What does the operator algebra of quantum statistics tell us about the objective causes of observable effects?
arXiv:2005.03822 · doi:10.3390/e22060638
Abstract
Quantum physics can only make statistical predictions about possible measurement outcomes, and these predictions originate from an operator algebra that is fundamentally different from the conventional definition of probability as a subjective lack of information regarding the physical reality of the system. In the present paper, I explore how the operator formalism accommodates the vast number of possible states and measurements by characterizing its essential function as a description of causality relations between initial conditions and subsequent observations. It is shown that any complete description of causality must involve non-positive statistical elements that cannot be associated with any directly observable effects. The necessity of non-positive elements is demonstrated by the uniquely defined mathematical description of ideal correlations which explains the physics of maximally entangled states, quantum teleportation and quantum cloning. The operator formalism thus modifies the concept of causality by providing a universally valid description of deterministic relations between initial states and subsequent observations that cannot be expressed in terms of directly observable measurement outcomes. Instead, the identifiable elements of causality are necessarily non-positive and hence unobservable. The validity of the operator algebra therefore indicates that a consistent explanation of the various uncertainty limited phenomena associated with physical objects is only possible if we learn to accept the fact that the elements of causality cannot be reconciled with a continuation of observable reality in the physical object.
arXiv comment13 pages, feature article for the special issue of Entropy on Quantum Probability, Statistics and Control. Improved explanation of the U_SWAP equivalence in Eq.(11) and added comments and references in the section on quasi-probabilities
References in corpus (24)
- Non-maximally entangled states: production, characterization and utilization
- Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement
- Operationally Invariant Information in Quantum Measurements
- Direct measurement of general quantum states using weak measurement
- Towards a Formulation of Quantum Theory as a Causally Neutral Theory of Bayesian Inference
- Proof of Heisenberg's error-disturbance relation
- Process tomography of ion trap quantum gates
- Full characterization of a three-photon GHZ state using quantum state tomography
- Fidelity and information in the quantum teleportation of continuous variables
- Uncertainty Relation Revisited from Quantum Estimation Theory
- Complex joint probabilities as expressions of determinism in quantum mechanics
- Certainty in Heisenberg's uncertainty principle: Revisiting definitions for estimation errors and disturbance
- On the role of complex phases in the quantum statistics of weak measurements
- An Information-Geometric Reconstruction of Quantum Theory, I: The Abstract Quantum Formalism
- How weak values emerge in joint measurements on cloned quantum systems
- Quantum mechanics emerges from information theory applied to causal horizons
- How to simulate a quantum computer using negative probabilities
- Uncertainty characteristics of generalized quantum measurements
- Reasonable conditions for joint probabilities of non-commuting observables
- Local measurement uncertainties impose a limit on non-local quantum correlations
- The role of system-meter entanglement in controlling the resolution and decoherence of quantum measurements
- Causality in quantum teleportation: information extraction and noise effects in entanglement distribution
- An investigation of the transfer dynamics of quantum teleportation by weak measurement statistics
- Quantum causality relations and the emergence of reality from coherent superpositions