Schedule for: 23w5083 - Non-Markovianity in Open Quantum Systems

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

Across a wide range of time and length scales, processes appear classical, Markovian and obey local detailed balance. This behaviour is easily explained by assuming that the hidden or irrelevant degrees of freedom rethermalize on a short time scale ("Born approximation", "repeated randomness assumption", "quantum regression theorem", etc.). Unfortunately, these assumptions are in blatant contradiction to the microscopic reversibility of the underlying quantum dynamics. After recalling the problem, I report on recent progress demonstrating the effective validity of such "repeated maximum entropy reasoning" for coarse and slow observables of isolated many-body systems. Importantly, this progress is based on unitarily evolving pure states and invokes the eigenstate thermalization hypothesis and typicality argument. It is thus fully compatible with the microscopic description. I also emphasize the essential importance to overcome the idea of ensemble averages for a satisfactory explanation of classicality and (non-)Markovianity, a problem which is frequently overlooked by using conventional models of open quantum systems theory.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Meet in the PDC front desk for a guided tour of The Banff Centre campus.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

The generally non-Markovian influence of a (strongly) coupled physical environment on the evolution of a quantum system can be formally captured with an object known as a Process Tensor (PT). Numerical evaluation of the ensuing dynamics then typically requires compression of this object, which is achievable when expressing the PTs in matrix product operator from (a PT-MPO). In this talk, I will discuss a method for constructing such PT-MPOs for most types of environment which are not themselves highly correlated. Specifically, this includes non-Gaussian environments, combining influences from different types of environment, and dealing with more complex forms of interaction between system and environment.

More than a century after the birth of quantum theory, the question of which properties and phenomena are fundamentally quantum – i.e., they cannot be reproduced by any classical theory – remains under active investigation. In this talk, we will see when and to what extent non-classicality can be unambiguously linked to specific features of the evolution of an open quantum system and its interaction with the environment, focusing on the difference between the Markovian and the non-Markovian scenarios. We will consider an open system that is undergoing sequential measurements of one observable at different times, and exploit the Kolmogorov consistency conditions to discriminate the resulting multi-time statistics from the statistics of any classical process, in the same spirit as the Leggett-Garg inequalities [1]. In the Markovian case, the multi-time statistics cannot be accounted for by means of any classical process if and only if the dynamics generates coherences (with respect to the measured observable) and subsequently turns them into populations [2]. On the other hand, such a direct connection between the dynamics of quantum coherences and non-classicality cannot be extended to general non-Markovian processes, where, instead, non-classicality is related to a global property of the system-environment evolution [3] that is fully captured by higher-order quantum maps, i.e., quantum combs [4]. The approach presented here is fully operational, since it relies on the observed multi-time probability distributions, and it thus directly applies to detect and quantify non-classicality in a variety of experimental platforms [5]. References [1]A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985) [2]A. Smirne, D. Egloff, M. G. Diaz, M. B. Plenio, and S. F. Huelga, Quantum Sci. Technol. 4, 01LT01 (2018) [3]S. Milz, D. Egloff, P. Taranto, T. Theurer, M. B. Plenio, A. Smirne, and S. F. Huelga, Phys. Rev. X 10, 041049 (2020) [4]G. Chiribella, G. M. D’Ariano, and P. Perinotti, Phys. Rev. Lett. 101, 060401 (2008). [5]A. Smirne, T. Nitsche, D. Egloff, S. Barkhofen, S. De, I. Dhand, C. Silberhorn, S. F. Huelga, and M. B. Plenio, Quantum Sci. Technol. 5, 04LT01 (2020)

At the nanoscale, strong system-reservoir interactions are ubiquitous and could potentially play a significant role in the development of novel nanoscale quantum machines. As a result, a formulation of thermodynamics, which is to be valid in the quantum regime, must incorporate the effects of strong system reservoir couplings. The reaction coordinate (RC) mapping tackles the strong coupling regime by reshaping the system-environment boundary to include a collective degree of freedom from the environment. This process results in an enlarged system, which in turn, is weakly coupled to its surroundings, thus allowing the use of weak-coupling tools for simulations. Nevertheless, this approach is limited due to the growing Hilbert space of the extended system, and it does not offer analytical insights onto the strong coupling regime. I will present our efforts to push beyond these limitations and develop a general, transparent, and efficient theory for strong coupling thermodynamics. By combing the RC mapping with the polaron transformation, followed by a judicious truncation of the Hamiltonian, we relocated strong coupling effects from the system-bath boundary into the energy parameters of the system, ending with a computationally tractable expression for an “effective" Hamiltonian. We exemplified the power of this approach on canonical models for quantum thermalization, quantum heat transport, phonon- assisted charge transport, and energy conversion devices. We showed that the effective Hamiltonian method is numerically accurate and that it gathers analytical insights into strong coupling effects within a broad window of applicability.

We propose a highly-scalable method to compute the statistics of charge transfer in driven conductors. The framework can be applied in situations of non-zero temperature, strong coupling to terminals and in the presence of non-periodic light-matter interactions, away from equilibrium. The approach combines the so-called mesoscopic leads formalism with full counting statistics. It results in a generalised quantum master equation that dictates the dynamics of current fluctuations and higher order moments of the probability distribution function of charge exchange. For generic time-dependent quadratic Hamiltonians, we provide closed-form expressions for computing noise in the non-perturbative regime of the parameters of the system, reservoir or system-reservoir interactions. Having access to the full dynamics of the current and its noise, the method allows us to compute the variance of charge transfer over time in non-equilibrium configurations. The dynamics reveals that in driven systems, the average noise should be defined operationally with care over which period of time is covered.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Abstract: The Kirkwood-Dirac (KD) quasiprobability sounds monstrously obscure, but it's recently proven useful across quantum thermodynamics, chaos, foundations, and metrology. Quasiprobabilities are quantum generalizations of probabilities and can represent quantum states. You've probably heard of one quasiprobability distribution: the Wigner function. The KD quasiprobability is richer and more flexible. I'll introduce the KD quasiprobability in a manner whose informality I hope you've gleaned from this abstract. I hope to convince you that the KD distribution is the best little quasiprobability you've never heard of. Select serious references: [1] N. Yunger Halpern, B. Swingle, and J. Dressel, “Quasiprobability behind the out-of-time-ordered correlator,” Phys. Rev. A 97, 042105 (2018). [2] D. Arvidsson-Shukur, J. Chevalier-Drori, and N. Yunger Halpern, “Conditions tighter than noncommutation needed for nonclassicality,” J. Phys. A 54, 284001 (2021). Suggested bedtime reading: [1] https://quantumfrontiers.com/2016/12/11/the-weak-shall-inherit-the-quasiprobability/ [2] https://quantumfrontiers.com/2017/04/23/glass-beads-and-weak-measurement-schemes/ [3] https://quantumfrontiers.com/2020/08/30/if-the-quantum-metrology-key-fits/ [4] https://quantumfrontiers.com/2017/02/19/its-chaos/ [5] https://quantumfrontiers.com/2019/03/24/a-theorist-i-can-actually-talk-with/ [6] https://quantumfrontiers.com/2019/08/25/quantum-conflict-resolution/ [7] https://quantumfrontiers.com/2021/06/27/cutting-the-quantum-mustard/

In this talk I will review the characterization of quantum non-Markovianity via divisibility conditions, explaining the main motivations and features of it. In addition, I will comment on the similarities and differences of this approach to quantum non-Markovianity with others, and present some recent results on non-invertible quantum evolutions.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

It is shown that the geodesics on the manifold of invertible density matrices equipped with the Bures distance correspond to physical evolutions of the quantum system coupled to an ancilla. The explicit forms of the geodesics and of the corresponding system-ancilla coupling Hamiltonian are obtained. The non-Markovian character of the geodesic evolutions is studied quantitatively using a measure of non-Markovianity introduced in the literature. We briefly outline some potential applications of these geodesics in quantum metrology and quantum control.

We investigate the behavior of the stochastic entropy production in open two-level quantum systems thermalizing after a non-Markovian transient. We show the existence of time intervals where both the average entropy production and the variance decrease. This happens when the quantum evolution fails to be P-divisible, i.e. when it is a so-called "essentially non-Markovian dynamics". For a simple model, we provide analytical bounds on the parameters of the dynamics that ensure the mentioned phenomenology. From a physical point of view, although the dynamics of the system is overall irreversible, our result may be interpreted as a transient tendency towards reversibility, described by zero stochastic entropy production. (Joint work with S. Gherardini and E. Fiorelli, arXiv:2210.07866)

One of the key tasks in the development of quantum technologies is predicting and eventually controlling the behaviour of a general open quantum system for long times. Often, if not always, predicting the behaviour of system and bath is impossible, and so one is restricted to studying the reduced dynamics of the system. This represents a loss of information and is the main difficulty in long time analysis. To mitigate this problem, we introduce a technique which keeps tracks not only of the evolution of the system but also of (measurable) bath-related quantities which influence the dynamics of the quantum system of interest. This allows us to predict the behaviour of the system for longer times, as compared to existing tools with the same seed information, e.g., with the same perturbative order. Finally, we show how our technique allows us to (in principle) exactly track the evolution of high order correlations of the dephasing spin boson model even when the state is non-Gaussian.

One detects entanglement of a bipartite quantum state shared between distant laboratories measuring in a Bell scenario a non-local observable called entanglement witnesses. We will discuss how to optimise an entanglement witness, i.e. how to improve an existing setting, to detect more entangled states without losing states already detected. We will show the families of entanglement witnesses equivalent to non-linear entanglement criteria and discuss their optimality.

We consider a slowly varying time dependent d-level atom interacting with a photon field. Restricted to the single excitation atom-field sector, the model is a time- dependent generalization of the Wigner-Weisskopf model describing spontaneous emission of an atomic excitation into the radiation field. We analyze the dynamics of the atom and of the radiation field in the adiabatic and small coupling approximations, in various regimes. In particular, starting with an excited atomic state, we provide a description of both the radiative decay of the atom and of the buildup of the photon excitation in the field, and we discuss some properties of the effective evolution of the atom. This is joint work with Marco Merkli.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

In the past few years we have witnessed a growing interest in computational paradigms beyond the gate paradigm. Among these, Extreme Learning Machines and Reservoir Computers are two particularly interesting new computational paradigms. Their key feature is the use of a fixed, nonlinear dynamics to efficiently extract information from a given dataset. Such a goal, in the classical scenario, is achieved by processing the data as input of some fixed nonlinear dynamics of a suitable (neural) network – the reservoir - which enlarges the dimensionality of the data, making it easier to extract the properties of interest. The difference between Extreme Learning Machines and Reservoir Computers is whether the reservoir being used can deploy an internal memory. More precisely, Reservoir Computers hold memory of the inputs seen at previous iterations, a feature which plays a crucial role when processing time sequences. Extreme Learning Machines on the other hand use memoryless reservoirs. Although this makes the training of ELMs easier, it also makes them unsuitable for temporal data processing. We will review some recent results on the quantum counterpart of the above.

Describing the open system dynamics of many-body systems is in general extremely challenging due to their large sizes and the potential non-Markovian effects coming from the system-bath interactions. Non-Markovianity emerges for strong coupling with a structured bath but also when one derives a reduced description of a larger Markovian system - an operation particularly desirable for many-body systems as it makes it possible to significantly shrink the size of the Hilbert space. In this talk, I will present a number of recently developed theoretical methods [based on the hybridization of non-Markovian stochastic methods, Hierarchical Equations of Motion (HEOM) and Matrix Product States (MPS) techniques] and how they can be used to capture non-Markovianity in the context of dissipative phase transitions [1], system dynamics conditioned on measurement [2], and 1D dynamics in strongly correlated systems [3]. [1] F. Damanet, et al., PRA 99, 033845 (2019). R. Palacino and J. Keeling, PRR 3, 032016 (2021). [2] Link et al., PRX Quantum 3, 020348 (2022). [3] S. Flannigan, et al., PRL 128, 063601 (2022). M. Moroder et al., arXiv:2207.08243.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Open quantum systems are ubiquitous in nature, but challenging to model due to the complexity of environmental interactions. While the idea of using quantum computing platforms to simulate these dynamical processes in either a digital or analog fashion has been around for decades, it wasn’t until recently that the hardware has become sufficiently accessible to verify these methods. Here, I will give an overview of recent developments in the field of quantum computation and algorithms for modelling the dynamics of open quantum systems, with an emphasis on digital simulation, or gate-based, techniques. This will include a brief survey of the field, an overview of dilation techniques, a discussion of a few open system algorithms and their generalization to non-Markovian dynamics, and their potential applications in chemistry, physics, and materials science.

A well-known approach for the description of memory effects in the reduced quantum dynamics of an open system is based on the notion of information exchange between the open system and its environment. This exchange has typically been quantified studying the variation in time of the trace distance between distinct initial system states. We point to the fact that such an information exchange can actually be described by a large class of quantum divergences, including not only distances, but also entropic quantifiers. We derive general upper bounds on the revivals of quantum divergences conditioned and determined by the formation of correlations and changes in the environment. We will discuss in particular the different relationship between distinguishability and divisibility for the trace distance and the Jensen-Shannon divergence.

The paradigm of open quantum systems gives rise to a temporal structure, as seen in quantum stochastic processes. System-environment dynamics can precipitate non-Markovian processes, which generate quantum correlations between different times. Formally speaking, these correlations can be placed on the same footing as correlations in a many-body state. This invites the question: to what extent can temporal quantum correlations be as interesting as spatial ones, and how can we access them? In this talk, I will discuss recent work in which we show how to fully characterise non-Markovian processes in practice. We develop the fully-general formalism of non-Markovian quantum process tomography, as well as extensions to make learning both efficient and self-consistent. By applying this, we show how to determine process features — such as temporal entanglement — even with limited control. Remarkably, we find that many of these complex properties are already present in naturally occurring noise on near-term computers. Hence, the characterisation and optimal control of such processes have direct application not only to the general study of non-Markovianity, but also to the development of fault-tolerant quantum devices.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Control over excitons and their dynamics enables energy to be directed and harnessed for light harvesting and molecular electronics, but is challenging in condensed phase systems owing to the large number of degrees of freedom. Here, we introduce a DNA-based platform that spatially organizes chromophores with nanoscale precision to construct tunable excitonic systems. We characterize these constructs with 2D electronic spectroscopy and single-molecule spectroscopy and show that this platform enables independent control over the nature and magnitude of the coupling among the chromophores and between the chromophores and the environment. Using this platform, we demonstrate that a more flexible environment enhances the efficiency of energy transport and specific chromophore geometries activate symmetry-breaking charge transfer. These studies highlight the key role of the environment in driving exciton dynamics.

In this talk I will describe a method for simulating exciton dynamics in protein–pigment complexes, including effects from charge transfer as well as fluorescence. The method combines the hierarchical equations of motion, which are used to describe quantum dynamics of excitons, and the Nakajima–Zwanzig quantum master equation, which is used to describe slower charge transfer processes. We have studied the charge transfer quenching in light harvesting complex II, a protein postulated to control non-photochemical quenching in many plant species. Our calculations reveal that the exciton energy funnel plays an important role in determining quenching efficiency, a conclusion we expect to extend to other proteins that perform protective excitation quenching.

Interactions are the fundamental tool for generating entanglement between quantum degrees of freedom. All-to-all interactions between neutral atoms have been used to generate entanglement in a single spatial mode, with applications in quantum-enhanced sensing. However, many envisioned protocols in quantum sensing and simulation require greater control over the spatial structure of entanglement. In our experiment, we couple an array of four atomic ensembles to a single mode of light inside an optical cavity, realizing an all-to-all connected graph of interactions between the atoms. By combining these global interactions with local operations we gain control over the spatial structure of entanglement. We demonstrate this capability by tuning the entanglement between two subsystems from unentangled to exhibiting an especially strong form of entanglement, known as Einstein-Podolsky-Rosen steering. By extending the control over the quantum correlations to all four ensembles we engineer a square graph state, an essential resource for quantum computation. These capabilities set the stage for generating entangled states tailored to specific tasks, such as quantum-enhanced sensing of spatially varying fields and quantum computation.

Could quantum physics help answer some of the big open questions in neuroscience? Could nature have discovered quantum information processing before we did? Motivated by these questions, I discuss two potential ways in which quantum effects might be important in the brain. The first direction concerns biophotons, which could serve as classical and quantum information carriers. We have shown that axons could serve as natural waveguides for these photons, and there is recent experimental evidence for this idea. The second direction concerns radical pairs, i.e. pairs of entangled electron spins that, together with nearby nuclear spins, might serve as quantum memories and processors. We have shown that radical pair models can explain otherwise puzzling experimental observations (magnetic field effects and isotope effects) related to anesthesia, bipolar disorder, the circadian clock, microtubules, and neurogenesis, while also proposing new experimental tests. While these results are still far from establishing the existence of functioning quantum networks, they suggest that key components that would be required for such networks might indeed be available in the brain.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

We consider two exactly solvable models of open quantum dynamics: model of pure decoherence and a spin-boson model, and study the long-time behaviour without restrictions on the system-bath coupling constant. We show that, under certain conditions on the spectral density function, the dynamics becomes asymptotically Markovian on long times. From the other side, a popular way of addressing non-Markovian dynamics of an open quantum system is to try to embed the system into an extended system whose dynamics is Markovian. However, if the conditions of asymptotic Markovianity in these exactly solvable models are not satisfied, then the relaxation to a steady state can be non-exponential and, thus, such non-Markovian dynamics cannot be embedded into an extended Markovian one.

Repeated-interaction models are receiving increasing attention as they describe many nontrivial phenomena in the dynamics of open quantum systems [1,2]. In a general scenario of both fundamental and practical interest, a quantum system repeatedly interacts with individual particles or modes, forming a correlated and structured reservoir; however, classical and quantum environment correlations greatly complicate the calculation and interpretation of the system dynamics. We propose an exact solution to this problem based on the tensor network formalism [3]. We find a natural Markovian embedding for the system dynamics, where the role of an auxiliary system is played by virtual indices of the network. The constructed embedding is amenable to an analytical treatment for a number of timely problems such as the system interaction with two-photon wave packets, structured photonic states, and one-dimensional spin chains. We also derive a time-convolution master equation and relate its memory kernel with the environment correlation function, thus revealing a clear physical picture of memory effects in the dynamics. The results advance tensor-network methods in the fields of quantum optics and quantum transport. Higher-order stroboscopic limits for the collisional dynamics and a transition from non-Markovian to Markovian regime (even if the environment is correlated) is discussed too [4]. [1] F. Ciccarello, S. Lorenzo, V. Giovannetti, and G. M. Palma, Quantum collision models: Open system dynamics from repeated interactions, Phys. Rep. 954, 1 (2022). [2] S. Campbell and B. Vacchini, Collision models in open system dynamics: A versatile tool for deeper insights? Europhys. Lett. 133, 60001 (2021). [3] S. N. Filippov, I. A. Luchnikov. Collisional open quantum dynamics with a generally correlated environment: Exact solvability in tensor networks. Phys. Rev. A 105, 062410 (2022). [4] S. N. Filippov. Multipartite correlations in quantum collision models. Entropy 24, 508 (2022).

5-day workshop participants are welcome to use BIRS facilities (TCPL ) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 11AM.