Bok av Mark M. Wilde. Tanker og notater: - Introduksjonen av [[Den første kvanterevolusjonen]] er nyttig inspo til skriving av [[Den Andre Kvanterevolusjonen]]. - [[Shannon's bit entropy measures our surprise at an outcome]] ### Konsepter Gjør til eviggrønne notater etter hvert. - Fidelity - Trace distance: [[Trace-avstand]] - Typical subspace - Kvanteanalog til Shannons "typical set", introdusert av Schumacher - Schumacher compression - Kvanteanalog til Shannon compression - Schumachers 1995 paper om dette var faktisk der begrepet "qubit" ble introdusert. (p.23) - HSW coding - How much classical information can be transmitted through a noisy quantum channel? - p.16: "The HSW coding theorem is one quantum generalization of Shannon's channel coding theorem." - Finnes også en generalisering av teoremet hvor partene deler [[Sammenfiltring]]; dette gir generelt høyere kapasitet. Kjent som *entanglement-assisted classical communication*. - Quantum channel capacity theorem - Lower bound: LSD coding theorem. - Characterizes the *highest* rate at which perfectly-recoverable quantum information can be sent over a noisy quantum channel. - "The rate is generally lower than the classical capacity because it is more difficult to keep quantum information intact." - p.17: "The LSD coding theorem does not refer to the synthetic crystalline compound, lysergic acid diethylamide (which one may potentially use as a hallucinogenic drug), but refersnrather to Lloyd (1997), Shor (2002b), and Devetak (2005), all of whom gave separate proofs of the lower bound on the quantum capacity with increasing standards of rigor." - "One goal of this book is to unravel the mathematical machinery behind Devetak's proof of the quantum channel coding theorem." Indeed: "All efforts and technical developments in preceding chapters have this goal in mind." Teoremet blir endelig diskutert i kap. 24 av 26, og beskrives som "the pinnacle of this book". - Holevo bound - Roughly: It is not possible to transmit more than one cbit per qubit while maintaining reliable decoding. - (... Uten [[Sammenfiltring]]—med dette får vi så klart Superdense coding.) - Generalisert av div entropy bounds, som "the strong subadditivity of quantum entropy" og "the monotonicity of quantum relative entropy" (p.20). - Dog introdusert i 1973, var det først på slutten av 90-tallet at "the Holevo information of a quantum channel is an achievable rate for classical communication over it." - Super-dense coding - oppdaget av Bennett og Wiesner først i 1992! - "This protocol consumes one noiseless ebit of entanglement and one noiseless qubit channel to to simulate two noiseless classical bit channels." - "The next year, Bennett and some other coauthors reversed the operations in the super-dense coding protocol to devise a protocol that has more profound implications." Det var så klart... - [[Kvanteteleportering]] - "This protocol consumes two classical bit channels and one ebit to transmit a qubit from a sender to a receiver." - Conditional quantum entropy - (p.24) Horodecki, Oppenheim, and Winter in 2005/2007 gave this notion an operational interpretation by showing that a protocol in which Alice akd Bob consume noiseless qubits in order for Alice to send her share of a quantum state to Bob has exactly the conditional quantum entropy as its qubit consumption rate. - "What was most fascinating about this result is that the conditional quantum entropy can be negative in quantum Shannon theory. Prior to their work, no one really understood what it meant for the conditional quantum entropy to become negative, but this state-mergonf result gave a compelling operational interpretation. A negative rate implies that Alice and Bob gain the ability for future quantum communication, instead of consuming quantum communication as when the rate is positive." - Superactivation - Selv om to kvantekanaler individuelt har null kapasitet, kan de samlet ha positiv kapasitet. Dette ble vist i 2008. (p.24) - "It is not clear yet how we might practically take advantage of such a 'superactivation' effect, but the result is nonetheless fascinating, counterintuitive, and not yet fully understood." ### Flere sitater p.14: > We have more knowledge of the system in question if we gain less information from performing measurements on it. (...) Is there a measurement that we can perform in which we learn the least amount of information? Recall that learning the least amount of information is ideal because it has the interpretation that we require fewer questions on average to learn the result of a random experiment. Kontraintuitivt! p.15: > One measure, the *fidelity*, has the operational interpretation that it gives the probability that one quantum state would pass a test for being another. The *trace distance* is another distance measure that is perhaps more similar to a classical distance measure—its classical analog is a measure of the closeness of two probability distributions. p.17: > There are strong connections between the goals of keeping classical information private and keeping quantum information coherent. Det gir jo mening—minner om den gamle idéen min om at "dersom jeg hadde en magisk knapp som automatisk ga meg kunnskapen om hvor et partikkel er, uten å behøve å måle det, så ville bølgefunksjonen likevel kollapset." (Fordi, skjønner jeg nå, mange år senere, å lære hvor partikkelet er er å sammenfiltres med tilstanden.) Continuing, om at man kan tenke på sammenhengen som at omgivelsene "lærer" om kvantetilstandene: > This effect is related to the information-disturbance trade-off that is fundamental in quantum information theory. (...) The role of the environment in quantum coding is similar to the role of the eavesdropper in private coding, and the goal in both scenarios is to decouple either the environment or eavesdropper from the picture. (...) In fact, we can say that the quantum code inherits its structure from that of the private code Om Wiesners [[Kvantepenger]]: > This work was *way* ahead of its time