I briefly review the ''decohering histories'' or ''consistent histories'' formulation of quantum theory, due to Griffiths, Omnes, and Gell-Mann and Hartle (and the subject of my graduate work with George Sudarshan). I also sift through the many meanings that have been attached to decohering histories, with an emphasis on the most basic one: Decoherence of appropriate histories is needed to establish that quantum mechanics has the correct classical limit. Then I will describe efforts to find physical mechanisms that do this. Since most work has focused on density matrix versions of decoherence, I'll consider the relation between the two formulations, which historically has not been straightforward. Finally, I'll suggest a line of research that would use recent results by Sudarshan to illuminate this aspect of the classical limit of quantum theory.
An introduction is given to an algebraic formulation and generalisation of the consistent histories approach to quantum theory. The main technical tool in this theory is an orthoalgebra of history propositions that serves as a generalised temporal analogue of the lattice of propositions of standard quantum logic. Particular emphasis is placed on those cases in which the history propositions can be represented by projection operators in a Hilbert space, and on the associated concept of a `history group'.
We continue our efforts to understand, within the framework of the quantum mechanics of the universe as a whole, the quasiclassical realm of familiar experience as a feature emergent from the Hamiltonian of the elementary particles and the initial condition of the universe. Quantum mechanics assigns probabilities to exhaustive sets of alternative decoherent histories of the universe. We introduce and define the notion of strong decoherence. We replace the notion of maximal sets of alternative decohering histories by defining the more useful concept of "full" sets of alternative strongly decohe…
The geometry of decoherence in generalized "consistent histories" quantum theory is explored, revealing properties of the theory that are independent of any particular application of it. It is shown how the decoherence functional of a closed quantum system may be regarded as an Hermitian form on the space of linear operators on the Hilbert space of the system. This identification makes manifest a number of structural properties of decoherence functionals. For example, a bound on the maximum number of histories in a consistent set is determined. When the decoherence functional is positive -- as…
We study propagation of the decohering influence caused by a local measurement performed on a distributed quantum system. As an example, the gas of bosons forming a Bose-Einstein condensate is considered. We demonstrate that the local decohering perturbation exerted on the measured region propagates over the system in the form of a decoherence wave, whose dynamics is governed by elementary excitations of the system. We argue that the post-measurement evolution of the system (determined by elementary excitations) is of importance for transfer of decoherence, while the initial collapse of the wa…
We calculate the geometric phase of a spin-1/2 system driven by a one and two mode quantum field subject to decoherence. Using the quantum jump approach, we show that the corrections to the phase in the no-jump trajectory are different when considering an adiabatic and non-adiabatic evolution. We discuss the implications of our results from both the fundamental as well as quantum computational perspective.
The decoherent histories approach is a natural medium in which to address problems in quantum theory which involve time in a non-trivial way. This article reviews the various attempts and difficulties involved in using the decoherent histories approach to calculate the probability for crossing the surface $x=0$ during a finite interval of time. The commonly encountered difficulties in assigning crossing times arise here as difficulties in satisfying the consistency (no-interference) condition. This can be overcome by introducing an environment to produce decoherence, and probabilities exhibiti…
In this paper we introduce a diagnostic for measuring the quantum-classical difference for open quantum systems, which is the normalized size of the quantum terms in the Master equation for Wigner function evolution. For a driven Duffing oscillator, this measure shows remarkably precise scaling over long time-scales with the parameter $ζ_0=\hbar^2/D$. We also see that, independent of $ζ_0$ the dynamics follows a similar pattern. For small $ζ_0$ all of our curves collapses to essentially a single curve when scaled by the maximum value of the quantum-classical difference. In both limits of large…
Tensor network quantum machine learning (QML) models are promising applications on near-term quantum hardware. While decoherence of qubits is expected to decrease the performance of QML models, it is unclear to what extent the diminished performance can be compensated for by adding ancillas to the models and accordingly increasing the virtual bond dimension of the models. We investigate here the competition between decoherence and adding ancillas on the classification performance of two models, with an analysis of the decoherence effect from the perspective of regression. We present numerical …
We investigate the entanglement dynamics of two interacting qubits in a common vacuum environment. The inevitable environment interaction leads to entanglement sudden death (ESD) in a two qubit entangled state system. The entanglement dynamics can be modified by the use of local unitary operations (quantum gates), applied on the system during its evolution. We show that these operations not only delays or avoids the ESD but also advances the entanglement revival with high concurrence value depending on the time of operation. We have analytically found out different time windows for switching w…
Adaptive data collection and analysis, where data are being fed back to update the measurement settings, can greatly increase speed, precision, and reliability of the characterization of quantum systems. However, decoherence tends to make adaptive characterization difficult. As an example, we consider two coupled discrete quantum systems. When one of the systems can be controlled and measured, the standard method to characterize another, with an unknown frequency $ω_{\rm r}$, is swap spectroscopy. Here, adapting measurements can provide estimates whose error decreases exponentially in the numb…
"How much information about a system $\mathcal{S}$ can one extract from a fragment $\mathcal{F}$ of the environment $\mathcal{E}$ that decohered it?" is the central question of Quantum Darwinism. To date, most answers relied on the quantum mutual information of $\mathcal{SF}$, or on the Holevo bound on the channel capacity of $\mathcal{F}$ to communicate the classical information encoded in $\mathcal{S}$. These are reasonable upper bounds on what is really needed but much harder to calculate -- the accessible information in the fragment $\mathcal{F}$ about $\mathcal{S}$. We consider a model ba…
The finite time end of entanglement between two decohering qubits can be modified by local, unitary actions performed during the decohering process. Depending on the time when such action is taken, the end can be speeded up or slowed down, or even averted all together. This phenomenon offers practical applications for the stabilization of entangled quantum states. Details concerning hastening or delaying the finite time end of entanglement are presented for two qubits which decay spontaneously into statistically independent reservoirs.
Certain physical aspects of quantum error correction are discussed for a quantum computer (n-qubit register) in contact with a decohering environment. Under rather plausible assumptions upon the form of the computer-environment interaction, the efficiency of a general correcting procedure is evaluated as a function of the spontaneous-decay duration and the rank of errors covered by the procedure. It is proved that the probability of errors can be made arbitrarily small by enhancing the correction method, provided the decohering interaction is represented by a bounded operator.
As a model of decohering environment, we show that quantum chaotic system behave equivalently as many-body system. An approximate formula for the time evolution of the reduced density matrix of a system interacting with a quantum chaotic environment is derived. This theoretical formulation is substantiated by the numerical study of decoherence of two qubits interacting with a quantum chaotic environment modeled by a chaotic kicked top. Like the many-body model of environment, the quantum chaotic system is efficient decoherer, and it can generate entanglement between the two qubits which have n…
Current quantum orthodoxy claims that the statistical collapse of the wave-function arises from the interaction of the measuring instrument with its environment through the phenomenon known as environment induced decoherence. Here it is shown that there exists a measurement scheme that is exactly decohering without the aid of an environment. The scheme relies on the assumption that the meter is decomposable into probe and pointer, with the probe taken to be inaccessible for observation. Under the assumption that the probe and the pointer initial states are momentum limited, it is shown that co…
We prove that, when two local quantum channels are used paralleled, the quantum-correlating power (QCP) of the composed channel is no less than the sum of QCP of the two channels. For local channels with zero QCP, the super-activation of QCP is a fairly common effect, and proved to exist except for the trivial case where both of the channels are completely decohering channels or unitary operators. For general quantum channels, we show that the (not-so-common) additivity of QCP can be observed for the situation where a measuring-and-preparing channel is used together with a completely decoherin…
In this work we study temporal quantum correlations, quantified by Leggett-Garg (LG) and LG-type inequalities, in the $B$ and $K$ meson systems. We use the tools of open quantum systems to incorporate the effect of decoherence which is quantified by a single phenomenological parameter. The effect of $CP$ violation is also included in our analysis. We find that the LG inequality is violated for both $B$ and $K$ meson systems, the violation being most prominent in the case of $K$ mesons and least for $B_s$ system. Since the systems with no coherence do not violate LGI, incorporating \textit{deco…
We show that a local channel cannot create quantum discord (QD) for zero QD states of size $d\geq3$ if and only if either it is a completely decohering channel or it is a nontrivial isotropic channel. For the qubit case this propertiy is additionally characteristic to the completely decohering channel or the commutativity-preserving unital channel. In particular, the exact forms of the completely decohering channel and the commutativity-preserving unital qubit channel are proposed. Consequently, our results confirm and improve the conjecture proposed by X. Hu et al. for the case of $d\geq3$ an…
Multiparticle entanglement leads to richer correlations than two-particle entanglement and gives rise to striking contradictions with local realism, inequivalent classes of entanglement, and applications such as one-way or topological quantum computing. When exposed to decohering or dissipative environments, multiparticle entanglement yields subtle dynamical features and access to new classes of states and applications. Here, using a string of trapped ions, we experimentally characterize the dynamics of entanglement of a multiparticle state under the influence of decoherence. By embedding an e…
We generalize the scattering theory of quantum shot noise to include the full spin-density matrix of electrons injected from a spin-filtering or ferromagnetic electrode into a quantum-coherent nanostructure governed by various spin-dependent interactions. This formalism yields the spin-resolved shot noise power for different experimental measurement setups--with ferromagnetic source and ferromagnetic or normal drain electrodes--whose evaluation for the diffusive multichannel quantum wires with the Rashba (SO) spin-orbit coupling shows how spin decoherence and dephasing lead to substantial enha…
In the consistent histories formulation of quantum theory it was shown that it is possible to retrodict contrary properties. We show that this problem do not appear in our formalism of generalized contexts for quantum histories.
Suppressing undesired nonunitary effects is a major challenge in quantum computation and quantum control. In this work, by considering the adiabatic dynamics in presence of a surrounding environment, we theoretically and experimentally analyze the robustness of adiabaticity in open quantum systems. More specifically, by considering a decohering scenario, we exploit the validity conditions of the adiabatic approximation as well as its sensitiveness to the resonance situation, which typically harm adiabaticity in closed systems. As an illustration, we implement an oscillating Landau-Zener Hamilt…
A brief introduction to the decoherent histories approach to quantum theory is given, with emphasis on its role in the discussion of the emergence of classicality from quantum theory. Some applications are discussed, including quantum-classical couplings, the relationship of the histories approach to quantum state diffusion, and the application of the histories approach to situations involving time in a non-trivial way.
In this article we reconstruct the Frauchiger and Renner argument, taking into account that the assertions of the argument are made at different times. To do this, we use a formalism of quantum histories, namely the Theory of Consistent Histories. We show that the supposedly contradictory conclusion of the argument requires computing probabilities in a family of histories that does not satisfy the consistency condition, i.e., an invalid family of histories for the theory.
A central principle of consistent histories quantum theory, the requirement that quantum descriptions be based upon a single framework (or family), is employed to show that there is no conflict between consistent histories and a no-hidden-variables theorem of Bell, and Kochen and Specker, contrary to a recent claim by Bassi and Ghirardi. The argument makes use of ``truth functionals'' defined on a Boolean algebra of classical or quantum properties.
The quantum random walk has drawn special interests because its remarkable features to the classical counterpart could lead to new quantum algorithms. In this paper, we propose a feasible scheme to implement quantum random walks on a line using only linear optics elements. With current single-photon interference technology, the steps that could be experimentally implemented can be extended to very large numbers. We also show that, by decohering the quantum states, our scheme for quantum random walk tends to be classical.
A formulation of the consistent histories approach to quantum mechanics in terms of generalized observables (POV measures) and effect operators is provided. The usual notion of `history' is generalized to the notion of `effect history'. The space of effect histories carries the structure of a D-poset. Recent results of J.D. Maitland Wright imply that every decoherence functional defined for ordinary histories can be uniquely extended to a bi-additive decoherence functional on the space of effect histories. Omnes' logical interpretation is generalized to the present context. The result of this …
Quantum entanglement is a key resource, which grants quantum systems the ability to accomplish tasks that are classically impossible. Here, we apply Feynman's sum-over-histories formalism to interacting bipartite quantum systems and introduce entanglement measures for bipartite quantum histories. Based on the Schmidt decomposition of the matrix comprised of the Feynman propagator complex coefficients, we prove that bipartite quantum histories are entangled if and only if the Schmidt rank of this matrix is larger than 1. The proposed approach highlights the utility of using a separable basis fo…
In this work a generalization of the consistent histories approach to quantum mechanics is presented. We first critically review the consistent histories approach to nonrelativistic quantum mechanics in a mathematically rigorous way and give some general comments about it. We investigate to what extent the consistent histories scheme is compatible with the results of the operational formulation of quantum mechanics. According to the operational approach nonrelativistic quantum mechanics is most generally formulated in terms of effects, states and operations. We formulate a generalized consiste…
We introduce a new notion of consistency for 2-events quantum histories, based on the concept of mirror projection. Contrary to all notions of consistency so far introduced, our consistency, named self-decoherence, is an individual property, i.e., it can be attributed to every single sample of the physical system. Furthermore, self-decoherence forbids contrary inferences.
Modal interpretations of quantum mechanics assign definite properties to physical systems and specify single-time joint probabilities of these properties. We show that a natural extension, applying to properties at several times, can be given if a decoherence condition is satisfied. This extension defines "consistent histories" of modal properties. We suggest a new form of the modal scheme, that offers prospects of a more general applicability of the histories concept. Finally, we discuss a possible way of applying these ideas to relativistic quantum field theory.
Since Deutsch (1985), quantum computers have been modeled exclusively in the language of state vectors and the Schroedinger equation. We present a complementary view of quantum circuits inspired by the path integral formalism of quantum mechanics, and examine its application to some simple textbook problems.
We sketch a quantum mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the quasiclassical domain of familiar experience and for characterizing the process of measurement. Predictions in quantum mechanics are made from probabilities for sets of alternative histories. Probabilities can be assigned only to sets of histories that approximately decohere. Decoherence is defined and the mechanism of decoherence is reviewed. Decoherence requires a sufficiently coarse-grained description of alternative …
A simplified Bogoliubov transform reduces a fully-interacting many-fermion spin-1/2 system-plus-environment to a more tractable many-to-one variant. The transform additionally yields exact solutions for bosonic multi-particle interactions sans the approximation introduced by using discrete time steps to deal with quantum parallelism. The decohering effect of relatively general finite environments is therewith modeled and compared to the decohering effect of an infinite environmental "bath." The anti-symmetric singlet state formed by two maximally-entangled two-state particles is shown to be in…
We elaborate on the distinction between geometric and dynamical phase in quantum theory and show that the former is intrinsically linked to the quantum mechanical probabilistic structure. In particular, we examine the appearance of the Berry phase in the consistent histories scheme and establish that it is the basic building block of the decoherence functional. These results are consequences of the novel temporal structure of histories-based theories.
In the consistent histories formalism one specifies a family of histories as an exhaustive set of pairwise exclusive descriptions of the dynamics of a quantum system. We define branching families of histories, which strike a middle ground between the two available mathematically precise definitions of families of histories, viz., product families and Isham's history projector operator formalism. The former are too narrow for applications, and the latter's generality comes at a certain cost, barring an intuitive reading of the ``histories''. Branching families retain the intuitiveness of produc…
The relationship between quantum logic, standard propositional logic, and the (consistent) histories rules for quantum reasoning is discussed. It is shown that Maudlin's claim [Am. J. Phys. 79 (2011) 954] that the histories approach is inconsistent, is incorrect. The histories approach is both internally consistent and adequate for discussing the physical situations considered by Maudlin.
Although quantum computers are predicted to have many commercial applications, less attention has been given to their potential for resolving foundational issues in quantum mechanics. Here we focus on quantum computers' utility for the Consistent Histories formalism, which has previously been employed to study quantum cosmology, quantum paradoxes, and the quantum-to-classical transition. We present a variational hybrid quantum-classical algorithm for finding consistent histories, which should revitalize interest in this formalism by allowing classically impossible calculations to be performed.…
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity operator on a Hilbert space of histories. Provided a consistency condition is satisfied, the corresponding Boolean algebra of histories, called a {\it framework}, can be assigned probabilities in the usual way, and within a single framework quantum reasoning is identical to ordinary probabilistic reasoning. A refinement rule, which allows a probability distributio…
Quantum open systems are described in the Markovian limit by master equations in Lindblad form. I argue that common ``quantum trajectory'' techniques corresponding to continuous measurement schemes, which solve the master equation by unraveling its evolution into stochastic trajectories in Hilbert space, correspond closely to particular sets of decoherent (or consistent) histories. This is illustrated by a simple model of photon counting. An equivalence is shown for these models between standard quantum jumps and the orthogonal jumps of Diósi, which have already been shown to correspond to dec…
The Two-State-Vector formalism and the Entangled Histories formalism are attempts to better understand quantum correlations in time. The main objective of this paper is to show that, with appropriately defined scalar products, both formalisms can be made isomorphic. We show that they treat operators and states on equal footing leading to the same statistics for all measurements. In particular, we discuss the topic of quantum correlations in time and show how they can be generated and analyzed in a consistent way in these formalisms. Furthermore, we elaborate on a novel behavior of quantum hist…
We show the equivalence of the functions $G_{\rm p}(t)$ and $|Ψ(d,t)|^2$ for the ``passage time'' in tunneling. The former, obtained within the framework of the real time Feynman histories approach to the tunneling time problem, using the Gell-Mann and Hartle's decoherence functional, and the latter involving an exact analytical solution to the time-dependent Schrödinger equation for cutoff initial waves.
In the arrival time problem in quantum mechanics, a standard formula that frequently emerges as the probability for crossing the origin during a given time interval is the current integrated over that time interval. This is semiclassically correct but can be negative due to backflow. Here, we show that this formula naturally arises in a decoherent histories analysis of the arrival time problem. For a variety of initial states, we show that histories crossing during different time intervals are approximately decoherent. Probabilities may therefore be assigned and coincide with the standard form…
Based on the framework of consistent history theory, the quantum entangled history was proposed in 2015 and experimentally verified through temporal Greenberger-Horne-Zeilinger (GHZ) test with $3$ time nodes in 2016. In this paper, we extend the temporal GHZ test to arbitrary time nodes and even system dimensions. Then, we define a witness to distinguish between the quantum entangled histories and the classical histories. The minimums of the witness for the classical histories are calculated for arbitrary number of time nodes and the system dimensions $2$ and $\infty$. It is found that the min…
Motivated by the advances of quantum Darwinism and recognizing the role played by redundancy in identifying the small subset of quantum states with resilience characteristic of objective classical reality, we explore the implications of redundant records for consistent histories. The consistent histories formalism is a tool for describing sequences of events taking place in an evolving closed quantum system. A set of histories is consistent when one can reason about them using Boolean logic, i.e., when probabilities of sequences of events that define histories are additive. However, the vast m…
We review recent progress in understanding the arrival time problem in quantum mechanics, from the point of view of the decoherent histories approach to quantum theory. We begin by discussing the arrival time problem, focussing in particular on the role of the probability current in the expected classical solution. After a brief introduction to decoherent histories we review the use of complex potentials in the construction of appropriate class operators. We then discuss the arrival time problem for a particle coupled to an environment, and review how the arrival time probability can be expres…
The most general description of the classical world is in terms of local densities (such as number, momentum, energy), and these typically evolve according to evolution equations of hydrodynamic form. To explain the emergent classicality of these variables from an underlying quantum theory, it is therefore necessary to show, firstly, that these variables exhibit negligible interference, and secondly, that the probabilities for histories of them are peaked around hydrodynamic evolution. The implementation of this programme in the context of the decoherent histories approach to quantum theory is…
The quantum Zeno effect arises due to frequent observation. That implies the existence of some experimenter and its interaction with the system. In this contribution, we examine what happens for a closed system if one considers a quantum Zeno type of question, namely: "what is the probability of a system, remaining always in a particular subspace". This has implications to the arrival time problem that is also discussed. We employ the decoherent histories approach to quantum theory, as this is the better developed formulation of closed system quantum mechanics, and in particular, dealing with …
An idealised experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of topology is suggested. The correspondence between these models and discretised spacetime models is established.
D. Wallace has tried to use decoherence to solve the preferred basis problem of Everettian Quantum Mechanics, and this solution lays the foundation for his proof of the Born rule. But this is a circular argument, as approximations used in decoherence usually rely on the probabilistic interpretation of the Hilbert space norm. He claims the norm can measure approximations even without probabilities, but this assumption has not been properly justified. Without it, the combination of the Everettian and decoherent histories formalisms leads to strange consequences, such as a proliferation of small …
Recent work with Dowker on the scientific status of the consistent histories approach to quantum theory is reviewed and summarised. The approach is compared with formulations of quantum theory, such as Bohmian mechanics and the Copenhagen interpretation a la Landau-Lifshitz, in which classical variables are explicitly appended. I try to explain why the consistent histories formulation is scientifically problematic, in that it is a very weak theory, but also scientifically interesting, shedding new light on quantum theory.
We present a decomposition of the general quantum mechanical evolution operator, that corresponds to the path decomposition expansion, and interpret its constituents in terms of the quantum Zeno effect (QZE). This decomposition is applied to a finite dimensional example and to the case of a free particle in the real line, where the possibility of boundary conditions more general than those hitherto considered in the literature is shown. We reinterpret the assignment of consistent probabilities to different regions of spacetime in terms of the QZE. The comparison of the approach of consistent h…
Quantum state diffusion shows how stochastic interaction with the environment may cause localisation of the wave-function, and thereby demonstrates that quantum mechanics need not invoke a separate axiom of measurement to explain the emergence of the classical world. It has not been clear whether quantum state diffusion requires some new physics. We set up an explicit numerical calculation of the evolution of the wave-function of a two-state system under interaction using only the physics explicitly contained in quantum mechanics without an axiom of measurement. The wave-function does indeed l…
The theory of decoherent histories allows one to talk of the behavior of quantum systems in the absence of measurement. This paper generalizes the idea of decoherent histories to arbitrary open system operations and proposes experimentally testable criteria for decoherence.
The interpretations of a particular quantum gedanken experiment provided by Bohmian mechanics and consistent histories are shown to contradict each other, both in the absence and in the presence of a measuring device. The consistent history result seems closer to standard quantum mechanics, and shows no evidence of the mysterious nonlocal influences present in the Bohmian description.
We present a short survey of a novel approach, called "ETH approach", to the quantum theory of events happening in isolated physical systems and to the effective time evolution of states of systems featuring events. In particular, we attempt to present a clear explanation of what is meant by an "event" in quantum mechanics and of the significance of this notion. We then outline a theory of direct (projective) and indirect observations or recordings of physical quantities and events. Some key ideas underlying our general theory are illustrated by studying a simple quantum-mechanical model of a …
