 Deutsch’s example shows how quantum information and quantum entanglement can be exploited to compute a disjunctive or global property of a function in one step that would take two steps classically. While Deutsch’s problem is rather trivial, there now exist several quantum algorithms with interesting applications, notably Shor’s factorization algorithm for factoring large composite integers in polynomial time (with direct application to ‘public key’ cryptography, a widely used classical cryptographic scheme) and Grover’s database search algorithm. Shor’s algorithm achieves an exponential speed-up over any known classical algorithm. For algorithms that are allowed access to oracles (whose internal structure is not considered), the speed-up can be shown to be exponential over any classical algorithm in some cases, e.g., Simon’s algorithm. See Nielsen and Chuang 2000, Barenco’s article “Quantum Computation: An Introduction” in Lo, Popescu, and Spiller 1998, Bub 2006 (Section 6), as well as the entry on  quantum computing.