One of the main challenges of quantum information is the reliable verification of quantum entanglement. The conventional detection schemes require repeated measurement on a large number of identically prepared systems. This is hard to achieve in practice when dealing with large-scale entangled quantum systems. In this letter we formulate verification as a decision procedure, i.e. entanglement is seen as the ability of quantum system to answer certain "yes-no questions". We show that for a variety of large quantum states even a single copy suffices to detect entanglement with a high probability by using local measurements. For example, a single copy of a 16-qubit k-producible state or one copy of 24-qubit linear cluster state suffices to verify entanglement with more than 95% confidence. Our method is applicable to many important classes of states, such as cluster states or ground states of local Hamiltonians in general.

Many future quantum technologies rely on the generation of entangled states. Quantum devices will require verification of their operation below some error threshold, but the reliable detection of quantum entanglement remains a considerable challenge for large-scale quantum systems. Well-established techniques for this task rely on the measurement of expectation values of entanglement witnesses, which however require many measurements settings to be extracted. Here we develop a generic framework for efficient entanglement detection that translates any entanglement witness into a resource-efficient probabilistic scheme, whose confidence grows exponentially with the number of individual detection events, namely copies of the quantum state. To benchmark our findings, we experimentally verify the presence of entanglement in a photonic six-qubit cluster state generated using three single-photon sources operating at telecommunication wavelengths. We find that the presence of entanglement can be certified with at least 99:74% confidence by detecting 20 copies of the quantum state. Additionally, we show that genuine six-qubit entanglement is verified with at least 99% confidence by using 112 copies of the state. Our protocol can be carried out with a remarkably low number of copies and in the presence of experimental imperfections, making it a practical and applicable method to verify large-scale quantum devices.

We study the fundamental limits of noise spectroscopy using estimation theory, Faraday rotation probing of an atomic spin system, and squeezed light. We find a simple and general expression for the Fisher information, which quantifies the sensitivity to spectral parameters such as resonance frequency and linewidth. For optically-detected spin noise spectroscopy, we find that shot noise imposes "local" standard quantum limits for any given probe power and atom number, and also "global" standard quantum limits when probe power and atom number are taken as free parameters. We confirm these estimation theory results using non-destructive Faraday rotation probing of hot Rb vapor, observing the predicted optima and finding good quantitative agreement with a firstprinciples calculation of the spin noise spectra. Finally, we show sensitivity beyond the atom-and photon-number-optimized global standard quantum limit using squeezed light. , and quantum information processing [12][13][14][15][16]. By the fluctuation-dissipation theorem, the noise spectrum under thermal equilibrium gives the same information as do driven spectroscopies, with the advantage of characterizing the system in its natural, undisturbed state [17]. Understanding the statistical sensitivity of noise spectroscopy is essential for rigorous use of the technique in any of these fields. We study this problem from the perspective of parameter estimation theory, to derive the covariance matrix for spectral parameters obtained by fitting experimental spectra.We illustrate and test the results using spin noise spectroscopy (SNS), a versatile technique that measures magnetic resonance features from thermal spin fluctations [18]. Non-optical SNS based on resonance force microscopy [19,20] Quantum statistical fluctuations such as shot noise are often limiting in noise spectroscopies [6,27,34], making it important to understand quantum limits and techniques to overcome them. A general framework to estimate the spectra of noisy classical forces influencing quantum systems has been applied to spectroscopy by homodyne detection of an externally-imposed noisy phase [35]. This framework provides fundamental limits but can be applied to noise spectroscopies only in the weak probing regime, due to the assumed "classical," i.e., imperturbable, nature of the estimated force.In contrast, our results make no classicality assumption. For FR-SNS we show two new results concerning the quantum limits of the technique: first, availability of unlimited particle-number resources gives rise to an optimal sensitivity at finite number, in contrast to standard models from quantum metrology [36,37], which have sensitivity monotonic in particle number and thus must assume an externally-imposed constraint to give meaningful results, and second, the number-optimized standard-quantum-limit sensitivity can be surpassed using squeezed-light probes. These theoretical predictions are tested by comparison against FR-SNS of hot rubidium vapor using a quantum-noise-limited probing system [34] and...

Despite much greater life expectancy of HIV/AIDS-patients, treatment-related toxicities still remain a major concern. Monitoring of lipodystrophy, as side effect of HAART, is particularly important.