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Quantum enhancements of precision in metrology can be compromised by system imperfections. These may be mitigated by appropriate optimization of the input state to render it robust, at the expense of making the state difficult to prepare. In this paper, we identify the major sources of imperfection an optical sensor: input state preparation inefficiency, sensor losses, and detector inefficiency. The second of these has received much attention; we show that it is the least damaging to surpassing the standard quantum limit in a optical interferometric sensor. Further, we show that photonic states that can be prepared in the laboratory using feasible resources allow a measurement strategy using photon-number-resolving detectors that not only attains the Heisenberg limit for phase estimation in the absence of losses, but also deliver close to the maximum possible precision in realistic scenarios including losses and inefficiencies. In particular, we give bounds for the trade off between the three sources of imperfection that will allow true quantum-enhanced optical metrology.
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Weak value amplification (WVA) is a metrological protocol that amplifies ultra-small physical effects. However, the amplified outcomes necessarily occur with highly suppressed probabilities, leading to the extensive debate on whether the overall measurement precision is improved in comparison to that of conventional measurement (CM). Here, we experimentally demonstrate the unambiguous advantages of WVA that overcome practical limitations including noise and saturation of photo-detection and maintain a shot-noise-scaling precision for a large range of input light intensity well beyond the dynamic range of the photodetector. The precision achieved by WVA is six times higher than that of CM in our setup. Our results clear the way for the widespread use of WVA in applications involving the measurement of small signals including precision metrology and commercial sensors.
The impact of measurement imperfections on quantum metrology protocols has been largely ignored, even though these are inherent to any sensing platform in which the detection process exhibits noise that neither can be eradicated, nor translated onto the sensing stage and interpreted as decoherence. In this work, we approach this issue in a systematic manner. Focussing firstly on pure states, we demonstrate how the form of the quantum Fisher information must be modified to account for noisy detection, and propose tractable methods allowing for its approximate evaluation. We then show that in canonical scenarios involving $N$ probes with local measurements undergoing readout noise, the optimal sensitivity dramatically changes its behaviour depending whether global or local control operations are allowed to counterbalance measurement imperfections. In the former case, we prove that the ideal sensitivity (e.g. the Heisenberg scaling) can always be recovered in the asymptotic $N$ limit, while in the latter the readout noise fundamentally constrains the quantum enhancement of sensitivity to a constant factor. We illustrate our findings with an example of an NV-centre measured via the repetitive readout procedure, as well as schemes involving spin-1/2 probes with bit-flip errors affecting their two-outcome measurements, for which we find the input states and control unitary operations sufficient to attain the ultimate asymptotic precision.
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.
We discuss the effects of imperfect photon detectors suffering from loss and noise on the reliability of linear optical quantum computers. We show that for a given detector efficiency, there is a maximum achievable success probability, and that increasing the number of ancillary photons and detectors used for one controlled sign flip gate beyond a critical point will decrease the probability that the computer will function correctly. We have also performed simulations of some small logic gates and estimate the efficiency and noise levels required for the linear optical quantum computer to function properly.
Quantum technologies exploit entanglement to revolutionize computing, measurements, and communications. This has stimulated the research in different areas of physics to engineer and manipulate fragile many-particle entangled states. Progress has been particularly rapid for atoms. Thanks to the large and tunable nonlinearities and the well developed techniques for trapping, controlling and counting, many groundbreaking experiments have demonstrated the generation of entangled states of trapped ions, cold and ultracold gases of neutral atoms. Moreover, atoms can couple strongly to external forces and light fields, which makes them ideal for ultra-precise sensing and time keeping. All these factors call for generating non-classical atomic states designed for phase estimation in atomic clocks and atom interferometers, exploiting many-body entanglement to increase the sensitivity of precision measurements. The goal of this article is to review and illustrate the theory and the experiments with atomic ensembles that have demonstrated many-particle entanglement and quantum-enhanced metrology.
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