Evidence for the epistemic view of quantum states: A toy theory

@article{Spekkens2004EvidenceFT,
  title={Evidence for the epistemic view of quantum states: A toy theory},
  author={Robert W. Spekkens},
  journal={Physical Review A},
  year={2004},
  volume={75},
  pages={032110}
}
  • R. Spekkens
  • Published 9 January 2004
  • Physics
  • Physical Review A
We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge. Many quantum phenomena are found to have analogues within this toy theory. These include the noncommutativity of measurements, interference, the multiplicity of convex decompositions of a mixed state, the impossibility of discriminating nonorthogonal states, the… 

Figures and Tables from this paper

ψ-Epistemic models are exponentially bad at explaining the distinguishability of quantum states.

  • M. Leifer
  • Philosophy
    Physical review letters
  • 2014
This Letter exhibits a family of states for which the ratio of these two quantities must be ≤2de-cd in Hilbert spaces of dimension d that are divisible by 4, which implies that the epistemic explanation of indistinguishability becomes implausible at an exponential rate as the Hilbert space dimension increases.

Einstein, Incompleteness, and the Epistemic View of Quantum States

It is shown that for models wherein the quantum state has the status of something real, the failure of locality can be established through an argument considerably more straightforward than Bell’s theorem.

Experimental refutation of a class of ψ -epistemic models

The quantum state $\ensuremath{\psi}$ is a mathematical object used to determine the outcome probabilities of measurements on physical systems. Its fundamental nature has been the subject of

The operational reality of the quantum state and of its reduction

It is argued that it is possible, surprisingly, to address ontological questions concerning quantum mechanics on the basis of only operational considerations, and it is shown that the operational perspective itself provides an intrinsic interpretation of QM.

The Essence of Entanglement

Entanglement, according to Erwin Schroedinger the essence of quantum mechanics, is at the heart of the Einstein-Podolsky-Rosen paradox and of the so called quantum-nonlocality - the fact that a local

Classicality without local discriminability: Decoupling entanglement and complementarity

It is demonstrated that the presence of entanglement is independent of the existence of incompatible measurements, and on the basis of the fact that every separable state of the theory is a statistical mixture of entangled states, a no-go conjecture is formulated for theexistence of a local-realistic ontological model.

Linear Superposition as a Core Theorem of Quantum Empiricism

Clarifying the nature of the quantum state |Ψ⟩ is at the root of the problems with insight into counter-intuitive quantum postulates. We provide a direct—and math-axiom free—empirical derivation of

No ψ-epistemic model can fully explain the indistinguishability of quantum states.

This work considers models that are defined for a single quantum system of dimension d, such that the independence condition does not arise, and derives an upper bound on the extent to which the probability distributions can overlap.

Ψ-epistemic Interpretations of Quantum Theory Have a Measurement Problem

It is demonstrated that all known epistemic ontological models of quantum theory in dimension $d\geq3, including those designed to evade the conclusion of the PBR theorem, cannot represent state update correctly.

Report of On the reality of the quantum state article

Quantum states are the fundamental elements in quantum theory. However, there are a lot of discussions and debates about what a quantum state actually represents. Is it corresponding directly to
...

References

SHOWING 1-10 OF 75 REFERENCES

The statistical interpretation of quantum mechanics

The Statistical Interpretation of quantum theory is formulated for the purpose of providing a sound interpretation using a minimum of assumptions. Several arguments are advanced in favor of

Foundations of quantum theory and quantum information applications

This thesis establishes a number of connections between foundational issues in quantum theory, and some quantum information applications. It starts with a review of quantum contextuality and

Information-tradeoff relations for finite-strength quantum measurements

In this paper we describe a way to quantify the folkloric notion that quantum measurements bring a disturbance to the system being measured. We consider two observers who initially assign identical

Quantum probabilities as Bayesian probabilities

In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper, we show that,

Quantum Mechanics as Quantum Information (and only a little more)

In this paper, I try once again to cause some good-natured trouble. The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion

Information Gain vs. State Disturbance in Quantum Theory

Several aspects of the information–disturbance principle are explored in an attempt to make it firmly quantitative and flesh out its significance for quantum theory as a whole.

Unknown Quantum States: The Quantum de Finetti Representation

We present an elementary proof of the quantum de Finetti representation theorem, a quantum analog of de Finetti’s classical theorem on exchangeable probability assignments. This contrasts with the

Universal state inversion and concurrence in arbitrary dimensions

Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the concurrence of the joint density operator.

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?

Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that one is led to conclude that the description of reality as given by a wave function is not complete.

Quantum nonlocality without entanglement

We exhibit an orthogonal set of product states of two three-state particles that nevertheless cannot be reliably distinguished by a pair of separated observers ignorant of which of the states has
...