On the Power of Quantum Computation
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Computing with highly mixed states (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Quantum computation and quantum information
Quantum computation and quantum information
Speed-up and entanglement in quantum searching
Quantum Information & Computation
Quantum advantage without entanglement
Quantum Information & Computation
The Deutsch---Jozsa problem: de-quantisation and entanglement
Natural Computing: an international journal
A study of quantum correlations in open quantum systems
Quantum Information & Computation
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It is generally believed that entanglement is essential for quantum computing. We present here a few simple examples in which quantum computing without entanglement is better than anything classically achievable, in terms of the reliability of the outcome after a fixed number of oracle calls. Using a separable (that is, unentangled) state, we show that the Deutsch-Jozsa problem and the Simon problem can be solved more reliably by a quantum computer than by the best possible classical algorithm, even probabilistic. We conclude that: (a) entanglement is not essential for quantum computing; and (b) some advantage of quantum algorithms over classical algorithms persists even when the quantum state contains an arbitrarily small amount of information--that is, even when the state is arbitrarily close to being totally mixed.