Precision measurements are important across all fields of science. In particular, optical phase measurements can be used to measure distance, position, displacement, acceleration, and optical path length. Quantum entanglement enables higher precision than would otherwise be possible. We demonstrated an optical phase measurement with an entangled four-photon interference visibility greater than the threshold to beat the standard quantum limit-the limit attainable without entanglement. These results open the way for new high-precision measurement applications.
We report the first experimental demonstration of an optical quantum controlled-NOT gate without any path interference, where the two interacting path interferometers of the original proposals have been replaced by three partially polarizing beam splitters with suitable polarization dependent transmittance and reflectance. The performance of the device is evaluated using a recently proposed method, by which the quantum process fidelity and the entanglement capability can be estimated from the 32 measurement results of two classical truth tables, significantly less than the 256 measurement results required for full quantum tomography.
Among the applications of optical phase measurement, the differential interference contrast microscope is widely used for the evaluation of opaque materials or biological tissues. However, the signal to noise ratio for a given light intensity is limited by the standard quantum limit (SQL), which is critical for the measurements where the probe light intensity is limited to avoid damaging the sample. The SQL can only be beaten by using N quantum correlated particles, with an improvement factor of √ N . Here we report the first demonstration of an entanglement-enhanced microscope, which is a confocal-type differential interference contrast microscope where an entangled photon pair (N=2) source is used for illumination. An image of a Q shape carved in relief on the glass surface is obtained with better visibility than with a classical light source. The signal to noise ratio is 1.35±0.12 times better than that limited by the SQL.Quantum metrology involves using quantum mechanics to realize more precise measurements than can be achieved classically [1]. The canonical example uses entanglement of N particles to measure a phase with a precision ∆φ = 1/N , known as the Heisenberg limit. Such a measurement outperforms the ∆φ = 1/ √ N precision limit possible with N unentangled particles-the standard quantum limit (SQL). Progress has been made with trapped ions [2-4] and atoms [5], while high-precision optical phase measurements have many important applications, including microscopy, gravity wave detection, measurements of material properties, and medical and biological sensing. Recently, the SQL has been beaten with two photons [6][7][8][9][10] and four photons [11][12][13].Perhaps the natural next step is to demonstrate entanglement-enhanced metrology [14][15][16]. Among the applications of optical phase measurement, microscopy is essential in broad areas of science from physics to biology. The differential interference contrast microscope [17] (DIM) is widely used for the evaluation of opaque materials or the label-free sensing of biological tissues [18]. For instance, the growth of ice crystals has recently been observed with a single molecular step resolution using a laser confocal microscope combined with a DIM [19]. The depth resolution of such measurements is determined by the signal to noise ratio (SNR) of the measurement, and the SNR is in principle limited by the SQL. In the advanced measurements using DIM, the intensity of the probe light, focused onto a tiny area of ∼ 10 −13 m 2 , is tightly limited for a noninvasive measurement, and the limit of the SNR is becoming a critical issue.In this work, we demonstrated an entanglementenhanced microscope, consisting of a confocal-type differential interference contrast microscope equipped with an entangled photon source as a probe light source, with an SNR of 1.35 times better than that of the SQL. We use an entangled two-photon source with a high fidelity of 98%, resulting in a high two-photon interference visibility in the confocal microscope setup of 95.2%. An i...
Quantum metrology promises greater sensitivity for optical phase measurements than could ever be achieved classically. Here we present a theory of the phase sensitivity for the general case where the detection probability is given by an N photon interference fringe. We find that the phase sensitivity has a complex dependence on both the intrinsic efficiency of detection η and the interference fringe visibility V . Most importantly, the phase that gives maximum phase sensitivity is in general not the same as the phase at which the slope of the interference fringe is a maximum, as has previously been assumed. We determine the parameter range where quantum enhanced sensitivity can be achieved. In order to illustrate these theoretical results, we perform a four photon experiment with η = 3/4 and V = 82 ± 6% (an extension of our previous work [Science 316, 726 (2007)]) and find a phase sensitivity 1.3 times greater than the standard quantum limit at a phase different to that which gives maximum slope of the interference fringe.
The first experimental demonstration of an adaptive quantum state estimation (AQSE) is reported. The strong consistency and asymptotic efficiency of AQSE have been mathematically proven [J. Phys. A:Math. Gen. 39 12489 (2006)]. In this Letter, the angle of linear polarization of single photons, or the phase parameter between the right and the left circularly polarization, is estimated using AQSE, and the strong consistency and asymptotic efficiency are experimentally verified. AQSE will provide a general useful method in both quantum information processing and metrology.PACS numbers: 03.65. Wj, 42.50.Dv, Quantum theory is inherently statistical. This entails repetition of experiments over a number of identically prepared quantum objects, for example, quantum states, if one wants to know the "true state" or the "true value" of the parameter that specifies the quantum state [1][2][3][4]. Such an estimation procedure is particularly important for quantum communication and quantum computation [5], and is also indispensable to quantum metrology [6][7][8][9][10]. In applications, one needs to design the estimation procedure in such a way that the estimated value of the parameter should be close to the true value (consistency), and that the uncertainty of the estimated value should be as small as possible (efficiency) for a given limited number of samples. In order to realize these requirements, Nagaoka advocated an adaptive quantum state estimation (AQSE) procedure [11,12], and recently Fujiwara proved the strong consistency and asymptotic efficiency for AQSE [13,14].In this letter, we report the first experimental demonstration of AQSE using photons. The angle of a half wave plate (HWP) that initializes the linear polarization of input photons is estimated using AQSE. A sequence of AQSE is carried out with 300 input photons, and the sequence is repeated 500 times for four different settings of HWP. The statistical analysis of these results verifies the strong consistency and asymptotic efficiency of AQSE. Recently, it has been mathematically proven that the precision of AQSE outperforms the conventional state tomography [15]. It is thus expected that AQSE will provide a useful methodology in the broad area of quantum information processing, communication, and metrology.Let us first explain AQSE in detail. For simplicity, we restrict ourselves to one-dimensional quantum statistical model S = {ρ θ ; θ ∈ Θ (⊂ R)}, a smooth parametric family of density operators on a Hilbert space H having a one-dimensional parameter θ. Our aim is to estimate the true value of θ by means of a certain quantum estimation scheme. An estimator is represented by a pair (M,θ), where M = {M (x); x ∈ X } is a positive operator-valued measure (POVM) that takes values on a set X , andθ : X → Θ is a map that gives the estimated valueθ(x) from each observed data x ∈ X . The observed data x ∈ X has probability densitywhich depends on both the parameter θ and the measurement M . In traditional statistics, it is often the case to confine our attention t...
N00N states -maximally path-entangled states of N photons -exhibit spatial interference patterns sharper than any classical interference pattern. This is known as super-resolution. However, even with perfectly efficient number-resolving detectors, the detection efficiency of all previously demonstrated methods to measure such interference decreases exponentially with the number of photons in the N00N state, often leading to the conclusion that N00N states are unsuitable for spatial measurements. Here, we create spatial super-resolution fringes with two-, three-, and fourphoton N00N states, and demonstrate a scalable implementation of the so-called "optical centroid measurement" which provides an in-principle perfect detection efficiency. Moreover, we compare the N00N-state interference to the corresponding classical super-resolution interference. Although both provide the same increase in spatial frequency, the visibility of the classical fringes decreases exponentially with the number of detected photons, while the visibility of our experimentally measured N00N-state super-resolution fringes remains approximately constant with N. Our implementation of the optical centroid measurement is a scalable method to measure high photon-number quantum interference, an essential step forward for quantum-enhanced measurements, overcoming what was believed to be a fundamental challenge to quantum metrology.Many essential techniques in modern science and technology, from precise position sensing to high-resolution imaging to nanolithography, rely on the creation and detection of the finest possible spatial interference fringes using light. Classically, all such measurements face a fundamental barrier related to the "diffraction limit," which is determined by the wavelength of the light [1], but quantum entanglement can be used to surpass this limit by making the spatial interference fringes sharper (a result referred to as super-resolution) [2,3]. In particular, the N-photon entangled "N00N" state can display an interference pattern N times finer than that of classical light [4,5]. However, N00N states suffer from a weakness that has made their advantage controversial: the probability of all N photons arriving at the same place, and thus the detection efficiency, decreases exponentially with N [6,7]. Here we implement the optical centroid measurement (OCM) proposed by Tsang [8] to completely overcome this problem. A proof-of-principle experiment confirming the underlying concept of the OCM was recently performed [9], but, being limited to only two photons and two 'movable' detectors, it could not probe the scaling properties nor demonstrate the efficiency gain of the OCM. In our experiment, using an array of 11 fixed detectors, we measure two-, three-, and four-photon spatial fringes, and find that their visibility does not degrade with the number of entangled photons, clearly displaying the enhanced efficiency and scalability of the OCM. The visibility of an unentangled OCM, on the other hand, decays exponentially. In doing...
Quantum information science addresses how uniquely quantum mechanical phenomena such as superposition and entanglement can enhance communication, information processing, and precision measurement. Photons are appealing for their low-noise, lightspeed transmission and ease of manipulation using conventional optical components. However, the lack of highly efficient optical Kerr nonlinearities at the single photon level was a major obstacle. In a breakthrough, Knill, Laflamme, and Milburn (KLM) showed that such an efficient nonlinearity can be achieved using only linear optical elements, auxiliary photons, and measurement [Knill E, Laflamme R, Milburn GJ (2001) Nature 409:46-52]. KLM proposed a heralded controlled-NOT (CNOT) gate for scalable quantum computation using a photonic quantum circuit to combine two such nonlinear elements. Here we experimentally demonstrate a KLM CNOT gate. We developed a stable architecture to realize the required four-photon network of nested multiple interferometers based on a displaced-Sagnac interferometer and several partially polarizing beamsplitters. This result confirms the first step in the original KLM "recipe" for all-optical quantum computation, and should be useful for on-demand entanglement generation and purification. Optical quantum circuits combining giant optical nonlinearities may find wide applications in quantum information processing, communication, and sensing.nonlinear optics | quantum optics | linear optics | quantum gates S everal physical systems are being pursued for quantum computing (1)-promising candidates include trapped ions, neutral atoms, nuclear spins, quantum dots, superconducting systems, and photons-while photons are indispensable for quantum communication (2, 3) and are particularly promising for quantum metrology (4, 5). In addition to low-noise quantum systems (typically two-level "qubits") quantum information protocols require a means to interact qubits to generate entanglement. The canonical example is the controlled-NOT (CNOT) gate, which flips the state of the polarization of the "target" photon conditional on the "control" photon being horizontally polarized (the logical "1" state). The gate is capable of generating maximally entangled two-qubit states, which together with onequbit rotations provide a universal set of logic gates for quantum computation.The low-noise properties of single photon qubits are a result of their negligible interaction with the environment, however, the fact that they do not readily interact with one-another is problematic for the realization of a CNOT or other entangling interaction. Consequently it was widely believed that matter systems, such as an atom or atom-like system (6), or an ensemble of such systems (7), would be required to realize such efficient optical nonlinearities. Indeed the first proposals for using linear optics to benchmark quantum algorithms require exponentially large physical resources (8-10).In 2001, KLM made the surprising discovery that a scalable quantum computer could be built from o...
The ability to filter quantum states is a key capability in quantum information science and technology, in which one-qubit filters, or polarizers, have found wide application. Filtering on the basis of entanglement requires extension to multi-qubit filters with qubit-qubit interactions. We demonstrated an optical entanglement filter that passes a pair of photons if they have the desired correlations of their polarization. Such devices have many important applications to quantum technologies.
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