Consistent Histories Research Articles

Decoherent histories approach to the cosmological measure problem

The method of decoherent histories allows probabilities to be assigned to sequences of quantum events in systems, such as the universe as a whole, where there is no external observer to make measurements. This paper applies the method of decoherent histories to address cosmological questions. Using a series of simple examples, beginning with the harmonic oscillator, we show that systems in a stationary state such as an energy eigenstate or thermal state can exhibit decoherent histories with non-trivial dynamics. We then examine decoherent histories in a universe that undergoes eternal inflation. Decoherent histories that assign probabilities to sequences of events in the vicinity of a timelike geodesic supply a natural cosmological measure. Under reasonable conditions, such sequences of events do not suffer from the presence of unlikely statistical fluctuations that mimic reality.

Consistent Histories and Many Worlds

This paper discusses the fundamental assumptions and background of the consistent histories (CH) approach to quantum mechanics. The focus of the paper is on the concept of frameworks. It is proposed that frameworks should be interpreted objectively as observer-independent realities. Two further options are considered: a hidden-variables variant of the CH approach, and a many-worlds version, which considers each individual history belonging to a given family as describing a separate world. The latter interpretation is subsequently compared and contrasted with the standard many-worlds interpretation. Finally, the solution to the measurement problem offered by the many-worlds variant of CH is analyzed and amended.

Branch-counting in the Everett interpretation of quantum mechanics

A defence is offered of a version of the branch-counting rule in the Everett interpretation (otherwise known as many worlds interpretation) of quantum mechanics that both depends on the state and is continuous in the norm topology on Hilbert space. The well-known branch-counting rule, for realistic models of measurements, in which branches are defined by decoherence theory, fails this test. The new rule hinges on the use of decoherence theory in defining branching structure, and specifically decoherent histories theory. On this basis ratios of branch numbers are defined, free of any convention. They agree with the Born rule and deliver a notion of objective probability similar to naive frequentism, save that the frequencies of outcomes are not confined to a single world at different times, but spread over worlds at a single time. Nor is it ad hoc : it is recognizably akin to the combinatorial approach to thermodynamic probability, as introduced by Boltzmann in 1879. It is identical to the procedure followed by Planck, Bose, Einstein and Dirac in defining the equilibrium distribution of the Bose–Einstein gas. It also connects in a simple way with the decision-theory approach to quantum probability.

Discrete Hilbert space, the Born Rule, and quantum gravity

Quantum gravitational effects suggest a minimal length, or spacetime interval, of order of the Planck length. This in turn suggests that Hilbert space itself may be discrete rather than continuous. One implication is that quantum states with norm below some very small threshold do not exist. The exclusion of what Everett referred to as maverick branches is necessary for the emergence of the Born Rule in no collapse quantum mechanics. We discuss this in the context of quantum gravity, showing that discrete models (such as simplicial or lattice quantum gravity) indeed suggest a discrete Hilbert space with minimum norm. These considerations are related to the ultimate level of fine-graining found in decoherent histories (of spacetime geometry plus matter fields) produced by quantum gravity.

Comment on “Particle path through a nested Mach-Zehnder interferometer”

In a recent paper, arXiv:1604.04596, Griffiths questioned - based on an informative consistent-histories (CH) argument - the counterfactuality, for one of the bit choices, of Salih et al.'s protocol for communicating without sending physical particles, Phys. Rev. Lett. 110, 170502 (2013). Here, we first show that for the Mach-Zehnder version used to explain our protocol, no family of consistent histories exists where any history has the photon travelling through the communication channel, thus rendering the question of whether the photon was in the communication channel meaningless from a CH viewpoint. We then show that for the actual Michelson-type protocol, there are consistent-histories families that include histories where the photon travels through the communication channel. We show that the probability of finding the photon in the communication channel is zero - thus proving complete counterfactuality.

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 any unifying probability for combinations of incompatible sets which replicates the consistent histories result when restricted to a single consistent set. A number of examples are exhibited in which this classification can be made, in some cases with the assistance of the Bell, CHSH or Leggett-Garg inequalities together with Fine's theorem. When a unifying probability exists logical deductions in different consistent sets can in fact be combined, an extension of the "single framework rule". It is argued that this classification coincides with intuitive notions of the boundary between classical and quantum regimes and in particular, the absence of a unifying probability for certain combinations of consistent sets is regarded as a measure of the "quantumness" of the system. The proposed approach and results are closely related to recent work on the classification of quasi-probabilities and this connection is discussed.

Comment on “Particle path through a nested Mach-Zehnder interferometer”

Griffiths [Phys. Rev. A 94, 032115 (2016)] analyzed, in the framework of a consistent histories interpretation, the controversy regarding the approach to the past of a quantum particle introduced by Vaidman [Phys. Rev. A 87, 052104 (2013)]. I argue that Griffith's criticism of my approach using an analysis of experiments with weak probes is unfounded.

Decoherent histories and measurement of temporal correlation functions for Leggett-Garg inequalities

We consider two protocols for the measurement of the temporal correlation functions of a dichotomic variable $Q$ appearing in Leggett-Garg-type inequalities. The protocols measure solely whether $Q$ has the same or a different sign at the end of a given time interval, thereby measuring no more than is required for determination of the correlation function. They are inspired, in part, by a decoherent histories analysis of the two-time histories of $Q$, which yields a number of useful insights, although the protocols are ultimately expressed in macrorealistic form independent of quantum theory. The first type involves an ancilla coupled to the system with two sequential controlled-not (cnot) gates, and the two-time histories of the system (whose probabilities yield the correlation function) are determined in a single final time measurement of the ancilla. It is noninvasive for special choices of initial system states and partially invasive for more general choices. Modified Leggett-Garg-type inequalities which accommodate the partial invasiveness are discussed. The quantum picture of the protocol shows that for certain choices of the primary system initial state, the final state is unaffected by the two cnot gate interactions, hence the protocol is undetectable with respect to final system-state measurements, although it is still invasive at intermediate times. This invasiveness can be reduced with different choices of ancilla states and the protocol is then similar in flavor to a weak measurement. The second type of protocol is based on the fact that the behavior of $Q$ over a time interval can be determined from knowledge of the dynamics together with a measurement of certain initial (or final) data. Its quantum version corresponds to the known fact that when sets of histories are decoherent, their probabilities may be expressed in terms of a record projector, hence the two-time histories in which $Q$ has the same or a different sign can be determined by a single projective measurement. The resulting protocol resembles the decay-type protocol proposed by Huelga and collaborators (which is noninvasive but requires a stationarity assumption).

The consistent histories approach to loop quantum cosmology

We review the application of the consistent (or decoherent) histories formulation of quantum theory to canonical loop quantum cosmology. Conventional quantum theory relies crucially on “measurements” to convert unrealized quantum potentialities into physical outcomes that can be assigned probabilities. In the early universe and other physical contexts in which there are no observers or measuring apparatus (or indeed, in any closed quantum system), what criteria determine which alternative outcomes may be realized and what their probabilities are? In the consistent histories formulation it is the vanishing of interference between the branch wave functions describing alternative histories — as determined by the system’s decoherence functional — that determines which alternatives may be assigned probabilities. We describe the consistent histories formulation and how it may be applied to canonical loop quantum cosmology, describing in detail the application to homogeneous and isotropic cosmological models with scalar matter. We show how the theory may be used to make definite physical predictions in the absence of “observers”. As an application, we demonstrate how the theory predicts that loop quantum models “bounce” from large volume to large volume, while conventional “Wheeler–DeWitt”-quantized universes are invariably singular. We also briefly indicate the relation to other work.

Global coherence of quantum evolutions based on decoherent histories: Theory and application to photosynthetic quantum energy transport

Assessing the role of interference in natural and artificial quantum dyanamical processes is a crucial task in quantum information theory. To this aim, an appopriate formalism is provided by the decoherent histories framework. While this approach has been deeply explored from different theoretical perspectives, it still lacks of a comprehensive set of tools able to concisely quantify the amount of coherence developed by a given dynamics. In this paper we introduce and test different measures of the (average) coherence present in dissipative (Markovian) quantum evolutions, at various time scales and for different levels of environmentally induced decoherence. In order to show the effectiveness of the introduced tools, we apply them to a paradigmatic quantum process where the role of coherence is being hotly debated: exciton transport in photosynthetic complexes. To spot out the essential features that may determine the performance of the transport we focus on a relevant trimeric subunit of the FMO complex and we use a simplified (Haken-Strobl) model for the system-bath interaction. Our analysis illustrates how the high efficiency of environmentally assisted transport can be traced back to a quantum recoil avoiding effect on the exciton dynamics, that preserves and sustains the benefits of the initial fast quantum delocalization of the exciton over the network. Indeed, for intermediate levels of decoherence, the bath is seen to selectively kill the negative interference between different exciton pathways, while retaining the initial positive one. The concepts and tools here developed show how the decoherent histories approach can be used to quantify the relation between coherence and efficiency in quantum dynamical processes.

The universal path integral

Path integrals calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration. This paper defines a universal path integral, which sums over all computable structures. This path integral contains as sub-integrals all possible computable path integrals, including those of field theory, the standard model of elementary particles, discrete models of quantum gravity, string theory, etc. The universal path integral possesses a well-defined measure that guarantees its finiteness. The probabilities for events corresponding to sub-integrals can be calculated using the method of decoherent histories. The universal path integral supports a quantum theory of the universe in which the world that we see around us arises out of the interference between all computable structures.

Consistent quantum measurements

In response to recent criticisms by Okon and Sudarsky, various aspects of the consistent histories (CH) resolution of the quantum measurement problem(s) are discussed using a simple Stern‐Gerlach device, and compared with the alternative approaches to the measurement problem provided by spontaneous localization (GRW), Bohmian mechanics, many worlds, and standard (textbook) quantum mechanics. Among these CH is unique in solving the second measurement problem: inferring from the measurement outcome a property of the measured system at a time before the measurement took place, as is done routinely by experimental physicists. The main respect in which CH differs from other quantum interpretations is in allowing multiple stochastic descriptions of a given measurement situation, from which one (or more) can be selected on the basis of its utility. This requires abandoning a principle (termed unicity), central to classical physics, that at any instant of time there is only a single correct description of the world.

Contrary Inferences in Consistent Histories and a Set Selection Criterion

The best developed formulation of closed system quantum theory that handles multiple-time statements, is the consistent (or decoherent) histories approach. The most important weaknesses of the approach is that it gives rise to many different consistent sets, and it has been argued that a complete interpretation should be accompanied with a natural mechanism leading to a (possibly) unique preferred consistent set. The existence of multiple consistent sets becomes more problematic because it allows the existence of contrary inferences (Kent 1997). We analyse the conceptual difficulties that arise from the existence of multiple consistent sets and provide a suggestion for a natural set selection criterion. This criterion does not lead to a unique physical consistent set, however it evades the existence of consistent sets with contrary inferences. The criterion is based on the concept of preclusion and the requirement that probability one propositions and their inferences should be noncontextual. The allowed consistent sets turn-out to be compatible with coevents which are the ontology of an alternative, histories based, formulation.

The New Quantum Logic

It is shown how all the major conceptual difficulties of standard (textbook) quantum mechanics, including the two measurement problems and the (supposed) nonlocality that conflicts with special relativity, are resolved in the consistent or decoherent histories interpretation of quantum mechanics by using a modified form of quantum logic to discuss quantum properties (subspaces of the quantum Hilbert space), and treating quantum time development as a stochastic process. The histories approach in turn gives rise to some conceptual difficulties, in particular the correct choice of a framework (probabilistic sample space) or family of histories, and these are discussed. The central issue is that the principle of unicity, the idea that there is a unique single true description of the world, is incompatible with our current understanding of quantum mechanics.

A quantum measure of the multiverse

It has been recently suggested that probabilities of different events in the multiverse are given by the frequencies at which these events are encountered along the worldline of a geodesic observer (the ``watcher''). Here I discuss an extension of this probability measure to quantum theory. The proposed extension is gauge-invariant, as is the classical version of this measure. Observations of the watcher are described by a reduced density matrix, and the frequencies of events can be found using the decoherent histories formalism of Quantum Mechanics (adapted to open systems). The quantum watcher measure makes predictions in agreement with the standard Born rule of QM.

On the Consistency of the Consistent Histories Approach to Quantum Mechanics

The Consistent Histories (CH) formalism aims at a quantum mechanical framework which could be applied even to the universe as a whole. CH stresses the importance of histories for quantum mechanics, as opposed to measurements, and maintains that a satisfactory formulation of quantum mechanics allows one to assign probabilities to alternative histories of a quantum system. It further proposes that each realm, that is, each set of histories to which probabilities can be assigned, provides a valid quantum-mechanical account, but that different realms can be mutually incompatible. Finally, some of its proponents offer an “evolutionary” explanation of our existence in the universe and of our preference for quasiclassical descriptions of nature. The present work questions the validity of claims offered by CH proponents asserting that it solves many interpretational problems in quantum mechanics. In particular, we point out that the interpretation of the framework leaves vague two crucial points, namely, whether realms are fixed or chosen and the link between measurements and histories. Our claim is that by doing so, CH overlooks the main interpretational problems of quantum mechanics. Furthermore, we challenge the evolutionary explanation offered and we critically examine the proposed notion of a realm-dependent reality.

Epistemic restrictions in Hilbert space quantum mechanics

A resolution of the quantum measurement problem(s) using the consistent histories interpretation yields in a rather natural way a restriction on what an observer can know about a quantum system, one that is also consistent with some results in quantum information theory. This analysis provides a quantum mechanical understanding of some recent work that shows that certain kinds of quantum behavior are exhibited by a fully classical model if by hypothesis an observer's knowledge of its state is appropriately limited.

Is the consistent histories approach to quantum mechanics consistent?

The Consistent Histories (CH) formalism attempts to construct a quantum framework which can be used without the need to introduce observers external to the studied system. The prime motivation in mind is the application of the formalism to the universe as a whole. In order to achieve this, CH maintains that a formulation of quantum mechanics should allow for the assignment of probabilities to alternative histories of a system. Therefore, it provides an observer-independent criterion to decide which sets of histories can be given probabilities and states rules to determine them. The framework establishes that each realm, that is, each set of histories to which probabilities can be assigned, provides a valid quantum-mechanical account of a system. Furthermore, the version of CH first presented in [1, 2] proposes an "evolutionary" explanation of our existence in the universe and of our preference for quasiclassical descriptions of nature. The present work critically evaluates claims to the effect that the formalism offered in [1, 2] solves many interpretational problems in quantum mechanics. In particular, it is pointed out that the interpretation of the proposed framework leaves vague two crucial points, namely, whether realms are fixed or chosen and the link between measurements and histories. The claim of this work is that by doing so, CH overlooks the main interpretational problems of quantum mechanics. Furthermore, we challenge the evolutionary explanation offered and we critically examine the proposed notion of a realm-dependent reality.

Amplitudes for spacetime regions and the quantum Zeno effect: pitfalls of standard path integral constructions

Path integrals appear to offer natural and intuitively appealing methods for defining quantum-mechanical amplitudes for questions involving spacetime regions. For example, the amplitude for entering a spatial region during a given time interval is typically defined by summing over all paths between given initial and final points but restricting them to pass through the region at any time. We argue that there is, however, under very general conditions, a significant complication in such constructions. This is the fact that the concrete implementation of the restrictions on paths over an interval of time corresponds, in an operator language, to sharp monitoring at every moment of time in the given time interval. Such processes suffer from the quantum Zeno effect – the continual monitoring of a quantum system in a Hilbert subspace prevents its state from leaving that subspace. As a consequence, path integral amplitudes defined in this seemingly obvious way have physically and intuitively unreasonable properties and in particular, no sensible classical limit. In this paper we describe this frequently-occurring but little-appreciated phenomenon in some detail, showing clearly the connection with the quantum Zeno effect. We then show that it may be avoided by implementing the restriction on paths in the path integral in a "softer" way. The resulting amplitudes then involve a new coarse graining parameter, which may be taken to be a timescale ϵ, describing the softening of the restrictions on the paths. We argue that the complications arising from the Zeno effect are then negligible as long as ϵ >> 1/E, where E is the energy scale of the incoming state. Our criticisms of path integral constructions largely apply to approaches to quantum theory such as the decoherent histories approach or quantum measure theory, which do not specifically involve measurements. We address some criticisms of our approach by Sokolovksi, concerning the relevance of our results to measurement-based models.

A consistent quantum ontology

The (consistent or decoherent) histories interpretation provides a consistent realistic ontology for quantum mechanics, based on two main ideas. First, a logic (system of reasoning) is employed which is compatible with the Hilbert-space structure of quantum mechanics as understood by von Neumann: quantum properties and their negations correspond to subspaces and their orthogonal complements. It employs a special (single framework) syntactical rule to construct meaningful quantum expressions, quite different from the quantum logic of Birkhoff and von Neumann. Second, quantum time development is treated as an inherently stochastic process under all circumstances, not just when measurements take place. The time-dependent Schrödinger equation provides probabilities, not a deterministic time development of the world.The resulting interpretive framework has no measurement problem and can be used to analyze in quantum terms what is going on before, after, and during physical preparation and measurement processes. In particular, appropriate measurements can reveal quantum properties possessed by the measured system before the measurement took place. There are no mysterious superluminal influences: quantum systems satisfy an appropriate form of Einstein locality.This ontology provides a satisfactory foundation for quantum information theory, since it supplies definite answers as to what the information is about. The formalism of classical (Shannon) information theory applies without change in suitable quantum contexts, and this suggests the way in which quantum information theory extends beyond its classical counterpart.