Path entanglement is a key resource for quantum metrology. Using path-entangled states, the standard quantum limit can be beaten and the Heisenberg limit can be achieved. However, the preparation and detection of such states scales unfavourably with the number of photons. Here we introduce sequential path entanglement, in which photons are distributed across distinct time bins with arbitrary separation, as a resource for quantum metrology. We demonstrate a scheme for converting polarization Greenberger-Horne-Zeilinger entanglement into sequential path entanglement. We observe the same enhanced phase resolution expected for conventional path entanglement, independent of the delay between consecutive photons. Sequential path entanglement can be prepared comparably easily from polarization entanglement, can be detected without using photon-number-resolving detectors and enables novel applications.
Path entanglement is a key resource for quantum metrology. Using path-entangled states, the standard quantum limit can be beaten and the Heisenberg limit can be achieved. However, the preparation and detection of such states scales unfavourably with the number of photons. Here we introduce sequential path entanglement, in which photons are distributed across distinct time bins with arbitrary separation, as a resource for quantum metrology. We demonstrate a scheme for converting polarization Greenberger-Horne-Zeilinger entanglement into sequential path entanglement. We observe the same enhanced phase resolution expected for conventional path entanglement, independent of the delay between consecutive photons. Sequential path entanglement can be prepared comparably easily from polarization entanglement, can be detected without using photon-number-resolving detectors and enables novel applications.
We introduce the concept of entanglement enhanced interferometry from the viewpoint of the detected photons. The standard quantum limit is achieved when sequentially detected photons are assumed to be in an uncorrelated product state. However when we access the correlations between the detected photons that existed before the interferometer it becomes clear that entanglement enhanced measurement beyond the quantum limit could be achieved independent of loss. We describe possible realisations of this post-measurement entanglement detection using a small array of spin photon entangling gates. We then describe a proof of principle experiment using only linear optics resources.
We introduce a super-sensitive phase measurement technique that yields the Heisenberg limit without using either a squeezed state or a many-particle entangled state. Instead, we use a many-particle separable quantum state to probe the phase and we then retrieve the phase through single-particle interference. The particles that physically probe the phase are never detected. Our scheme involves no coincidence measurement or many-particle interference and yet exhibits phase super-resolution. We also analyze in detail how the loss of probing particles affects the measurement sensitivity and find that the loss results in the generation of many-particle entanglement and the reduction of measurement sensitivity. When the loss is maximum, the system produces a many-particle Greenberger-Horne-Zeilinger (GHZ) state, and the phase measurement becomes impossible due to very high phase uncertainty. In striking contrast to the super-sensitive phase measurement techniques that use entanglement involving two or more particles as a key resource, our method shows that having many-particle entanglement can be counterproductive in quantum metrology.
Quantum number-path entanglement is a resource for supersensitive quantum metrology and in particular provides for sub-shot-noise or even Heisenberg-limited sensitivity. However, such number-path entanglement is thought to have been resource intensive to create in the first place, typically requiring either very strong nonlinearities or nondeterministic preparation schemes with feedforward, which are difficult to implement. Recently [K. R. Motes et al., Phys. Rev. Lett. 114, 170802 (2015)], it was shown that number-path entanglement from a BosonSampling inspired interferometer can be used to beat the shot-noise limit. In this paper we compare and contrast different interferometric schemes, discuss resource counting, calculate exact quantum Cram\'er-Rao bounds, and study details of experimental errors.
Quantum number-path entanglement is a resource for supersensitive quantum metrology and in particular provides for sub-shot-noise or even Heisenberg-limited sensitivity. However, such number-path entanglement has been thought to be resource intensive to create in the first place--typically requiring either very strong nonlinearities, or nondeterministic preparation schemes with feedforward, which are difficult to implement. Very recently, arising from the study of quantum random walks with multiphoton walkers, as well as the study of the computational complexity of passive linear optical interferometers fed with single-photon inputs, it has been shown that such passive linear optical devices generate a superexponentially large amount of number-path entanglement. A logical question to ask is whether this entanglement may be exploited for quantum metrology. We answer that question here in the affirmative by showing that a simple, passive, linear-optical interferometer--fed with only uncorrelated, single-photon inputs, coupled with simple, single-mode, disjoint photodetection--is capable of significantly beating the shot-noise limit. Our result implies a pathway forward to practical quantum metrology with readily available technology.
High-precision measurement of oscillating signal is a ubiquitous issue in fundamental science and a critical task in practical technologies. In quantum metrology, quantum lock-in detection provide an efficient method for measuring such signal. In general, when the initial phase of the oscillating signal is unknown,quantum double lock-in detection can effectively extract complete information about the signal's amplitude, frequency, and initial phase. Conventional quantum double lock-in detection requires two individual quantum interferometry, each of which must undergo state preparation and readout. However, the time for state preparation and readout need not be negligible in practical experiments. In particular, the time for state preparation is longer than the time for sensing. To save experimental resources, it is challenging to achieve quantum double lock-in detection just via a single quantum interferometry while still extracting complete information about the signal's amplitude, frequency, and initial phase. Here, we present a general protocol for achieving a quantum double lock-in detection just via a single quantum interferometry under a sequential orthogonal periodic multipulse sequences. In particular, if the input state is a Greenberger-Horne-Zeilinger state and two interaction-based operations are applied during interferometry, the measurement precisions for frequency, amplitude, and initial phase can both approach the Heisenberg limit. Our study paves a new way for measuring oscillating signals with a single quantum interferometry, and provides a feasible method for achieving Heisenberg-limited detection of alternating signals.
Quantum metrology enables parameter estimation beyond classical limits by exploiting nonclassical resources such as squeezing and entanglement. In distributed quantum sensing, Heisenberg scaling has been extended from 1/N2 to 1/(NM)2 through entanglement across both particles and spatial modes, where N denotes the photon number and M the number of spatially distributed modes. However, the overall sensitivity has remained limited to linear scaling with the number of measurement repetitions R. Here, we show that exploiting entanglement across temporal modes via time-domain multiplexing enables a scaling advantage with respect to R. As a result, the sensitivity can asymptotically approach simultaneous Heisenberg scaling in photons, spatial modes, and repetitions, yielding an overall sensitivity approaching Δ2φ∝1/(NMR)2. Using the Bogoliubov transformation formalism, we prove the optimality of the protocol within the class of Gaussian states and show that the scaling is realizable via homodyne detection and maximum-likelihood estimation. We further show that the advantage persists under optical loss and propose an experimentally feasible loop-based photonic sensing scheme. Our results open a route to incorporating time-multiplexing techniques into quantum metrology.