Entanglement is an essential resource for quantum communication and quantum computation, similar to shared random bits in the classical world. Entanglement distillation extracts nearly-perfect entanglement from imperfect entangled state. The classical communication complexity of these protocols is the minimal amount of classical information that needs to be exchanged for the ... more >>>

We introduce the problem of *shadow tomography*: given an unknown D-dimensional quantum mixed state \rho, as well as known two-outcome measurements E_{1},\ldots,E_{M}, estimate the probability that E_{i} accepts \rho, to within additive error \varepsilon, for each of the M measurements. How many copies of \rho are needed to achieve this, ... more >>>