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Computation and metrology with cold atoms in mixed states

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The use of Rydberg interactions and ensembles of cold atoms in mixed state for the implementation of a protocol for deterministic quantum computation with one quantum bit (DQC1 [1]) is discussed. This protocol relies on one pure control qubit together with a register of completely-mixed qubits. DQC1 is a non-universal model that can speed up some computational tasks for which no efficient classical algorithms are known. Whilst requiring only a single qubit with coherence, for these specific tasks, its power scales up with the number of qubits in a mixed state. Although it has been shown that this scheme contains little to no entanglement, non-classical correlations are present in the output state of the DQC1 which can be quantified in terms of quantum discord. To date, successful experiments based on DQC1 have evaluated the normalised trace of a two-by-two unitary matrix [2] and performed the approximation to the Jones polynomial with a system of four qubits, thus demonstrating the ground principle of mixed state computation. We propose an experimental test for the true scalability of the protocol based on cold atoms and Ryderg interactions and to study the physics of discord, as well as the strategy for extending to non-trivial problems [3], such as many-body physics. A scheme is also presented for quantum phase estimation. This is derived from the DQC1 model and promises to enable quantum enhanced measurement, without relying on quantum entanglement and only using discord in the probe states [4]. Modelling of this scheme, using cold atoms in dipole traps, demonstrates that the register of partly mixed qubits becomes a powerful resource for phase estimation when supplied with the coherence from the control qubit.

References [1] Knill E and Laflamme R 1998 Power of one bit of quantum information Phys. Rev. Lett. 81, 5672 (1998)

[2] Lanyon B P , Barbieri M, Almeida M P and White A G 2008 Experimental quantum computing without entanglement Phys. Rev. Lett. 101 200501 (2008)

[3] C W Mansell, S Bergamini A cold-atoms based processor for deterministic quantum computation with one qubit in intractably large Hilbert spaces New J. Phys. 16 053045 (2014)

[4] Modi K, Cable H, Williamson M and Vedral V 2011 Quantum correlations

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