Large Scale Entanglement

Entanglement is a key feature of quantum mechanics and has become an important resource in quantum information processing. While quantum mechanics is well established and widely tested at the microscopic level - especially for small systems-, its extensions to larger systems and in particular the macroscopic realm is subject of ongoing research. At a fundamental level, the possibility that macroscopic objects can be in a superposition of two distinct states highlights the counter-intuitive features of quantum mechanics. With the spectacular experimental advances of the last years, investigations of such superposition states and large-scale entangled states has become into reach. Decoherence is believed to play an important role in this context, displaying a fundamental obstacle to observations and possible applications of macroscopically entangled states. This project is concerned with fundamental and practical aspects of large-scale entanglement, where the influence of decoherence on many-body quantum systems shall be investigated. Thereby fundamental questions relating to macroscopic superposition states, in particular their effective size and stability, as well as applications in the context of quantum metrology (parameter estimation) will be considered. Microscopic spin-bath models for decoherence will be studied, focusing on the effects on entanglement and coherence of large-scale systems. Thereby entanglement related effects in the environment, coming from initial state entanglement or interactions will be investigated. In particular, we plan to carry out the following work: Comparison and unification of different measures to assess an effective size of macroscopic quantum superposition states, with applications to different experimental proposals and realizations. Investigation of macroscopic "Schrödinger cat"-type entangled states, including stability studies and possible applications in quantum metrology for parameter estimation beyond the standard quantum limit, when taking noise and imperfections (decoherence) into account. Study of the stability of different multipartite entangled states under decoherence using different decoherence models, including Markovian local noise channels and microscopic spin bath models. For the latter, the influence of different system-environment interactions, couplings within the environment as well as initial states of the environment and environments far from thermal equilibrium will be investigated.

The project has dealt with various aspects of large-scale entanglement. We have considered fundamental questions regarding the validity of quantum mechanics on a macroscopic scale, in particular how to classify, prepare and certify macroscopic quantum superposition states. We have also dealt with possible applications of large-scale entangled states in the context of noisy quantum metrology and in (measurement-based) quantum communication and computation. The results we found include a classification of macroscopicity in terms of certain measures that we introduce. We provide a connection between different measures, thereby paving the way towards a better understanding of what makes a quantum state a macroscopic superposition. We also deal with possible limitations and difficulties of how to prepare and measure such states. We find that preparing and certifying macroscopic superposition states is very fragile under imperfections and noise, rendering this task very challenging, if not experimentally impossible. Quantum error correction and encoding might be a way to circumvent such problems, as we found that there exist large-scale quantum superposition states that are stable under decoherence. For mesoscopic systems, we have established improved strategies to experimentally detect such states with imperfect detectors. A problem of more practical relevance is quantum metrology, i.e. high precision measurements that are enhanced by quantum mechanics. Such measurements play a fundamental role in all natural sciences and beyond. We have established ultimate limits on a possible quantum advantage in realistic situations, i.e. when taking noise and imperfections into account. We have also established ways to deal with certain kinds of noise, using quantum error correction or fast control, and showed that a quantum scaling advantage in the reachable precision can be maintained. We have found optimal states and sensing strategies for different metrological scenarios, which are designed in such a way that they are experimentally accessible. We have also investigated the usage of large-scale entangled states in quantum information processing, where we found that a measurement-based approach --where specific resource states (that we identify) are processed by measurements-- leads to very high error thresholds. In particular, we show that such an approach is applicable to entanglement purification, quantum communication, quantum error correction and fault-tolerant quantum computation, where the acceptable noise per qubit as above 10%. Together with the first experimental demonstrations of these principles, this might have some impact on the future design of quantum communication and computation devices. Additional results include an analysis of what limits the no-signalling principle poses on the optimal performance of quantum mechanical tasks such as cloning or metrology, and the possibility to use an operation N times to deterministically mimic its action on N2 systems.