Interplay between entanglement and non-stabilizerness in quantum many-body systems

Speaker's Name: Barbara Jasser
Speaker's Affiliation: Scuola Superiore Meridionale
Speaker's Research Theme(s): Mathematical Physics, Quantum information and metrology
Abstract:
The first layer of quantumness in a many-body quantum state is embodied by entanglement, the resource for quantum correlations. However, when addressing quantum complexity, entanglement alone is not sufficient. One must go beyond, and consider the so-called non-stabilizerness (also known as magic), the resource that quantifies deviations from the Clifford theory, characterizing operations that are essential for universal computation. It is well known that a state can be maximally entangled yet classically simulable, as in the case of stabilizer states, as shown by the Gottesman–Knill theorem. On the other hand, states with low entanglement but high magic can still be simulated efficiently using tensor network techniques, such as matrix product states (MPS). Hence, the interplay between entanglement and non-stabilizerness is crucial to understand the emergence of quantum complexity in many-body systems. In this talk, we show how the antiflatness of the entanglement spectrum is related to both entanglement and magic, and we will present suitable quantifiers for this property. Finally, we will discuss how these quantities behave in the eigenstates of the Sachdev–Ye–Kitaev (SYK) model, a paradigmatic example of a maximally chaotic quantum system.

Venue: Physics C29