Quantum enhanced positioning and clock synchronization

A wide variety of positioning and ranging procedures are based on repeatedly sending electromagnetic pulses through space and measuring their time of arrival. This paper shows that quantum entanglement and squeezing can be employed to overcome the classical power/bandwidth limits on these procedures, enhancing their accuracy. Frequency entangled pulses could be used to construct quantum positioning systems (QPS), to perform clock synchronization, or to do ranging (quantum radar): all of these techniques exhibit a similar enhancement compared with analogous protocols that use classical light. Quantum entanglement and squeezing have been exploited in the context of interferometry, frequency measurements, lithography, and algorithms. Here, the problem of positioning a party (say Alice) with respect to a fixed array of reference points will be analyzed.Comment: 4 pages, 2 figures. Accepted for publication by Natur

Entanglement-free Heisenberg-limited phase estimation

Measurement underpins all quantitative science. A key example is the measurement of optical phase, used in length metrology and many other applications. Advances in precision measurement have consistently led to important scientific discoveries. At the fundamental level, measurement precision is limited by the number N of quantum resources (such as photons) that are used. Standard measurement schemes, using each resource independently, lead to a phase uncertainty that scales as 1/sqrt(N) - known as the standard quantum limit. However, it has long been conjectured that it should be possible to achieve a precision limited only by the Heisenberg uncertainty principle, dramatically improving the scaling to 1/N. It is commonly thought that achieving this improvement requires the use of exotic quantum entangled states, such as the NOON state. These states are extremely difficult to generate. Measurement schemes with counted photons or ions have been performed with N <= 6, but few have surpassed the standard quantum limit and none have shown Heisenberg-limited scaling. Here we demonstrate experimentally a Heisenberg-limited phase estimation procedure. We replace entangled input states with multiple applications of the phase shift on unentangled single-photon states. We generalize Kitaev's phase estimation algorithm using adaptive measurement theory to achieve a standard deviation scaling at the Heisenberg limit. For the largest number of resources used (N = 378), we estimate an unknown phase with a variance more than 10 dB below the standard quantum limit; achieving this variance would require more than 4,000 resources using standard interferometry. Our results represent a drastic reduction in the complexity of achieving quantum-enhanced measurement precision.Comment: Published in Nature. This is the final versio

De Broglie Wavelength of a Nonlocal Four-Photon

Superposition is one of the most distinct features of quantum theory and has been demonstrated in numerous realizations of Young's classical double-slit interference experiment and its analogues. However, quantum entanglement - a significant coherent superposition in multiparticle systems - yields phenomena that are much richer and more interesting than anything that can be seen in a one-particle system. Among them, one important type of multi-particle experiments uses path-entangled number-states, which exhibit pure higher-order interference and allow novel applications in metrology and imaging such as quantum interferometry and spectroscopy with phase sensitivity at the Heisenberg limit or quantum lithography beyond the classical diffraction limit. Up to now, in optical implementations of such schemes lower-order interference effects would always decrease the overall performance at higher particle numbers. They have thus been limited to two photons. We overcome this limitation and demonstrate a linear-optics-based four-photon interferometer. Observation of a four-particle mode-entangled state is confirmed by interference fringes with a periodicity of one quarter of the single-photon wavelength. This scheme can readily be extended to arbitrary photon numbers and thus represents an important step towards realizable applications with entanglement-enhanced performance.Comment: 19 pages, 4 figures, submitted on November 18, 200

Manipulation of multiphoton entanglement in waveguide quantum circuits

On-chip integrated photonic circuits are crucial to further progress towards quantum technologies and in the science of quantum optics. Here we report precise control of single photon states and multiphoton entanglement directly on-chip. We manipulate the state of path-encoded qubits using integrated optical phase control based on resistive elements, observing an interference contrast of 98.2 plusminus 0.3%. We demonstrate integrated quantum metrology by observing interference fringes with two- and four-photon entangled states generated in a waveguide circuit, with respective interference contrasts of 97.2 plusminus 0.4% and 92 plusminus 4%, sufficient to beat the standard quantum limit. Finally, we demonstrate a reconfigurable circuit that continuously and accurately tunes the degree of quantum interference, yielding a maximum visibility of 98.2 plusminus 0.9%. These results open up adaptive and fully reconfigurable photonic quantum circuits not just for single photons, but for all quantum states of light