ARE QUANTUM STATES REAL

In this paper we consider theories in which reality is described by some underlying variables, λ. Each value these variables can take represents an ontic state (a particular state of reality). The preparation of a quantum state corresponds to a distribution over the ontic states, λ. If we make three basic assumptions, we can show that the distributions over ontic states corresponding to distinct pure states are nonoverlapping. This means that we can deduce the quantum state from a knowledge of the ontic state. Hence, if these assumptions are correct, we can claim that the quantum state is a real thing (it is written into the underlying variables that describe reality). The key assumption we use in this proof is ontic indifference — that quantum transformations that do not affect a given pure quantum state can be implemented in such a way that they do not affect the ontic states in the support of that state. In fact this assumption is violated in the Spekkens toy model (which captures many aspects of quantum theory and in which different pure states of the model have overlapping distributions over ontic states). This paper proves that ontic indifference must be violated in any model reproducing quantum theory in which the quantum state is not a real thing. The argument presented in this paper is different from that given in a recent paper by Pusey, Barrett and Rudolph. It uses a different key assumption and it pertains to a single copy of the system in question.

[1]  Bill Edwards,et al.  Toy quantum categories , 2008, 0808.1037.

[2]  D. Bohm.  A SUGGESTED INTERPRETATION OF THE QUANTUM THEORY IN TERMS OF "HIDDEN" VARIABLES. II , 1952 .

[3]  P. Pearle.  Reduction of the state vector by a nonlinear Schrödinger equation , 1976 .

[4]  Robert W. Spekkens,et al.  Einstein, Incompleteness, and the Epistemic View of Quantum States , 2007, 0706.2661.

[5]  D. J. Miller.  Alternative Experimental Protocol for a PBR-Like Result , 2012 .

[6]  Maximilian Schlosshauer,et al.  On a recent quantum no-go theorem , 2012 .

[7]  Renato Renner,et al.  Is a system's wave function in one-to-one correspondence with its elements of reality? , 2011, Physical review letters.

[8]  Lucien Hardy,et al.  Substituting a qubit for an arbitrarily large number of classical bits. , 2003, Physical review letters.

[9]  Lucien Hardy,et al.  Quantum ontological excess baggage , 2004 .

[10]  Robert W. Spekkens,et al.  Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction , 2011, 1111.5057.

[11]  C. Fuchs.  QBism, the Perimeter of Quantum Bayesianism , 2010, 1003.5209.

[12]  Alberto Montina,et al.  Dynamics of a qubit as a classical stochastic process with time-correlated noise: minimal measurement invasiveness. , 2011, Physical review letters.

[13]  C. Fuchs,et al.  Conditions for compatibility of quantum-state assignments , 2002, quant-ph/0206110.

[14]  Michael J. W. Hall,et al.  Generalisations of the recent Pusey-Barrett-Rudolph theorem for statistical models of quantum phenomena , 2011 .

[15]  J. Bell.  On the Einstein-Podolsky-Rosen paradox , 1964 .

[16]  Antony Valentini.  Signal-locality in hidden-variables theories , 2002 .

[17]  Maximilian Schlosshauer,et al.  Implications of the Pusey-Barrett-Rudolph quantum no-go theorem. , 2012, Physical review letters.

[18]  R. Mcweeny.  On the Einstein-Podolsky-Rosen Paradox , 2000 .

[19]  D. Deutsch.  Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[20]  G Pelletier-Lapointe.  And all that jazz. , 1980, L' Infirmiere canadienne.

[21]  Reck,et al.  Experimental realization of any discrete unitary operator. , 1994, Physical review letters.

[22]  Alberto Montina,et al.  Exponential complexity and ontological theories of quantum mechanics , 2007, 0711.4770.

[23]  Yakir AharonovandLev Vaidman.  Measurement of the Schrodingerwaveof a single particle , 1993 .

[24]  H. Everett.  "Relative State" Formulation of Quantum Mechanics , 1957 .

[25]  R. Spekkens.  Evidence for the epistemic view of quantum states: A toy theory , 2004, quant-ph/0401052.

[26]  Robert W. Spekkens.  Why the quantum? Insights from classical theories with a statistical restriction , 2010 .

[27]  David Jennings,et al.  Distinct quantum states can be compatible with a single state of reality. , 2012, Physical review letters.

[28]  H. Westman,et al.  A minimalist pilot-wave model for quantum electrodynamics , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[29]  Bill Edwards,et al.  Phase Groups and the Origin of Non-locality for Qubits , 2010, QPL@MFPS.

[30]  Bill Edwards,et al.  Toy Quantum Categories (Extended Abstract) , 2011, QPL/DCM@ICALP.

[31]  E. Specker,et al.  The Problem of Hidden Variables in Quantum Mechanics , 1967 .

[32]  E. Beltrametti,et al.  A classical extension of quantum mechanics , 1995 .

[33]  Matthew S. Leifer.  PBR, EPR, and All That Jazz , 2012 .

[34]  D. J. Miller.  Alternative experimental protocol to demonstrate the Pusey-Barrett-Rudolph theorem , 2013 .

[35]  David Jennings,et al.  The quantum state can be interpreted statistically , 2012 .

[36]  Alberto Montina,et al.  State-space dimensionality in short-memory hidden-variable theories , 2010, 1008.4415.

[37]  Weber,et al.  Unified dynamics for microscopic and macroscopic systems. , 1986, Physical review. D, Particles and fields.

[38]  Martin Jähnert.  Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference Quantum theory at the Crossroads: Reconsidering the 1927 Solvay Conference , Guido Bacciagaluppi and Antony Valentini Cambridge U. Press, New York, 2009. $126.00 (530 pp.). ISBN 978-0-521-81421-8 , 2010 .

[39]  Matthew F Pusey,et al.  On the reality of the quantum state , 2011, Nature Physics.

[40]  J. Bell,et al.  Speakable and Unspeakable in Quantum Mechanics: Preface to the first edition , 2004 .

[41]  Aurelien Drezet.  Can quantum mechanics be considered as statistical? an analysis of the PBR theorem , 2012 .

[42]  Lucien Hardy.  Disentangling Nonlocality and Teleportation , 1999 .