ( λ 0 , λ δ ) , ( λ + , λ δ ) } 4 > < ξ 2 ( λ ) : = 1 if λ = ( λ + , λ 0 ) > 0 otherwise : System 2 8 1 / if λ 2 { ( λ δ , λ 0 ) , ( λ δ , λ + ) , ( λ 0 , λ δ ) , ( λ + , λ δ ) } | 0 i | + i 4 > < ξ 3 ( λ ) : = if λ = ( λ 0 , λ + ) λ δ λ 0 λ δ λ + 1 λ δ 0 1 / 0 1 / > 0 otherwise 4 4 : | 0 i λ 0 1 / 1 / 1 / 1 / 4 2 4 2 System 1 λ δ 0 1 / 0 1 / 8 4 4 if λ 2 { ( λ δ , λ 0 ) , ( λ δ , λ + ) , ( λ 0 , λ δ ) , ( λ + , λ δ ) } 1 / | + i 4 λ + 1 / 1 / 1 / 1 / > < 4 2 4 2 ξ 4 ( λ ) : = 1 if λ = ( λ + , λ + ) > 0 otherwise :

A Similar Proposal* λ A λ B preparation preparation device device λ s p A p B Z d λ s µ ( λ A , λ B , λ s | p A , p B ) = µ ( λ A | p A ) ⇥ µ ( λ B | p B ) Λ s Drawbacks: • λ s -dependence • Harder to motivate physically • Implies no-preparation-signalling *Emerson, Serbin, Sutherland & Veitch, arXiv:1312.1345 [quant-ph]

Conclusion Preparation Independence • An intuition of independence that was invalidated by Bell • Alarmingly strong no-go results, Bell is trivialised No-preparation-signalling • Rules out superluminal signalling • PBR argument no longer holds • ψ -epistemic interpretation still valid

Proceedings What if µ ψ , µ φ overlap on sets of measure zero? • Dualise to avoid this! What if ontic/epistemic definitions are applied to things other than ψ ? • Observable properties are ontic ( ) Correlations are local/non-contextual

Appendix: The Quantum State ψ — Real or Phenomenal? ψ -ontic: ψ -epistemic: • A real physical wave • ψ gives probabilistic information (on configuration space?) • Collapse ! Bayesian updating • Easiest way to think about interference • Can’t reliably distinguish • PBR theorem non-orthogonal ψ , φ • ψ is exponential in the number of systems • Can’t be cloned • Can be teleported