Scrambling and quantum chaos indicators from long-time properties of operator distributions

Scrambling is a key concept in the analysis of nonequilibrium properties of quantum many-body systems. Most studies focus on its characterization via out-of-time-ordered correlation functions (OTOCs), particularly through the early-time decay of the OTOC. However, scrambling is a complex process which involves operator spreading and operator entanglement, and a full characterization requires one to access more refined information on the operator dynamics at several timescales. In this work we analyze operator scrambling by expanding the target operator in a complete basis and studying the structure of the expansion coefficients treated as a coarse-grained probability distribution in the space of operators. We study different features of this distribution, such as its mean, variance, and participation ratio, for the Ising model with longitudinal and transverse fields, kicked collective spin models, and random circuit models. We show that the long-time properties of the operator distribution display common features across these cases, and discuss how these properties can be used as a proxy for the onset of quantum chaos. Finally, we discuss the connection with OTOCs and analyze the cost of probing the operator distribution experimentally using these correlation functions.Comment: Main text: 14 pages, 7 figures. Appendices: 3 pages, 3 figure

Probing scrambling and operator size distributions using random mixed states and local measurements

The dynamical spreading of quantum information through a many-body system, typically called scrambling, is a complex process that has proven to be essential to describe many properties of out-of-equilibrium quantum systems. Scrambling can, in principle, be fully characterized via the use of out-of-time-ordered correlation functions, which are notoriously hard to access experimentally. In this work, we put forward an alternative toolbox of measurement protocols to experimentally probe scrambling by accessing properties of the operator size probability distribution, which tracks the size of the support of observables in a many-body system over time. Our measurement protocols require the preparation of separable mixed states together with local operations and measurements, and combine the tools of randomized operations, a modern development of near-term quantum algorithms, with the use of mixed states, a standard tool in NMR experiments. We demonstrate how to efficiently probe the probability-generating function of the operator distribution and discuss the challenges associated with obtaining the moments of the operator distribution. We further show that manipulating the initial state of the protocol allows us to directly obtain the individual elements of the distribution for small system sizes

Probing scrambling and operator size distributions using random mixed states and local measurements

The dynamical spreading of quantum information through a many-body system, typically called scrambling, is a complex process that has proven to be essential to describe many properties of out-of-equilibrium quantum systems. Scrambling can, in principle, be fully characterized via the use of out-of-time-ordered correlation functions, which are notoriously hard to access experimentally. In this work, we put forward an alternative toolbox of measurement protocols to experimentally probe scrambling by accessing properties of the operator size probability distribution, which tracks the size of the support of observables in a many-body system over time. Our measurement protocols require the preparation of separable mixed states together with local operations and measurements, and combine the tools of randomized operations, a modern development of near-term quantum algorithms, with the use of mixed states, a standard tool in NMR experiments. We demonstrate how to efficiently probe the probability-generating function of the operator distribution and discuss the challenges associated with obtaining the moments of the operator distribution. We further show that manipulating the initial state of the protocol allows us to directly obtain the individual elements of the distribution for small system sizes

Photoacoustic Sentinel Lymph Node Imaging with Self-Assembled Copper Neodecanoate Nanoparticles

Photoacoustic tomography (PAT) is emerging as a novel, hybrid, and non-ionizing imaging modality because of its satisfactory spatial resolution and high soft tissue contrast. PAT combines the advantages of both optical and ultrasonic imaging methods. It opens up the possibilities for noninvasive staging of breast cancer and may replace sentinel lymph node (SLN) biopsy in clinic in the near future. In this work, we demonstrate for the first time that copper can be used as a contrast metal for near-infrared detection of SLN using PAT. A unique strategy is adopted to encapsulate multiple copies of Cu as organically soluble small molecule complexes within a phospholipid-entrapped nanoparticle. The nanoparticles assumed a size of 80–90 nm, which is the optimum hydrodynamic diameter for its distribution throughout the lymphatic systems. These particles provided at least 6-fold higher signal sensitivity in comparison to blood, which is a natural absorber of light. We also demonstrated that high SLN detection sensitivity with PAT can be achieved in a rodent model. This work clearly demonstrates for the first time the potential use of copper as an optical contrast agent

Photoacoustic Sentinel Lymph Node Imaging with Self-Assembled Copper Neodecanoate Nanoparticles

Photoacoustic tomography (PAT) is emerging as a novel, hybrid, and non-ionizing imaging modality because of its satisfactory spatial resolution and high soft tissue contrast. PAT combines the advantages of both optical and ultrasonic imaging methods. It opens up the possibilities for noninvasive staging of breast cancer and may replace sentinel lymph node (SLN) biopsy in clinic in the near future. In this work, we demonstrate for the first time that copper can be used as a contrast metal for near-infrared detection of SLN using PAT. A unique strategy is adopted to encapsulate multiple copies of Cu as organically soluble small molecule complexes within a phospholipid-entrapped nanoparticle. The nanoparticles assumed a size of 80–90 nm, which is the optimum hydrodynamic diameter for its distribution throughout the lymphatic systems. These particles provided at least 6-fold higher signal sensitivity in comparison to blood, which is a natural absorber of light. We also demonstrated that high SLN detection sensitivity with PAT can be achieved in a rodent model. This work clearly demonstrates for the first time the potential use of copper as an optical contrast agent