In recent years, a close connection between the description of open quantum systems, the input-output formalism of quantum optics, and continuous matrix product states in quantum field theory has been established. So far, however, this connection has
not been extended to the condensed-matter context. In this work, we substantially develop further and apply a machinery of continuous matrix product states (cMPS) to perform tomography of transport experiments. We first present an extension of the tomographic possibilities of cMPS by showing that reconstruction schemes do not need to be based on low-order correlation functions only, but also on low-order counting probabilities. We show that fermionic quantum transport settings can be formulated within the cMPS framework. This allows us to present a reconstruction scheme based on the measurement of low-order correlation functions that provides access to quantities that are not directly measurable with present technology. Emblematic examples are high-order correlations functions and waiting times distributions (WTD). The latter are of particular interest since they offer insights into short-time scale physics. We demonstrate the functioning of the method with actual data, opening up the way to accessing WTD within the quantum regime.
Tensor network states and specifically matrix-product states have proven to be a powerful tool for simulating ground states of strongly correlated spin models. Recently, they have also been applied to interacting fermionic problems, specifically in t
he context of quantum chemistry. A new freedom arising in such non-local fermionic systems is the choice of orbitals, it being far from clear what choice of fermionic orbitals to make. In this work, we propose a way to overcome this challenge. We suggest a method intertwining the optimisation over matrix product states with suitable fermionic Gaussian mode transformations. The described algorithm generalises basis changes in the spirit of the Hartree-Fock method to matrix-product states, and provides a black box tool for basis optimisation in tensor network methods.
Interacting quantum many-body systems are usually expected to thermalise, in the sense that the evolution of local expectation values approach a stationary value resembling a thermal ensemble. This intuition is notably contradicted in systems exhibit
ing many-body localisation, a phenomenon receiving significant recent attention. One of its most intriguing features is that, in stark contrast to the non-interacting case, entanglement of states grows without limit over time, albeit slowly. In this work, we establish a novel link between quantum information theory and notions of condensed matter, capturing the phenomenon in the Heisenberg picture. We show that the existence of local constants of motion, often taken as the defining property of many-body localisation, together with a generic spectrum, is sufficient to rigorously prove information propagation: These systems can be used to send a signal over arbitrary distances, in that the impact of a local perturbation can be detected arbitrarily far away. We perform a detailed perturbation analysis of quasi-local constants of motion and also show that they indeed can be used to construct efficient spectral tensor networks, as recently suggested. Our results provide a detailed and model-independent picture of information propagation in many-body localised systems.
The experimental realisation of large scale many-body systems has seen immense progress in recent years, rendering full tomography tools for state identification inefficient, especially for continuous systems. In order to work with these emerging phy
sical platforms, new technologies for state identification are required. In this work, we present first steps towards efficient experimental quantum field tomography. We employ our procedure to capture ultracold atomic systems using atom chips, a setup that allows for the quantum simulation of static and dynamical properties of interacting quantum fields. Our procedure is based on cMPS, the continuous analogues of matrix product states (MPS), ubiquitous in condensed-matter theory. These states naturally incorporate the locality present in realistic physical settings and are thus prime candidates for describing the physics of locally interacting quantum fields. The reconstruction procedure is based on two- and four-point correlation functions, from which we predict higher-order correlation functions, thus validating our reconstruction for the experimental situation at hand. We apply our procedure to quenched prethermalisation experiments for quasi-condensates. In this setting, we can use the quality of our tomographic reconstruction as a probe for the non-equilibrium nature of the involved physical processes. We discuss the potential of such methods in the context of partial verification of analogue quantum simulators.
We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product states, a compl
ete set of variational states grasping states in quantum field theory. We innovate a practical method, making use of and developing tools in estimation theory used in the context of compressed sensing such as Prony methods and matrix pencils, allowing us to faithfully reconstruct quantum field states based on low-order correlation functions. In the absence of a phase reference, we highlight how specific higher order correlation functions can still be predicted. We exemplify the functioning of the approach by reconstructing randomised continuous matrix product states from their correlation data and study the robustness of the reconstruction for different noise models. We also apply the method to data generated by simulations based on continuous matrix product states and using the time-dependent variational principle. The presented approach is expected to open up a new window into experimentally studying continuous quantum systems, such as encountered in experiments with ultra-cold atoms on top of atom chips. By virtue of the analogy with the input-output formalism in quantum optics, it also allows for studying open quantum systems.
All physical systems are to some extent open and interacting with their environment. This insight, basic as it may seem, gives rise to the necessity of protecting quantum systems from decoherence in quantum technologies and is at the heart of the eme
rgence of classical properties in quantum physics. The precise decoherence mechanisms, however, are often unknown for a given system. In this work, we make use of an opto-mechanical resonator to obtain key information about spectral densities of its condensed-matter heat bath. In sharp contrast to what is commonly assumed in high-temperature quantum Brownian motion describing the dynamics of the mechanical degree of freedom, based on a statistical analysis of the emitted light, it is shown that this spectral density is highly non-Ohmic, reflected by non-Markovian dynamics, which we quantify. We conclude by elaborating on further applications of opto-mechanical systems in open system identification.
Among the possibly most intriguing aspects of quantum entanglement is that it comes in free and bound instances. Bound entangled states require entangled states in preparation but, once realized, no free entanglement and therefore no pure maximally e
ntangled pairs can be regained. Their existence hence certifies an intrinsic irreversibility of entanglement in nature and suggests a connection with thermodynamics. In this work, we present a first experimental unconditional preparation and detection of a bound entangled state of light. We consider continuous-variable entanglement, use convex optimization to identify regimes rendering its bound character well certifiable, and realize an experiment that continuously produced a distributed bound entangled state with an extraordinary and unprecedented significance of more than ten standard deviations away from both separability and distillability. Our results show that the approach chosen allows for the efficient and precise preparation of multimode entangled states of light with various applications in quantum information, quantum state engineering and high precision metrology.
In the study of relaxation processes in coherent non-equilibrium dynamics of quenched quantum systems, ultracold atoms in optical superlattices with periodicity two provide a very fruitful test ground. In this work, we consider the dynamics of a part
icular, experimentally accessible initial state prepared in a superlattice structure evolving under a Bose-Hubbard Hamiltonian in the entire range of interaction strengths, further investigating the issues raised in Ref. [Phys. Rev. Lett. 101, 063001 (2008)]. We investigate the relaxation dynamics analytically in the non interacting and hard core bosonic limits, deriving explicit expressions for the dynamics of certain correlation functions, and numerically for finite interaction strengths using the time-dependent density-matrix renormalization (t-DMRG) approach. We can identify signatures of local relaxation that can be accessed experimentally with present technology. While the global system preserves the information about the initial condition, locally the system relaxes to the state having maximum entropy respecting the constraints of the initial condition. For finite interaction strengths and finite times, the relaxation dynamics contains signatures of the relaxation dynamics of both the non-interacting and hard core bosonic limits.
The certificate of success for a number of important quantum information processing protocols, such as entanglement distillation, is based on the difference in the entanglement content of the quantum states before and after the protocol. In such case
s, effective bounds need to be placed on the entanglement of non-local states consistent with statistics obtained from local measurements. In this work, we study numerically the ability of a novel type of homodyne detector which combines phase sensitivity and photon-number resolution to set accurate bounds on the entanglement content of two-mode quadrature squeezed states without the need for full state tomography. We show that it is possible to set tight lower bounds on the entanglement of a family of two-mode degaussified states using only a few measurements. This presents a significant improvement over the resource requirements for the experimental demonstration of continuous-variable entanglement distillation, which traditionally relies on full quantum state tomography.
Measurement is the only part of a general quantum system that has yet to be characterized experimentally in a complete manner. Detector tomography provides a procedure for doing just this; an arbitrary measurement device can be fully characterized, a
nd thus calibrated, in a systematic way without access to its components or its design. The result is a reconstructed POVM containing the measurement operators associated with each measurement outcome. We consider two detectors, a single-photon detector and a photon-number counter, and propose an easily realized experimental apparatus to perform detector tomography on them. We also present a method of visualizing the resulting measurement operators.
