Multipartite quantum correlation (MQC) not only explains many novel microscopic and macroscopic quantum phenomena, but also holds promise for specific quantum technologies with superiorities. MQCs descriptions and measures have been an open topic, due to their rich and complex organization and structure. Here reconsidering MQC descriptions and their practical applications in some quantum technologies, we propose a novel description called multipartite two-partite QC, which provides an intuitive and clear physical picture. Specifically, we present three types of measures: one class based on minimal entropy-like difference of local measurement fore-and-aft multipartite two-partite density matrix such as multipartite two-partite quantum discord (QD), another class based on minimal trace-like geometric distance such as multipartite two-partite Hilbert-Schmidt Distance (HSD), and a third class based on decoherence such as multipartite two-partite Local Measurement-Induced Minimal Decoherence (LMIMD) and Local Eigen-Measurement-Induced Decoherence (LEMID). Their computations required for these measures are relatively easy. All of the advantages make them promising candidates for specific potential applications in various quantum technologies. Finally, we employ these three types of measures to explore the organization and structure of some typical genuine MQCs, and analyze their relative characteristics based on their physical implications and mathematical structures.
Local measurements cannot create entanglement, but they can convert short-range entanglement to long-range entanglement, as in quantum teleportation. This phenomenon of measurement-induced entanglement (MIE) has been widely discussed in recent work on measurement-induced entanglement phase transitions and related phenomena. Here, we situate MIE in a broader context of the growth of long-range conditional mutual information (CMI) under decoherence. We upper-bound the rate at which decoherence can generate long-range CMI and derive a characterization of states that saturate this bound. We point out that the structure of states saturating the CMI upper bound can be very different under different decoherent dynamics and provide explicit examples. We additionally explore the dynamics of CMI in random quantum circuits subject to random local decoherence, as a function of circuit depth. We argue that the universality class of the finite-depth teleportation transition, and its lower critical dimension, are different for erasures than for measurements.
We propose an extension of the classical Rényi divergences to quantum states through an optimization over probability distributions induced by restricted sets of measurements. In particular, we define the notion of locally-measured Rényi divergences, where the set of allowed measurements originates from variants of locality constraints between (distant) parties
A and
B. We then derive variational bounds on the locally-measured Rényi divergences and systematically discuss when these bounds become exact characterizations. As an application, we evaluate the locally-measured Rényi divergences on variants of highly symmetric data-hiding states, showcasing the reduced distinguishing power of locality-constrained measurements. For
n-fold tensor powers, we further employ our variational formulae to derive corresponding additivity results, which gives the locally-measured Rényi divergences operational meaning as optimal rate exponents in asymptotic locally-measured hypothesis testing.