Contexts in Quantum Measurement Theory

Howard M. Wiseman, Gerard J Milburn

Richard Healey

I take a pragmatist perspective on quantum theory. This is not a view of the world described by quantum theory. In this view quantum theory itself does not describe the physical world, nor our observatons, experiences or opinions of it. Instead, the theory offers reliable advice on when to expect an event of one kind or another, and on how strongly to expect each possible outcome of that event. The actual outcome is a perspectival fact: a fact relative to a physical context of assessment. Measurement outcomes and quantum states are both perspectival. By noticing that each must be relativized to an appropriate physical context one can resolve the measurement problem and the problem of nonlocal action. But if the outcome of a quantum measurement is not an absolute fact, then why shoud the statistics of such outcomes give us any objective reason to accept quantum theory? One can describe extensions of the scenario of Wigner's friend in which a statement expressing the outcome of a quantum measurement would be true relative to one such context but not relative to another. However, physical conditions in our world prevent us from realizing such scenarios. Since the outcome of every actual quantum measurement is certified at what is essentially a single context of assessment, the outcome relative to that context is an objective fact in the only sense that matters for science. We should accept quantum theory because the statistics these outcomes display are just those it leads us to expect.

Jerome R. Busemeyer, Zheng Wang

A general theory of measurement context effects, called Hilbert space multidimensional (HSM) theory, is presented. A measurement context refers to a subset of psychological variables that an individual evaluates on a particular occasion. Different contexts are formed by evaluating different but possibly overlapping subsets of variables. Context effects occur when the judgments across contexts cannot be derived from a single joint probability distribution over the complete set of values of the observed variables. HSM theory provides a way to model these context effects by using quantum probability theory, which represents all the variables within a low dimensional vector space. HSM models produce parameter estimates that provide a simple and informative interpretation of the complex collection of judgments across contexts. Comparisons of HSM model fits with Bayesian network model fits are reported for a new large experiment, demonstrating the viability of this new model. We conclude that the theory is broadly applicable to measurement context effects found in the social and behavioral sciences. (PsycINFO Database Record

L. E. Ballentine

Michael L. G. Redhead

Petr Lisoněk, Piotr Badziąg, José R. Portillo +1 more

The Kochen-Specker (KS) theorem is a central result in quantum theory and has applications in quantum information. Its proof requires several yes-no tests that can be grouped in contexts or subsets of jointly measurable tests. Arguably, the best measure of simplicity of a KS set is the number of contexts. The smaller this number is, the smaller the number of experiments needed to reveal the conflict between quantum theory and noncontextual theories and to get a quantum vs classical outperformance. The original KS set had 132 contexts. Here we introduce a KS set with seven contexts and prove that this is the simplest KS set that admits a symmetric parity proof.