We study the sensitivity and resolution of phase measurement in a Mach-Zehnder interferometer with two-mode squeezed vacuum (n photons on average). We show that super-resolution and subHeisenberg sensitivity is obtained with parity detection. In particular, in our setup, dependence of the signal on the phase evolvesn times faster than in traditional schemes, and uncertainty in the phase estimation is better than 1/n.PACS numbers: 07.60. Ly, 95.75.kK, 42.50.St Different physical mechanisms contribute to phase measurement. Thus, measuring phase provides insight into a number of physical processes. Therefore, improved phase estimation benefits multiple areas of scientific research, such as quantum metrology, imaging, sensing, and information processing. Consequently, enormous efforts have been devoted to improve the resolution and sensitivity of interferometers. Sensitivity is a measure of the uncertainty in the phase estimation, while resolution is rate at which signal changes with changing phase.In what follows, we direct our attention to quantum interferometry. The benchmark that quantum interferometry is compared against is one with coherent light input and intensity difference measurement at the output of a Mach-Zehnder interferometer (MZI). In general, phase sensitivity of this benchmark is shot-noise limited, namely ∆ϕ = 1/ √n , wheren is the average number of photons. However, better sensitivity is possible if nonlinear interaction between photons in the MZI takes place [1]. In what follows, we only consider phase accumulation due to linear processes.In 1981, Caves pointed out that by using coherent light and squeezed vacuum one could beat the shot-noise limit ∆ϕ < 1/ √n (super-sensitivity) [2]. In the work of Boto et al., it was shown that by exploiting quantum states of light, such as N00N states, it is possible to beat the Rayleigh diffraction limit in imaging and lithography (super resolution) while also beating the shot-noise limit in phase estimation [3,4,5,6]. Finally, it was shown in Ref.[7] that input state entanglement is important in order to achieve super-sensitivity in a linear interferometer.non-classical light Experimental realization of these predictions have been hindered by the fact that entangled states of light, with large numbers of photons, are difficult to obtain. Therefore we turn our attention to the brightest (experimentally available) nonclassical light -two-mode squeezed vacuum (TMSV). A state of TMSV is a superposition of twin Fock states |ψn = ∞ n=0 p n (n) |n, n , where the probability of a twin Fock state |n, n = |n A |n B to be present de- pends on average number of photons in both modes of TMSV,n, in the following way p n (n) = (1 − tn)t n n with tn = 1/ (1 + 2/n) [8].Light entering a MZI in TMSV state exits a lossless interferometer in the state |ψ f =Û MZI |ψn , where the MZI is described by the unitary transformation U MZI (Fig. 1). This transformation, in terms of the field operators for the optical modesâ andb, isÛ MZI =ÛP ϕÛ = exp ϕ â †b −b †â /2 , wherê P ϕ =exp −...

We propose a class of path-entangled photon Fock states for robust quantum optical metrology, imaging, and sensing in the presence of loss. We model propagation loss with beam-splitters and derive a reduced density matrix formalism from which we examine how photon loss affects coherence. It is shown that particular entangled number states, which contain a special superposition of photons in both arms of a Mach-Zehnder interferometer, are resilient to environmental decoherence. We demonstrate an order of magnitude greater visibility with loss, than possible with N00N states. We also show that the effectiveness of a detection scheme is related to super-resolution visibility.

Numerical optimization is used to design linear-optical devices that implement a desired quantum gate with perfect fidelity, while maximizing the success rate. For the 2-qubit CS (or CNOT) gate, we provide numerical evidence that the maximum success rate is S = 2/27 using two unentangled ancilla resources; interestingly, additional ancilla resources do not increase the success rate. For the 3-qubit Toffoli gate, we show that perfect fidelity is obtained with only three unentangled ancilla photons -less than in any existing scheme -with a maximum S = 0.00340. This compares well with S = (2/27) 2 /2 ≈ 0.00274, obtainable by combining two CNOT gates and a passive quantum filter [1]. The general optimization approach can easily be applied to other areas of interest, such as quantum error correction, cryptography, and metrology [2,3].PACS numbers: 03.67.Lx, 42.50.Dv Linear optics is considered as a viable method for scalable quantum information processing, due in large part to the seminal work of Knill, Laflamme, and Milburn (KLM) [4]. These authors showed that an elementary quantum logic gate on qubits, encoded in photonic states, can be constructed using a combination of linearoptical elements and quantum measurement. The tradeoff in this measurement-assisted scheme is that the gate is properly implemented only when the measurement yields a positive outcome, i.e., the gate is non-deterministic. Soon after the KLM scheme became a paradigm for linear optical quantum computation (LOQC), it became clear that there is a general unresolved theoretical problem of finding the optimal implementation for a desired quantum transformation [5].For the nonlinear sign (NS) gate, which acts on photons in a single optical mode, α 0 |0 + α 1 |1 + α 2 |2 → α 0 |0 + α 1 |1 − α 2 |2 , the maximum success probability without feed-forward has been theoretically proved to be 1/4 [6]. Here we focus on more complicated gates, taking as examples the two-qubit controlled sign (CS) gate (equivalently, the CNOT gate), and the three-qubit Toffoli gate. For these physically important gates, existing theoretical results are limited to upper or lower bounds on the success probability [1,7,8].A linear-optical quantum gate, or state generator (LO-QSG) [5], can be viewed formally as a device implementing a contraction transformation (for ideal detectors) that converts pure input states into desired pure output states. The goal of the optimization problem is to find a proper linear optical network (see Fig. 1), characterized by a unitary matrix U, that performs the desired transformation [9,10]. The problem is naturally partitioned into two tasks: i) finding a subspace of perfect fidelity within the space of all unitary matrices U, and ii) maximizing the success probability within this subspace. While in this paper we address transformations implemented by linear optics, the method is universal and with minor modifications can be successfully applied to any quantum-information problem involving unitary operations combined with measurements. Origina...

Information transfer rates in optical communications may be dramatically increased by making use of spatially non-Gaussian states of light. Here, we demonstrate the ability of deep neural networks to classify numerically generated, noisy Laguerre-Gauss modes of up to 100 quanta of orbital angular momentum with near-unity fidelity. The scheme relies only on the intensity profile of the detected modes, allowing for considerable simplification of current measurement schemes required to sort the states containing increasing degrees of orbital angular momentum. We also present results that show the strength of deep neural networks in the classification of experimental superpositions of Laguerre-Gauss modes when the networks are trained solely using simulated images. It is anticipated that these results will allow for an enhancement of current optical communications technologies.

We optimize two-mode, entangled, number states of light in the presence of loss in order to maximize the extraction of the available phase information in an interferometer. Our approach optimizes over the entire available input Hilbert space with no constraints, other than fixed total initial photon number. We optimize to maximize the Fisher information, which is equivalent to minimizing the phase uncertainty. We find that in the limit of zero loss the optimal state is the so-called N00N state, for small loss, the optimal state gradually deviates from the N00N state, and in the limit of large loss the optimal state converges to a generalized two-mode coherent state, with a finite total number of photons. The results provide a general protocol for optimizing the performance of a quantum optical interferometer in the presence of photon loss, with applications to quantum imaging, metrology, sensing, and information processing. PACS numbers: 42.50.St, 42.50.Ar, 42.50.Dv, Quantum states of light play an important role in applications including metrology, imaging, sensing, and quantum information processing [1]. In quantum interferometry, entangled states of light, such as the maximally path-entangled N00N states, replace conventional laser light to achieve a sensitivity below the shot-noise limit, even reaching the Heisenberg limit, and a resolution well below the Rayleigh diffraction limit [2]. For an overview of quantum metrology applications see, for example, Ref.[1]. However, for real-world applications, diffraction, scattering, and absorption of quantum states of light need to be taken into account. Recently it has been shown that many quantum-enhanced metrology schemes using N00N states perform poorly when a considerable amount of loss is present [3,4,5]. However, our team has also discovered a new class of entangled number states, which are more resilient to loss [6]. These so-called M &M ′ states still outperform classical light sources under a moderate 3 dB of loss.In this work, we systematize the numerical search for optimal quantum states in a two-mode interferometer in the presence of loss. We employ the Fisher information to obtain the phase sensitivity of the interferometer. An exhaustive review and application of the Fisher information concept to the sensitivity of a March-Zehnder interferometer, particularly in the zero loss case, has been presented in the recent work by Durkin and Dowling [7]. The chief utility of the Fisher information approach is that it provides a bound on the phase sensitivity, even in the absence of a fully specified detection scheme, and is now widely adopted in studies of interferometer sensitivity. Such numerical optimization has been previously carried out in the absence of loss, and with loss over a restricted class of input states [8,9]. Here, we provide a completely general optimization scheme that is applied to the two-mode interferometer, but also has application to the optimization of linear optical systems for quantum linear optical information processing [10,11].Using...