A quantum prediction as a collection of epistemically restricted classical predictions
arXiv:2107.02728 · doi:10.22331/q-2022-02-21-659
Abstract
Spekkens has introduced an epistemically restricted classical theory of discrete systems, based on discrete phase space. The theory manifests a number of quantum-like properties but cannot fully imitate quantum theory because it is noncontextual. In this paper we show how, for a certain class of quantum systems, the quantum description of an experiment can be decomposed into classical descriptions that are epistemically restricted, though in a different sense than in Spekkens' work. For each aspect of the experiment -- the preparation, the transformations, and the measurement -- the epistemic restriction limits the form of the probability distribution an imagined classical observer may use. There are also global constraints that the whole collection of classical descriptions must satisfy. Each classical description generates its own prediction regarding the outcome of the experiment. One recovers the quantum prediction via a simple but highly nonclassical rule: the "nonrandom part" of the predicted quantum probabilities is obtained by summing the nonrandom parts of the classically predicted probabilities. By "nonrandom part" we mean the deviation from complete randomness, that is, from what one would expect upon measuring the fully mixed state.
arXiv comment28 pages, 3 figures; revised title, introduction, and Figure 2 in v2; minor corrections and changes to notation in v3; v4 is the version accepted in Quantum; appendices changed in v5
References in corpus (41)
- In defense of the epistemic view of quantum states: a toy theory
- Contextuality for preparations, transformations, and unsharp measurements
- Symplectic tomography as classical approach to quantum systems
- Discrete phase space based on finite fields
- Einstein, incompleteness, and the epistemic view of quantum states
- Negative Quasi-Probability as a Resource for Quantum Computation
- Ancilla-assisted quantum process tomography
- Hudson's Theorem for finite-dimensional quantum systems
- Quantum-Bayesian Coherence: The No-Nonsense Version
- Is the quantum state real? An extended review of -ontology theorems
- Tomography of Quantum Operations
- SIC-POVMs and the Extended Clifford Group
- An introduction to the tomographic picture of quantum mechanics
- Quantum from principles
- Quasi-quantization: classical statistical theories with an epistemic restriction
- Introduction to the book "Quantum Theory: Informational Foundations and Foils"
- The completeness of quantum theory for predicting measurement outcomes
- Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction
- Wigner function negativity and contextuality in quantum computation on rebits
- Optimizing quantum process tomography with unitary 2-designs
- Contextuality and Wigner function negativity in qubit quantum computation
- Choi's Proof and Quantum Process Tomography
- Unconditionally Secure Key Distribution In Higher Dimensions By Depolarization
- The Weyl representation on the torus
- Phase space simulation method for quantum computation with magic states on qubits
- Non-negative Wigner functions in prime dimensions
- Non-local Operations: Purification, storage, compression, tomography, and probabilistic implementation
- Wigner Functions and Separability for Finite Systems
- Quasiprobability representations of quantum mechanics with minimal negativity
- A hidden variable model for universal quantum computation with magic states on qubits
- Finite-dimensional Schwinger basis, deformed symmetries, Wigner function, and an algebraic approach to quantum phase
- A contextual extension of Spekkens' toy model
- Point Estimation of States of Finite Quantum Systems
- State-injection schemes of quantum computation in Spekkens' toy theory
- Spekkens' toy model in all dimensions and its relationship with stabilizer quantum mechanics
- Wigner distributions for finite state systems without redundant phase point operators
- Quantum mechanics on profinite groups and partial order
- A classical formulation of quantum theory?
- Stationary quantum Markov process for the Wigner function
- A Contextual -Epistemic Model of the -Qubit Stabilizer Formalism
- Transition probabilities and transition rates in discrete phase space