Contrary Inferences in Consistent Histories and a Set Selection Criterion

Comment on ``Consistent Sets Yield Contrary Inferences in Quantum Theory''

In a recent paper Kent has pointed out that in consistent histories quantum theory it is possible, given initial and final states, to construct two different consistent families of histories, in each of which there is a proposition that can be inferred with probability one, and such that the projectors representing these two propositions are mutually orthogonal. In this note we stress that, according to the rules of consistent history reasoning two such propositions are not contrary in the usual logical sense namely, that one can infer that if one is true then the other is false, and both coul…

Quantum Histories and Their Implications

Classical mechanics and standard Copenhagen quantum mechanics respect subspace implications. For example, if a particle is confined in a particular region $R$ of space, then in these theories we can deduce that it is confined in regions containing $R$. However, subspace implications are generally violated by versions of quantum theory that assign probabilities to histories, such as the consistent histories approach. I define here a new criterion, ordered consistency, which refines the criterion of consistency and has the property that inferences made by ordered consistent sets do not violate s…

On the selection of preferred consistent sets

The theme of this paper is the multiplicity of the consistent sets appearing in the consistent histories approach to quantum mechanics. We propose one criterion for choosing preferred families among them: that the physically realizable quasiclassical domain ought to be one corresponding to classical histories. We examine the way classical mechanics arises as a particular window and the important role played by the canonical group and the Hamiltonian. We finally discuss possible implications of our having a selection criterion generally and of our criterion in particular.

Weak Values and Consistent Histories in Quantum Theory

A relation is obtained between weak values of quantum observables and the consistency criterion for histories of quantum events. It is shown that ``strange'' weak values for projection operators (such as values less than zero) always correspond to inconsistent families of histories. It is argued that using the ABL rule to obtain probabilities for counterfactual measurements corresponding to those strange weak values gives inconsistent results. This problem is shown to be remedied by using the conditional weight, or pseudo-probability, obtained from the multiple-time application of Luders' Rule…

Incompatible Multiple Consistent Sets of Histories and Measures of Quantumness

In the consistent histories (CH) approach to quantum theory probabilities are assigned to histories subject to a consistency condition of negligible interference. The approach has the feature that a given physical situation admits multiple sets of consistent histories that cannot in general be united into a single consistent set, leading to a number of counter-intuitive or contrary properties if propositions from different consistent sets are combined indiscriminately. An alternative viewpoint is proposed in which multiple consistent sets are classified according to whether or not there exists…

Properties of Consistent Histories

We describe some properties of consistent sets of histories in the Gell-Mann--Hartle formalism, and give an example to illustrate that one cannot recover the standard predictions, retrodictions and inferences of quasiclassical physics using the criterion of consistency alone.

Measurements according to Consistent Histories

We critically evaluate the treatment of the notion of measurement in the Consistent Histories approach to quantum mechanics. We find such a treatment unsatisfactory because it relies, often implicitly, on elements external to those provided by the formalism. In particular, we note that, in order for the formalism to be informative when dealing with measurement scenarios, one needs to assume that the appropriate choice of framework is such that apparatuses are always in states of well defined pointer positions after measurements. The problem is that there is nothing in the formalism to justify …

Consistent Sets Yield Contrary Inferences in Quantum Theory

In the consistent histories formulation of quantum theory, the probabilistic predictions and retrodictions made from observed data depend on the choice of a consistent set. We show that this freedom allows the formalism to retrodict contrary propositions which correspond to orthogonal commuting projections and which each have probability one. We also show that the formalism makes contrary probability one predictions when applied to Gell-Mann and Hartle's generalised time-neutral quantum mechanics.

The Consistent Histories Formalism and the Measurement Problem

In response to a recent rebuttal of [1] presented in [2], we defend the claim that the Consistent Histories formulation of quantum mechanics does not solve the measurement problem. In order to do so, we argue that satisfactory solutions to the problem must not only not contain anthropomorphic terms (such as measurement or observer) at the fundamental level, but also that applications of the formalism to concrete situations (e.g., measurements) should not require any input not contained in the description of the situation at hand at the fundamental level. Our assertion is that the Consistent Hi…

Approximate Consistency and Prediction Algorithms in Quantum Mechanics

This dissertation investigates questions arising in the consistent histories formulation of the quantum mechanics of closed systems. Various criteria for approximate consistency are analysed. The connection between the Dowker-Halliwell criterion and sphere packing problems is shown and used to prove several new bounds on the violation of probability sum rules. The quantum Zeno effect is also analysed within the consistent histories formalism and used to demonstrate some of the difficulties involved in discussing approximate consistency. The complications associated with null histories and infi…

用量子钟认证非经典固有时历史

Certifying Nonclassical Proper-Time Histories with a Quantum Clock

提出通道认证框架，通过Choi秩分离判据和双支Ramsey协议，证明量子钟可认证超出经典混合的固有时历史。

Quantum Histories

There are good motivations for considering some type of quantum histories formalism. Several possible formalisms are known, defined by different definitions of event and by different selection criteria for sets of histories. These formalisms have a natural interpretation, according to which nature somehow chooses one set of histories from among those allowed, and then randomly chooses to realise one history from that set; other interpretations are possible, but their scientific implications are essentially the same. The selection criteria proposed to date are reasonably natural, and certainly …

Information-entropy and the space of decoherence functions in generalised quantum theory

In standard quantum theory, the ideas of information-entropy and of pure states are closely linked. States are represented by density matrices $ρ$ on a Hilbert space and the information-entropy $-tr(ρ\logρ)$ is minimised on pure states (pure states are the vertices of the boundary of the convex set of states). The space of decoherence functions in the consistent histories approach to generalised quantum theory is also a convex set. However, by showing that every decoherence function can be written as a convex combination of two other decoherence functions we demonstrate that there are no `pure…