Tim J. Bartley

Direct observation of sub-binomial light

Nonclassical states of light are necessary resources for quantum technologies such as cryptography, computation and the definition of metrological standards. Distinguishing nonclassical states from those that can be described without invoking quantum mechanics is both a necessary practical task and of fundamental interest. In general, signatures of nonclassicality arise from apparently pathological behaviour of the quasi-probability distributions used to describe the states. While tomographic reconstruction of the state is therefore sufficient to show nonclassicality, it is often more convenient to probe photon-counting statistics of on-off detectors directly. This is formalised by the Mandel Q-parameter QM = 〈Δn〉 / 〈n〉 - 1, which is negative for sub-Poissonian statistics arising from nonclassical states. However, the Mandel Q-parameter can fail when using a multiplexed array of on-off detectors to measure states with several photons; splitting in this manner can corrupt its original statistics. A new parameter, QB = N 〈(Δ c) 2 〉 / 〈 c 〉 (N - 〈 c 〉) can be used to witness nonclassicality directly from such click statistics. For QB <; 0, such statistics are thus deemed sub-binomial and therefore arise from a nonclassical state.

Strategies for enhancing quantum entanglement by local photon subtraction

Subtracting photons from a two-mode squeezed state is a well-known method to increase entanglement. We analyze different strategies of local photon subtraction from a two-mode squeezed state in terms of entanglement gain and success probability. We develop a general framework that incorporates imperfections and losses in all stages of the process: before, during, and after subtraction. By combining all three effects into a single efficiency parameter, we provide analytical and numerical results for subtraction strategies using photon-number-resolving and threshold detectors. We compare the entanglement gain afforded by symmetric and asymmetric subtraction scenarios across the two modes. For a given amount of loss, we identify an optimized set of parameters, such as initial squeezing and subtraction beam splitter transmissivity, that maximize the entanglement gain rate. We identify regimes for which asymmetric subtraction of different Fock states on the two modes outperforms symmetric strategies. In the lossless limit, subtracting a single photon from one mode always produces the highest entanglement gain rate. In the lossy case, the optimal strategy depends strongly on the losses on each mode individually, such that there is no general optimal strategy. Rather, taking losses on each mode as the only input parameters, we can identify the optimal subtraction strategy and required beam splitter transmissivities and initial squeezing parameter. Finally, we discuss the implications of our results for the distillation of continuous-variable quantum entanglement.

Observing optical coherence across Fock layers with weak-field homodyne detectors

Quantum properties of optical modes are typically assessed by observing their photon statistics or the distribution of their quadratures. Both particle- and wave-like behaviours deliver important information and each may be used as a resource in quantum-enhanced technologies. Weak-field homodyne (WFH) detection provides a scheme that combines the wave- and particle-like descriptions. Here we show that it is possible to observe a wave-like property such as the optical coherence across Fock basis states in the detection statistics derived from discrete photon counting. We experimentally demonstrate these correlations using two WHF detectors on each mode of two classes of two-mode entangled states. Furthermore, we theoretically describe the response of WHF detection on a two-mode squeezed state in the context of generalized Bell inequalities. Our work demonstrates the potential of this technique as a tool for hybrid continuous/discrete-variable protocols on a phenomenon that explicitly combines both approaches.

Directly comparing entanglement-enhancing non-Gaussian operations

Single-photon-level non-Gaussian operations—photon addition, photon subtraction, and their coherent superposition—are powerful tools with which to increase entanglement in continuous-variable optical states. Although such operations are typically not deterministic, there may be other advantages such as noiseless manipulation. Therefore, to fully account for the efficacy of a particular non-Gaussian operation in a practical scenario, we develop figures of merit which trade off the advantages of such protocols against their success probability. Specifically, we define ‘entanglement enhancement rate’ as the increase in entanglement per trial of a generic non-Gaussian operation on a two-mode squeezed vacuum (TMSV) state. We consider states generated by photon-subtraction, photon-addition and a coherent superposition of subtraction and addition. We compare each strategy when applied to one or both modes of a TMSV state, and also in the presence of channel losses prior to the operation. In many cases, additional properties are analytically calculable, including excess noise arising from the operation and the fidelity of the resulting states to particular Gaussian and non-Gaussian states. Finally, by incorporating loss, we derive optimal interaction parameters for each non-Gaussian operation which maximize the effectiveness of the particular protocol under investigation.

Limits on the heralding efficiencies and spectral purities of spectrally filtered single photons from photon-pair sources

Photon pairs produced by parametric down-conversion or four-wave mixing can interfere with each other in multiport interferometers or carry entanglement between distant nodes for use in entanglement swapping. This requires the photons to be spectrally pure to ensure good interference and have high heralding efficiency to know accurately the number of photons involved and to maintain high rates as the number of photons grows. Spectral filtering is often used to remove noise and define spectral properties. For heralded single photons high purity and heralding efficiency are possible by filtering the heralding arm, but when both photons in typical pair sources are filtered, we show that the heralding efficiency of one or both of the photons is strongly reduced even by ideal spectral filters with 100% transmission in the passband: any improvement in reduced-state spectral purity from filtering comes at the cost of lowered heralding efficiency. We consider the fidelity to a pure, lossless single photon, symmetrize it to include both photons of the pair, and show this quantity is intrinsically limited for sources with spectral correlation. We then provide a framework for this effect for benchmarking common photon-pair sources and present an experiment where we vary the photon filter bandwidths and measure the increase in purity and corresponding reduction in heralding efficiency.

Quantum correlations from the conditional statistics of incomplete data

We study, in theory and experiment, the quantum properties of correlated light fields measured with click-counting detectors providing incomplete information on the photon statistics. We establish a correlation parameter for the conditional statistics, and we derive the corresponding nonclassicality criteria for detecting conditional quantum correlations. Classical bounds for Pearsons correlation parameter are formulated that allow us, once they are violated, to determine nonclassical correlations via the joint statistics. On the one hand, we demonstrate nonclassical correlations in terms of the joint click statistics of light produced by a parametric down-conversion source. On the other hand, we verify quantum correlations of a heralded, split single-photon state via the conditional click statistics together with a generalization to higher-order moments. We discuss the performance of the presented nonclassicality criteria to successfully discern joint and conditional quantum correlations. Remarkably, our results are obtained without making any assumptions on the response function, quantum efficiency, and dark-count rate of photodetectors.

Continuous phase stabilization and active interferometer control using two modes

We present a computer-based active interferometer stabilization method that can be set to an arbitrary phase difference and does not rely on modulation of the interfering beams. The scheme utilizes two orthogonal modes propagating through the interferometer with a constant phase difference between them to extract a common relative phase and generate a linear feedback signal. Switching times of 50 ms over a range of 0–6π radians at 632.8 nm are experimentally demonstrated. The relative interferometer phase can be stabilized up to several days to within ± 3°.

Requirements for two-source entanglement concentration

Abstract Entanglement enhancement is a key task for quantum technologies. This operation performed on states produced by parametric down-conversion sources has been the object of several recent experimental investigations. In particular, conditional preparation by photon-subtraction has been shown to improve the entanglement of these states. Here we analyse the role played by non-Gaussian and Gaussian measurements in more general entanglement concentration operations performed on a pair of two-mode squeezed vacua. We find stringent requirements for achieving an improved entanglement enhancement by measuring jointly these two resource states.

Free space quantum key distribution with coherent polarization states

Free space QKD over an atmospheric channel was demonstrated in 1996 for the first time [1]. Since then, several prepare-and-measure and entanglement-based schemes have been implemented (for a detailed overview, see [2]). All of these systems use single-photon detectors, and therefore have to employ spatial, spectral and/or temporal filtering in order to reduce background light. In our system, we use an alternative approach: with the help of a bright local oscillator (LO), we perform homodyne measurements on weak coherent polarization states [3].

Quantum state and mode profile tomography by the overlap

VS acknowledge support from the National Council for Scientific and Technological Development (CNPq) of Brazil, grant 304129/2015-1, and by the Sao Paulo Research Foundation (FAPESP), grant 2015/23296-8. DM acknowledge support from the EUproject Horizon-2020 SUPERTWIN id.686731, the National Academy of Sciences of Belarus program ‘Convergence’ and FAPESP grant 2014/21188-0. NK acknowledges the support from the Scottish Universities Physics Alliance (SUPA) and from the International Max Planck Partnership (IMPP) with Scottish Universities. JT and CS acknowledge support from European Union Grant No. 665148 (QCUMbER). TB acknowledges support from theDFG under TRR 142.