![]() Quantum refrigeration with indefinite causal order. Enhanced communication with the assistance of indefinite causal order. ![]() Exponential communication complexity advantage from quantum superposition of the direction of communication. Computational advantage from quantum-controlled ordering of gates. Perfect discrimination of no-signalling channels via quantum superposition of causal structures. Quantum correlations with no causal order. Towards quantum gravity: a framework for probabilistic theories with non-fixed causal structure. Quantum computations without definite causal structure. Preprint at (2009).Ĭhiribella, G., D’Ariano, G. Quantum metrology with indefinite causal order. Does nonlinear metrology offer improved resolution? Answers from quantum information theory. Optimal Heisenberg-style bounds for the average performance of arbitrary phase estimates. Ultimate limits to quantum metrology and the meaning of the Heisenberg limit. Interaction-based quantum metrology showing scaling beyond the Heisenberg limit. General optimality of the Heisenberg limit for quantum metrology. Bose-Einstein condensate as a nonlinear Ramsey interferometer operating beyond the Heisenberg limit. Exponentially enhanced quantum metrology. Generalized limits for single-parameter quantum estimation. Breaking the Heisenberg limit with inefficient detectors. ![]() Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit. Achieving Heisenberg-scaling precision with projective measurement on single photons. Heisenberg-scaling measurement of the single-photon Kerr non-linearity using mixed states. High-NOON states by mixing quantum and classical light. De Broglie wavelength of a non-local four-photon state. Optimal frequency measurements with maximally correlated states. Quantum-enhanced measurements: beating the standard quantum limit. Our experiment features the demonstration of indefinite causal order in a continuous-variable system, and opens up the experimental investigation of quantum metrology setups boosted by indefinite causal order. Using a superposition of causal orders outperforms every setup where the displacements are probed in a definite order. Our results only require a single-photon probe with an initial energy that is independent of N. Each process creates a phase-space displacement, and our setup is able to estimate a geometric phase associated with two sets of N displacements with an error that falls quadratically with N. Here we present a photonic implementation of a quantum metrology protocol surpassing the Heisenberg limit by probing two groups of independent processes in a superposition of two alternative causal orders. However, these proposals turned out to still obey the Heisenberg limit with respect to other relevant resources, such as the total energy of the probes. In the past, some proposals have challenged this belief, for example, using nonlinear interactions among the probes. The precision of quantum metrology is widely believed to be restricted by the Heisenberg limit, corresponding to a root mean square error that is inversely proportional to the number of independent processes probed in an experiment, N.
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