Entanglement Theory Beyond the Paradigm of Single-Copy Entanglement Characterization

Lisa T. Weinbrenner, Klára Baksová, Sophia Denker +4 more

Quantum correlations in the form of entanglement, quantum steering or Bell nonlocality are resources for various information-processing tasks, but their detailed quantification and characterization remains complicated. One counter-intuitive effect is the phenomenon of superactivation, meaning that two copies of a quantum state may exhibit forms of correlations which are absent on the single-copy level. We develop a systematic approach towards a full understanding of this phenomenon using the paradigm of genuine multipartite entanglement. We introduce systematic methods for studying superactivation of entanglement based on symmetries and generalized notions of multipartite distillability. With this, we present novel criteria for superactivation as well as a quantitative theory of it. Moreover, we present evidence for incompressible entanglement on multi-copy systems, which cannot be reduced to the single-copy level.

Hayata Yamasaki, Simon Morelli, Markus Miethlinger +3 more

Entanglement shared among multiple parties presents complex challenges for the characterisation of different types of entanglement. One of the most fundamental insights is the fact that some mixed states can feature entanglement across every possible cut of a multipartite system yet can be produced via a mixture of states separable with respect to different partitions. To distinguish states that genuinely cannot be produced from mixing such partition-separable states, the term genuine multipartite entanglement was coined. All these considerations originate in a paradigm where only a single copy of the state is distributed and locally acted upon. In contrast, advances in quantum technologies prompt the question of how this picture changes when multiple copies of the same state become locally accessible. Here we show that multiple copies unlock genuine multipartite entanglement from partially separable states, i.e., mixtures of the partition-separable states, even from undistillable ensembles, and even more than two copies can be required to observe this effect. With these findings, we characterise the notion of genuine multipartite entanglement in the paradigm of multiple copies and conjecture a strict hierarchy of activatable states and an asymptotic collapse of the hierarchy.

Mahmoud Abdel‐Aty

Allen Liu

Understanding and harnessing the power of quantum systems has the potential to transform many domains in science and technology. However, before we can achieve these aspirations, we must first build a better understanding of how quantum systems fundamentally behave. In this thesis, we approach this question through the lens of learning theory to develop new paradigms for learning about quantum systems and understanding their structural properties. We deliver several surprising results, upending previous beliefs about even fundamental laws and giving provably efficient algorithms for learning about quantum systems in settings previously conjectured to be intractable. Typically in quantum many-body systems, the particles in the system interact locally with respect to some geometry as described by a local Hamiltonian. Two key questions are first, understanding equilibrium properties of a system with a given Hamiltonian and second, recovering the Hamiltonian from measurements of the properties of the system. For the first, we prove a universal law that there is a sudden death of entanglement, at a critical temperature depending only on the geometry but not on the system size. For the second, we give the first efficient algorithm for recovering the Hamiltonian at any temperature, breaking a conjectured barrier at low temperatures. Beyond systems with local interactions, we also consider learning and testing properties of general quantum states, focusing on the interplay between statistical complexity and near-term quantum device constraints, only allowing for entangled measurements over a limited number of copies of the state. We characterize the optimal rates for learning and testing with single-copy measurements and for multi-copy measurements in many relevant near-term regimes.

Paweł Masiak, P. L. Knight