arXiv subjects

C. Jess Riedel

Publications and source records attributed to C. Jess Riedel.

At least 19 recordsLinked to original sources

arXiv2026

Emergent classicality and wavefunction branching in an isolated quantum many-body system

Decoherence in quantum systems is conventionally modeled as the effect of interactions with an external environment. However, such a prescription excludes isolated many-body systems, which are also expected to display classical behavior at macroscopic scales. In isolated systems, decoherence must emerge internally from microscopic degrees of freedom that are invisible to the macroscopic description. Here we explicitly show that classicality can emerge in such a fashion. We consider a weakly disordered, $3$-local chaotic kicked top of $N$ qubits, where the collective spin sector serves as the macroscopic description, while the microscopic permutation sector acts as an internal bath, decohering the collective spin sector. Starting from closed unitary dynamics, we derive and numerically confirm an effective Lindblad equation for the collective spin variables. In the thermodynamic limit these reduced dynamics converge to a classical chaotic Fokker--Planck equation with vanishingly small diffusion on the spherical phase space, producing a quantum-classical correspondence beyond the Ehrenfest time. The chaotic dynamics evolve the pure many-body wavefunction into continuously branching components associated with distinct classical trajectories. These branches acquire nearly orthogonal microscopic records in the permutation sector, preventing quantum interferences and ensuring the corresponding histories remain consistent.

quant-ph↗

arXiv2025

The threshold for quantum-classical correspondence is $D \sim \hbar^{\frac43}$

In chaotic quantum systems, an initially localized quantum state can deviate strongly from the corresponding classical phase-space distribution after the Ehrenfest time $t_{\mathrm{E}} \sim \log(\hbar^{-1})$, even in the limit $\hbar \to 0$. Decoherence by the environment is often invoked to explain the persistence of the quantum-classical correspondence at longer timescales. Recent rigorous results for Lindblad dynamics with phase-space diffusion strength $D$ show that quantum and classical evolutions remain close for times that are exponentially longer than the Ehrenfest time whenever $D \gg \hbar^{\frac43}$, in units set by the classical Hamiltonian. At the same time, some heuristic arguments have suggested the weaker condition $D \gg \hbar^{2}$ always suffices. Here we construct an explicit Lindbladian that demonstrates that the scaling $D \sim \hbar^{\frac43}$ is indeed the threshold for quantum-classical correspondence beyond the Ehrenfest time. Our example uses a smooth time-dependent Hamiltonian and linear Lindblad operators generating homogeneous isotropic diffusion. It exhibits an $\hbar$-independent quantum-classical discrepancy at the Ehrenfest time whenever $D \ll \hbar^{\frac43}$, even for $\hbar$-independent "macroscopic" smooth observables.

quant-ph↗

arXiv2025

Wavefunction branches demand a definition!

Under unitary evolution, a typical macroscopic quantum system is thought to develop wavefunction branches: a time-dependent decomposition into orthogonal components that (1) form a tree structure forward in time, (2) are approximate eigenstates of quasiclassical macroscopic observables, and (3) exhibit effective collapse of feasibly measurable observables. If they could be defined precisely, wavefunction branches would extend the theory of decoherence beyond the system-environment paradigm and could supplant anthropocentric measurement in the quantum axioms. Furthermore, when such branches have bounded entanglement and can be effectively identified numerically, sampling them would allow asymptotically efficient classical simulation of quantum systems. I consider a promising recent approach to formalizing branches on the lattice by Taylor & McCulloch [Quantum 9, 1670 (2025), arXiv:2308.04494], and compare it to prior work from Weingarten [Found. Phys. 52, 45 (2022), arXiv:2105.04545]. Both proposals are based on quantum complexity and argue that, once created, branches persist for long times due to the generic linear growth of state complexity. Taylor & McCulloch characterize branches by a large difference in the unitary complexity necessary to interfere vs. distinguish them. Weingarten takes branches as the components of the decomposition that minimizes a weighted sum of expected squared complexity and the Shannon entropy of squared norms. I discuss strengths and weaknesses of these approaches, and identify tractable open questions.

quant-ph↗

arXiv2025

Ehrenfest's theorem beyond the Ehrenfest time

In closed quantum systems, wavepackets can spread exponentially in time due to chaos, forming long-range superpositions in just seconds for ordinary macroscopic systems. A weakly coupled environment is conjectured to decohere the system and restore the quantum-classical correspondence while necessarily introducing diffusive noise -- but at what coupling strength, and under which conditions? For Markovian open systems with Hamiltonians of the form $H = p^2/2m+V(x)$ and Hermitian linear Lindblad operators, we prove the quantum and classical evolutions are close whenever the strength of the environment-induced diffusion satisfies $D \gg (\hbar/s_H)^{4/3} D_H$, where $s_H$ and $D_H$ are characteristic action and diffusion scales that we define precisely using the classical Hamiltonian $H$. The bound applies for all observables and for times exponentially longer than the Ehrenfest timescale, which is when the correspondence can break down in closed systems. The strength of the diffusive noise can vanish in the classical limit to give the appearance of reversible dynamics. The $4/3$ exponent may be optimal, suggested by heuristic arguments and prior numerical evidence. Based on our bound, we give an efficient classical algorithm for simulating quantum Lindblad dynamics, which becomes provably accurate when the strength of environmental coupling exceeds the above threshold.

quant-ph↗

arXiv2025

Classical correspondence beyond the Ehrenfest time for open quantum systems with general Lindbladians

Quantum and classical systems evolving under the same formal Hamiltonian $H$ may dramatically differ after the Ehrenfest timescale $t_E \sim \log(\hbar^{-1})$, even as $\hbar \to 0$. Coupling the system to a Markovian environment results in a Lindblad equation for the quantum evolution. Its classical counterpart is given by the Fokker-Planck equation on phase space, which describes Hamiltonian flow with friction and diffusive noise. The quantum and classical evolutions may be compared via the Wigner-Weyl representation. Due to decoherence, they are conjectured to match closely for times far beyond the Ehrenfest timescale as $\hbar \to 0$. We prove a version of this correspondence, bounding the error between the quantum and classical evolutions for any sufficiently regular Hamiltonian $H(x,p)$ and Lindblad functions $L_k(x,p)$. The error is small when the strength of the diffusion $D$ associated to the Lindblad functions satisfies $D \gg \hbar^{4/3}$, which allows vanishing noise in the classical limit. Our method uses a time-dependent semiclassical mixture of variably squeezed Gaussian states. The states evolve according to a local harmonic approximation to the Lindblad dynamics. Both the exact quantum trajectory and its classical counterpart can be expressed as perturbations of this semiclassical mixture, with the errors bounded using Duhamel's principle. We present heuristic arguments suggesting the $4/3$ exponent is optimal and defines a boundary in the sense that asymptotically weaker diffusion permits a breakdown of quantum-classical correspondence at the Ehrenfest timescale. In a shorter companion paper, we treat the special case of Hamiltonians that decompose into kinetic and potential energy with linear Lindblad operators, with explicit bounds that can be applied directly to physical systems.

math-ph↗

arXiv2023

A spin-energy operator inequality for Heisenberg-coupled qubits

We slightly strengthen an operator inequality identified by Correggi et al. that lower bounds the energy of a Heisenberg-coupled graph of $s=1/2$ spins using the total spin. In particular, $ΔH \ge C Δ\vec{S}^2$ for a graph-dependent constant $C$, where $ΔH$ is the energy above the ground state and $Δ\vec{S}^2$ is the amount by which the square of the total spin $\vec{S} = \sum_i \vecσ_i/2$ falls below its maximum possible value. We obtain explicit constants in the special case of a cubic lattice. We briefly discuss the interpretation of this bound in terms of low-energy, approximately non-interacting magnons in spin wave theory and contrast it with another inequality found by Bärwinkel et al.

quant-ph↗

arXiv2022

Rapidly Decaying Wigner Functions are Schwartz Functions

We show that if the Wigner function of a (possibly mixed) quantum state decays toward infinity faster than any polynomial in the phase space variables $x$ and $p$, then so do all of its derivatives, i.e., it is a Schwartz function on phase space. This is equivalent to the condition that the Husimi function is a Schwartz function, that the quantum state is a Schwartz operator in the sense of Keyl et al., and, in the case of a pure state, that the wavefunction is a Schwartz function on configuration space. We discuss the interpretation of this constraint on Wigner functions and provide explicit bounds on Schwartz seminorms.

quant-ph↗

arXiv2022

MAQRO -- BPS 2023 Research Campaign Whitepaper

The objective of the proposed MAQRO mission is to harness space for achieving long free-fall times, extreme vacuum, nano-gravity, and cryogenic temperatures to test the foundations of physics in macroscopic quantum experiments. This will result in the development of novel quantum sensors and a means to probe the foundations of quantum physics at the interface with gravity. Earlier studies showed that the proposal is feasible but that several critical challenges remain, and key technologies need to be developed. These new technologies will open up the potential for achieving additional science objectives. The proposed research campaign aims to advance the state of the art and to perform the first macroscopic quantum experiments in space. Experiments on the ground, in micro-gravity, and in space will drive the proposed research campaign during the current decade to enable the implementation of MAQRO within the subsequent decade.

quant-ph↗

arXiv2022

RAFT: A Real-World Few-Shot Text Classification Benchmark

Large pre-trained language models have shown promise for few-shot learning, completing text-based tasks given only a few task-specific examples. Will models soon solve classification tasks that have so far been reserved for human research assistants? Existing benchmarks are not designed to measure progress in applied settings, and so don't directly answer this question. The RAFT benchmark (Real-world Annotated Few-shot Tasks) focuses on naturally occurring tasks and uses an evaluation setup that mirrors deployment. Baseline evaluations on RAFT reveal areas current techniques struggle with: reasoning over long texts and tasks with many classes. Human baselines show that some classification tasks are difficult for non-expert humans, reflecting that real-world value sometimes depends on domain expertise. Yet even non-expert human baseline F1 scores exceed GPT-3 by an average of 0.11. The RAFT datasets and leaderboard will track which model improvements translate into real-world benefits at https://raft.elicit.org .

cs.CL↗

arXiv2020

Forecasting timelines of quantum computing

We consider how to forecast progress in the domain of quantum computing. For this purpose we collect a dataset of quantum computer systems to date, scored on their physical qubits and gate error rate, and we define an index combining both metrics, the generalized logical qubit. We study the relationship between physical qubits and gate error rate, and tentatively conclude that they are positively correlated (albeit with some room for doubt), indicating a frontier of development that trades-off between them. We also apply a log-linear regression on the metrics to provide a tentative upper bound on how much progress can be expected over time. Within the (generally optimistic) assumptions of our model, including the key assumption that exponential progress in qubit count and gate fidelity will continue, we estimate that that proof-of-concept fault-tolerant computation based on superconductor technology is unlikely (<5% confidence) to be exhibited before 2026, and that quantum devices capable of factoring RSA-2048 are unlikely (<5% confidence) to exist before 2039. It is of course possible that these milestones will in fact be reached earlier, but that this would require faster progress than has yet been seen.

quant-ph↗

arXiv2020

Mechanical Quantum Sensing in the Search for Dark Matter

Numerous astrophysical and cosmological observations are best explained by the existence of dark matter, a mass density which interacts only very weakly with visible, baryonic matter. Searching for the extremely weak signals produced by this dark matter strongly motivate the development of new, ultra-sensitive detector technologies. Paradigmatic advances in the control and readout of massive mechanical systems, in both the classical and quantum regimes, have enabled unprecedented levels of sensitivity. In this white paper, we outline recent ideas in the potential use of a range of solid-state mechanical sensing technologies to aid in the search for dark matter in a number of energy scales and with a variety of coupling mechanisms.

physics.ins-det↗

arXiv2019

Comment on 'The aestivation hypothesis for resolving Fermi's paradox'

In their article [arXiv:1705.03394], 'That is not dead which can eternal lie: the aestivation hypothesis for resolving Fermi's paradox', Sandberg et al. try to explain the Fermi paradox (we see no aliens) by claiming that Landauer's principle implies that a civilization can in principle perform far more (${\sim} 10^{30}$ times more) irreversible logical operations (e.g., error-correcting bit erasures) if it conserves its resources until the distant future when the cosmic background temperature is very low. So perhaps aliens are out there, but quietly waiting. Sandberg et al. implicitly assume, however, that computer-generated entropy can only be disposed of by transferring it to the cosmological background. In fact, while this assumption may apply in the distant future, our universe today contains vast reservoirs and other physical systems in non-maximal entropy states, and computer-generated entropy can be transferred to them at the adiabatic conversion rate of one bit of negentropy to erase one bit of error. This can be done at any time, and is not improved by waiting for a low cosmic background temperature. Thus aliens need not wait to be active. As Sandberg et al. do not provide a concrete model of the effect they assert, we construct one and show where their informal argument goes wrong.

physics.pop-ph↗

arXiv2017

Classical Entanglement Structure in the Wavefunction of Inflationary Fluctuations

We argue that the preferred classical variables that emerge from a pure quantum state are determined by its entanglement structure in the form of redundant records: information shared between many subsystems. Focusing on the early universe, we ask how classical metric perturbations emerge from vacuum fluctuations in an inflationary background. We show that the squeezing of the quantum state for super-horizon modes, along with minimal gravitational interactions, leads to decoherence and to an exponential number of records of metric fluctuations on very large scales, $λ/λ_{\rm Hubble}>Δ_ζ^{-2/3}$, where $Δ_ζ\lesssim 10^{-5}$ is the amplitude of scalar metric fluctuations. This determines a preferred decomposition of the inflationary wavefunction into orthogonal "branches" corresponding to classical metric perturbations, which defines an inflationary entropy production rate and accounts for the emergence of stochastic, inhomogeneous spacetime geometry.

gr-qc↗

arXiv2017

Classical branches and entanglement structure in the wavefunction of cosmological fluctuations

The emergence of preferred classical variables within a many-body wavefunction is encoded in its entanglement structure in the form of redundant classical information shared between many spatially local subsystems. We show how such structure can be generated via cosmological dynamics from the vacuum state of a massless field, causing the wavefunction to branch into classical field configurations on large scales. An accelerating epoch first excites the vacuum into a superposition of classical fields as well as a highly sensitive bath of squeezed super-horizon modes. During a subsequent decelerating epoch, gravitational interactions allow these modes to collect information about longer-wavelength fluctuations. This information disperses spatially, creating long-range redundant correlations in the wavefunction. The resulting classical observables, preferred basis for decoherence, and system/environment decomposition emerge from the translation invariant wavefunction and Hamiltonian, rather than being fixed by hand. We discuss the role of squeezing, the cosmological horizon scale, and phase information in the wavefunction, as well as aspects of wavefunction branching for continuous variables and in field theories.

quant-ph↗

arXiv2017

Decoherence as a way to measure extremely soft collisions with dark matter

A new frontier in the search for dark matter (DM) is based on the idea of detecting the decoherence caused by DM scattering against a mesoscopic superposition of normal matter. Such superpositions are uniquely sensitive to very small momentum transfers from new particles and forces, especially DM with a mass below 100 MeV. Here we investigate what sorts of dark sectors are inaccessible with existing methods but would induce noticeable decoherence in the next generation of matter interferometers. We show that very soft, but medium range (0.1 nm - 1 $μ$m) elastic interactions between nuclei and DM are particularly suitable. We construct toy models for such interactions, discuss existing constraints, and delineate the expected sensitivity of forthcoming experiments. The first hints of DM in these devices would appear as small variations in the anomalous decoherence rate with a period of one sidereal day. This is a generic signature of interstellar sources of decoherence, clearly distinguishing it from terrestrial backgrounds. The OTIMA experiment under development in Vienna will begin to probe Earth-thermalizing DM once sidereal variations in the background decoherence rate are pushed below one part in a hundred for superposed 5-nm gold nanoparticles. The proposals by Bateman et al. and Geraci et al. could be similarly sensitive, although they would require at least a month of data taking. DM that is absorbed or elastically reflected by the Earth, and so avoids a greenhouse density enhancement, would not be detectable by those three experiments. On the other hand, the aggressive proposals of the MAQRO collaboration and Pino et al. would immediately open up many orders of magnitude in DM mass, interaction range, and coupling strength, regardless of how DM behaves in bulk matter.

quant-ph↗

arXiv2017

Classical branch structure from spatial redundancy in a many-body wavefunction

When the wavefunction of a large quantum system unitarily evolves away from a low-entropy initial state, there is strong circumstantial evidence it develops "branches": a decomposition into orthogonal components that is indistinguishable from the corresponding incoherent mixture with feasible observations. Is this decomposition unique? Must the number of branches increase with time? These questions are hard to answer because there is no formal definition of branches, and most intuition is based on toy models with arbitrarily preferred degrees of freedom. Here, assuming only the tensor structure associated with spatial locality, I show that branch decompositions are highly constrained just by the requirement that they exhibit redundant local records. The set of all redundantly recorded observables induces a preferred decomposition into simultaneous eigenstates unless their records are highly extended and delicately overlapping, as exemplified by the Shor error-correcting code. A maximum length scale for records is enough to guarantee uniqueness. Speculatively, objective branch decompositions may speed up numerical simulations of nonstationary many-body states, illuminate the thermalization of closed systems, and demote measurement from fundamental primitive in the quantum formalism.

quant-ph↗

arXiv2016

The Objective Past of a Quantum Universe: Redundant Records of Consistent Histories

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 majority of the sets of histories that are merely consistent are flagrantly non-classical in other respects. This embarras de richesses (known as the set selection problem) suggests that one must go beyond consistency to identify how the classical past arises in our quantum Universe. The key intuition we follow is that the records of events that define the familiar objective past are inscribed in many distinct systems, e.g., subsystems of the environment, and are accessible locally in space and time to observers. We identify histories that are not just consistent but redundantly consistent using the partial-trace condition introduced by Finkelstein as a bridge between histories and decoherence. The existence of redundant records is a sufficient condition for redundant consistency. It selects, from the multitude of the alternative sets of consistent histories, a small subset endowed with redundant records characteristic of the objective classical past. The information about an objective history of the past is then simultaneously within reach of many, who can independently reconstruct it and arrive at compatible conclusions in the present.

quant-ph↗

arXiv2016

Amplification, Decoherence, and the Acquisition of Information by Spin Environments

Quantum Darwinism recognizes the role of the environment as a communication channel: Decoherence can selectively amplify information about the pointer states of a system of interest (preventing access to complementary information about their superpositions) and can make records of this information accessible to many observers. This redundancy explains the emergence of objective, classical reality in our quantum Universe. Here, we demonstrate that the amplification of information in realistic spin environments can be quantified by the quantum Chernoff information, which characterizes the distinguishability of partial records in individual environment subsystems. We show that, except for a set of initial states of measure zero, the environment always acquires redundant information. Moreover, the Chernoff information captures the rich behavior of amplification in both finite and infinite spin environments, from quadratic growth of the redundancy to oscillatory behavior. These results will considerably simplify experimental testing of quantum Darwinism, e.g., using nitrogen vacancies in diamond.

quant-ph↗