Controlled Quantum Amplification

We propose a new framework for turning quantum search algorithms that decide into quantum algorithms for finding a solution. Consider we are given an abstract quantum search algorithm A that can determine whether a target g exists or not. We give a general construction of another operator U that both determines and finds the target, whenever one exists. Our amplification method at most doubles the cost over using A, has little overhead, and works by controlling the evolution of A. This is the first known general framework to the open question of turning abstract quantum search algorithms into quantum algorithms for finding a solution. We next apply the framework to random walks. We develop a new classical algorithm and a new quantum algorithm for finding a unique marked element. Our new random walk finds a unique marked element using H update operations and 1/eps checking operations. Here H is the hitting time, and eps is the probability that the stationary distribution of the walk is in the marked state. Our classical walk is derived via quantum arguments. Our new quantum algorithm finds a unique marked element using H^(1/2) update operations and 1/eps^(1/2) checking operations, up to logarithmic factors. This is the first known quantum algorithm being simultaneously quadratically faster in both parameters. We also show that the framework can simulate Grover\u27s quantum search algorithm, amplitude amplification, Szegedy\u27s quantum walks, and quantum interpolated walks

Quantum privacy amplification and the security of quantum cryptography over noisy channels

Existing quantum cryptographic schemes are not, as they stand, operable in the presence of noise on the quantum communication channel. Although they become operable if they are supplemented by classical privacy-amplification techniques, the resulting schemes are difficult to analyse and have not been proved secure. We introduce the concept of quantum privacy amplification and a cryptographic scheme incorporating it which is provably secure over a noisy channel. The scheme uses an `entanglement purification' procedure which, because it requires only a few quantum Controlled-Not and single-qubit operations, could be implemented using technology that is currently being developed. The scheme allows an arbitrarily small bound to be placed on the information that any eavesdropper may extract from the encrypted message.Comment: 13 pages, Latex including 2 postcript files included using psfig macro

Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics

We experimentally demonstrate a nonlinear detection scheme exploiting time-reversal dynamics that disentangles continuous variable entangled states for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is used as the nonlinear mechanism which not only generates entangled states but can also be time reversed by controlled phase imprinting. For demonstration of a quantum-enhanced measurement we construct an active atom SU(1,1) interferometer, where entangled state preparation and nonlinear readout both consist of parametric amplification. This scheme is capable of exhausting the quantum resource by detecting solely mean atom numbers. Controlled nonlinear transformations widen the spectrum of useful entangled states for applied quantum technologies.Comment: 9 pages, 3 figures, 3 pages supplementary material, 2 supplementary figure

Coulomb-coupled quantum-dot thermal transistors

A quantum-dot thermal transistor consisting of three Coulomb-coupled quantum dots coupled to respective electronic reservoirs by tunnel contacts is established. The heat flows through the collector and emitter can be controlled by the temperature of the base. It is found that a small change in the base heat flow can induce a large heat flow change in the collector and emitter. The huge amplification factor can be obtained by optimizing the Coulomb interaction between the collector and the emitter or by decreasing the energy-dependent tunneling rate at the base. The proposed quantum-dot thermal transistor may open up potential applications in low-temperature solid-state thermal circuits at the nanoscale.Comment: 14 pages, 6 figure