One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are amongst the more actively-studied topics of quantum information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here we review different notions of classical and quantum correlations quantified by quantum discord and other related measures. In the first half, we review the mathematical properties of the measures of quantum correlations, relate them to each other, and discuss the classical-quantum division that is common among them. In the second half, we show that the measures identify and quantify the deviation from classicality in various quantuminformation-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. We show that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.

We analyze the effects of quantum correlations, such as entanglement and discord, on the efficiency of phase estimation by studying four quantum circuits that can be readily implemented using NMR techniques. These circuits define a standard strategy of repeated single-qubit measurements, a classical strategy where only classical correlations are allowed, and two quantum strategies where nonclassical correlations are allowed. In addition to counting space (number of qubits) and time (number of gates) requirements, we introduce mixedness as a key constraint of the experiment. We compare the efficiency of the four strategies as a function of the mixedness parameter. We find that the quantum strategy gives ffiffiffiffi N p enhancement over the standard strategy for the same amount of mixedness. This result applies even for highly mixed states that have nonclassical correlations but no entanglement.

We introduce fusion-based quantum computing (FBQC) -a model of universal quantum computation in which entangling measurements, called fusions, are performed on the qubits of small constant-sized entangled resource states. We introduce a stabilizer formalism for analyzing fault tolerance and computation in these schemes. This framework naturally captures the error structure that arises in certain physical systems for quantum computing, such as photonics. FBQC can offer significant architectural simplifications, enabling hardware made up of many identical modules, requiring an extremely low depth of operations on each physical qubit and reducing classical processing requirements. We present two pedagogical examples of fault-tolerant schemes constructed in this framework and numerically evaluate their threshold under a hardware agnostic fusion error model including both erasure and Pauli error. We also study an error model of linear optical quantum computing with probabilistic fusion and photon loss. In FBQC the non-determinism of fusion is directly dealt with by the quantum error correction protocol, along with other errors. We find that tailoring the fault-tolerance framework to the physical system allows the scheme to have a higher threshold than schemes reported in literature. We present a ballistic scheme which can tolerate a 10.4% probability of suffering photon loss in each fusion.

Quantum metrology aims to realise new sensors operating at the ultimate limit of precision measurement. However, optical loss, the complexity of proposed metrology schemes and interferometric instability each prevent the realisation of practical quantumenhanced sensors. To obtain a quantum advantage in interferometry using these capabilities, new schemes are required that tolerate realistic device loss and sample absorption. We show that loss-tolerant quantum metrology is achievable with photoncounting measurements of the generalised multi-photon singlet state, which is readily generated from spontaneous parametric downconversion without any further state engineering. The power of this scheme comes from coherent superpositions, which give rise to rapidly oscillating interference fringes that persist in realistic levels of loss. We have demonstrated the key enabling principles through the four-photon coincidence detection of outcomes that are dominated by the four-photon singlet term of the four-mode downconversion state. Combining state-of-the-art quantum photonics will enable a quantum advantage to be achieved without using post-selection and without any further changes to the approach studied here.

Absorption spectroscopy is routinely used to characterise chemical and biological samples. For the state-of-the-art in laser absorption spectroscopy, precision is theoretically limited by shot-noise due to the fundamental Poisson-distribution of photon number in laser radiation. In practice, the shotnoise limit can only be achieved when all other sources of noise are eliminated. Here, we use wavelength-correlated and tuneable photon pairs to demonstrate how absorption spectroscopy can be performed with precision beyond the shot-noise limit and near the ultimate quantum limit by using the optimal probe for absorption measurement-single photons. We present a practically realisable scheme, which we characterise both the precision and accuracy of by measuring the response of a control feature. We demonstrate that the technique can successfully probe liquid samples and using two spectrally similar types of haemoglobin we show that obtaining a given precision in resolution requires fewer heralded single probe photons compared to using an idealised laser.

We show how an idealised measurement procedure can condense photons from two modes into one, and how, by feeding forward the results of the measurement, it is possible to generate efficiently superpositions of components for which only one mode is populated, commonly called "N00N states". For the basic procedure, sources of number states leak onto a beam splitter, and the output ports are monitored by photodetectors. We find that detecting a fixed fraction of the input at one output port suffices to direct the remainder to the same port with high probability, however large the initial state. When instead photons are detected at both ports, Schrödinger cat states are produced. We describe a circuit for making the components of such a state orthogonal, and another for subsequent conversion to a N00N state. Our approach scales exponentially better than existing proposals. Important applications include quantum imaging and metrology.The fundamental limits to optical detection for metrology and imaging are quantum mechanical [1]. Of particular interest for reaching such quantum limits are pathentangled states of photons of the form |N 0 + e iφ |0N , in a basis of photon-number states, commonly referred to as "N 00N " states. A variety of applications have been suggested [2]. For lithography [3] and microscopy [4], N 00N state light would be used together with multiphoton absorbers to achieve enhanced resolution. This is because the de Broglie wavelength for an N -photon state is a factor 1/N smaller than the wavelength associated with the single photon, and the absorption rate scales linearly with the incident intensity, rather than as the N th power. Regarding applications to precision metrology, whereby an interferometric setup is used to measure small phase shifts, N 00N states achieve the Heisenberg limit, for which the phase uncertainty scales as 1/N [5,6,7], and entanglement is a fundamental requirement for achieving this limit. It has been rigorously demonstrated that the cost of improving sensitivity (without using entanglement) is higher intensities or longer coherence times [8]. Classically the shot-noise limit applies, attained for example by laser light, for which the uncertainty scales as 1/ √ N , already a restraint in applications such as magnetometry [9] and gyroscopy [10].However, building a source of N 00N states beyond two photons is challenging. Three, four and six photon experiments have been reported [11,12,13], but only in the first two references were N 00N states generated. In theory a source could be made using a nonlinear crystal [14]. However, the required optical nonlinearity is not readily available. An alternative is a non-deterministic approach using linear optics, wherein the desired state is generated on condition of a specific outcome at photodetectors. A variety of schemes have been suggested which typically rely on conditional destructive interference [15,16,17]. * Electronic address: hcable@lsu.edu However, so far none of these scales efficiently, that is they all share the featu...

Harnessing the unique properties of quantum mechanics offers the possibility to deliver new technologies that can fundamentally outperform their classical counterparts. These technologies only deliver advantages when components operate with performance beyond specific thresholds. For optical quantum metrology, the biggest challenge that impacts on performance thresholds is optical loss. Here we demonstrate how including an optical delay and an optical switch in a feed-forward configuration with a stable and efficient correlated photon pair source reduces the detector efficiency required to enable quantum enhanced sensing down to the detection level of single photons. When the switch is active, we observe a factor of improvement in precision of 1.27 for transmission measurement on a per input photon basis, compared to the performance of a laser emitting an ideal coherent state and measured with the same detection efficiency as our setup. When the switch is inoperative, we observe no quantum advantage.Quantum mechanics quantifies the highest precision that is achievable in each type of optical measurement [1][2][3]. Single photon probes measured with single photon detectors are in principle optimal for gaining the most precision per-unit intensity when measuring optical transmission [4]. However, in practice, optical loss and low component efficiencies prevent an advantage from being achieved using single photon detectors [5]. One way to reduce the impact of lower component efficiency is to incorporate fast optical switching and an optical delay with schemes that are based on heralded generation of quantum sates [6]. This then enables use of a quantum state conditioned on the successful detection of a correlated signal -this is referred to as feed-forward.Feed-forward is key for demonstrations of optical quantum computing [7], it has been used in experiments that increase the generation rate [8][9][10][11][12] and signal-to-noise ratio [13] of heralded single photons, it has been used to calibrate single photon detectors [14] and it has also been applied to gather evidence of single photon sensitivity in animal vision [15]. Jakeman and Rarity proposed in Ref.[6] using feed-forward with correlated photon pairs to enable sub shot noise optical transmission measurements when component efficiency is otherwise not sufficient to permit a quantum advantage in passive direct detection [16][17][18]. But despite becoming identified as key to more general multi-photon entangled quantum state engineering for quantum metrology [19,20], feed-forward has not been implemented for quantum enhanced parameter estimation. Here we implement the proposal featured in Ref.[6] (Fig. 1) to realise sub shot noise measurement of transmissitivity, using single photon detectors that are too low in efficiency to enable sub shot noise performance in a passive measurement.The transmissivity η of a sample is in general estimated by measuring the reduction of light intensity from a known mean input valueN in , to a reduced mean valueN out according ...

Quantum lithography proposes to adopt entangled quantum states in order to increase resolution in interferometry. In the present paper we experimentally demonstrate that the output of a high-gain optical parametric amplifier can be intense yet exhibits quantum features, namely, sub-Rayleigh fringes, as proposed by [Agarwal , Phys. Rev. Lett. 86, 1389 (2001)]. We investigate multiphoton states generated by a high-gain optical parametric amplifier operating with a quantum vacuum input for gain values up to 2.5. The visibility has then been increased by means of three-photon absorption. The present paper opens interesting perspectives for the implementation of such an advanced interferometrical setup