A class of problems is described which can be solved more efficiently by quantum computation than by any classical or stochastic method. The quantum computation solves the problem with certainty in… Expand

The class post-IQP of languages decided with bounded error by uniform families of IQP circuits with post-selection is introduced, and it is proved first that post- IQP equals the classical class PP, and that if the output distributions of uniform IQP circuit families could be classically efficiently sampled, then the infinite tower of classical complexity classes known as the polynomial hierarchy would collapse to its third level.Expand

Abstract We propose a definition of fidelity for mixed quantum states in terms of Uhlmann's ‘transition probability’ formula F(ϱ1, ϱ2) = {trace [(√ϱ1ϱ2 × √ϱ1)1/2]}2 and give new elementary proofs of… Expand

We give an explicit characterisation of the quantum states which saturate the strong subadditivity inequality for the von Neumann entropy. By combining a result of Petz characterising the equality… Expand

It is argued that it is nevertheless misleading to view entanglement as a key resource for quantum‐computational power, as it is necessary for any quantum algorithm to offer an exponential speed‐up over classical computation.Expand

Let G(A, B) denote the two-qubit gate that acts as the one-qubit SU(2) gates A and B in the even and odd parity subspaces, respectively, of two qubits. Using a Clifford algebra formalism, we show… Expand

An unknown quantum state ji can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical EPR correlations. To do so the sender, \Alice," and the… Expand

The authors give an exposition of Shor's algorithm together with an introduction to quantum computation and complexity theory, and discuss experiments that may contribute to its practical implementation.Expand

An account of the quantum noiseless coding theorem, including a new proof based on a simplified block coding scheme, and an illustrative example of quantum coding.Expand