One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction. Here, we experimentally ...demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.
It has been proposed that the ability to perform joint weak measurements on postselected systems would allow us to study quantum paradoxes. These measurements can investigate the history of those ...particles that contribute to the paradoxical outcome. Here we experimentally perform weak measurements of joint (i.e., nonlocal) observables. In an implementation of Hardy's paradox, we weakly measure the locations of two photons, the subject of the conflicting statements behind the paradox. Remarkably, the resulting weak probabilities verify all of these statements but, at the same time, resolve the paradox.
Interference phenomena are ubiquitous in physics, often forming the basis of demanding measurements. Examples include Ramsey interferometry in atomic spectroscopy, X-ray diffraction in ...crystallography and optical interferometry in gravitational-wave studies. It has been known for some time that the quantum property of entanglement can be exploited to perform super-sensitive measurements, for example in optical interferometry or atomic spectroscopy. The idea has been demonstrated for an entangled state of two photons, but for larger numbers of particles it is difficult to create the necessary multiparticle entangled states. Here we demonstrate experimentally a technique for producing a maximally entangled three-photon state from initially non-entangled photons. The method can in principle be applied to generate states of arbitrary photon number, giving arbitrarily large improvement in measurement resolution. The method of state construction requires non-unitary operations, which we perform using post-selected linear-optics techniques similar to those used for linear-optics quantum computing.
We study both experimentally and theoretically the generation of photon pairs by spontaneous four-wave mixing (SFWM) in standard birefringent optical fibers. The ability to produce a range of ...two-photon spectral states, from highly correlated (entangled) to completely factorable, by means of cross-polarized birefringent phase matching, is explored. A simple model is developed to predict the spectral state of the photon pair which shows how this can be adjusted by choosing the appropriate pump bandwidth, fiber length and birefringence. Spontaneous Raman scattering is modeled to determine the tradeoff between SFWM and background Raman noise, and the predicted results are shown to agree with experimental data.
Tomography of quantum detectors Lundeen, J. S; Walmsley, I. A; Feito, A ...
Nature physics,
01/2009, Letnik:
5, Številka:
1
Journal Article
Recenzirano
Odprti dostop
Measurement connects the world of quantum phenomena to the world of classical events. It has both a passive role-in observing quantum systems-and an active one, in preparing quantum states and ...controlling them. In view of the central status of measurement in quantum mechanics, it is surprising that there is no general recipe for designing a detector that measures a given observable. Compounding this, the characterization of existing detectors is typically based on partial calibrations or elaborate models. Thus, experimental specification (that is, tomography) of a detector is of fundamental and practical importance. Here, we present the realization of quantum detector tomography. We identify the positive-operator-valued measure describing the detector, with no ancillary assumptions. This result completes the triad, state, process and detector tomography, required to fully specify an experiment. We characterize an avalanche photodiode and a photon-number-resolving detector capable of detecting up to eight photons. This creates a new set of tools for accurately detecting and preparing non-classical light.
By using a systematic optimization approach, we determine quantum states of light with definite photon number leading to the best possible precision in optical two-mode interferometry. Our treatment ...takes into account the experimentally relevant situation of photon losses. Our results thus reveal the benchmark for precision in optical interferometry. Although this boundary is generally worse than the Heisenberg limit, we show that the obtained precision beats the standard quantum limit, thus leading to a significant improvement compared to classical interferometers. We furthermore discuss alternative states and strategies to the optimized states which are easier to generate at the cost of only slightly lower precision.
It is often said that measuring a system's position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a 'weak-measurement', ...this disturbance can be reduced. One might expect this comes at the cost of also reducing the measurement's precision. However, it was recently demonstrated that a sequence consisting of a weak position measurement followed by a regular momentum measurement can probe a quantum system at a single point, with zero width, in position-momentum space. Here, we study this 'joint weak-measurement' and reconcile its compatibility with the uncertainty principle. While a single trial probes the system with a resolution that can saturate Heisenberg's limit, we show that averaging over many trials can be used to surpass this limit. The weak-measurement does not trade away precision, but rather another type of uncertainty called 'predictability' which quantifies the certainty of retrodicting the measurement's outcome.
In a classical world, simultaneous measurements of complementary properties (e.g., position and momentum) give a system's state. In quantum mechanics, measurement-induced disturbance is largest for ...complementary properties and, hence, limits the precision with which such properties can be determined simultaneously. It is tempting to try to sidestep this disturbance by copying the system and measuring each complementary property on a separate copy. However, perfect copying is physically impossible in quantum mechanics. Here, we investigate using the closest quantum analog to this copying strategy, optimal cloning. The coherent portion of the generated clones' state corresponds to "twins" of the input system. Like perfect copies, both twins faithfully reproduce the properties of the input system. Unlike perfect copies, the twins are entangled. As such, a measurement on both twins is equivalent to a simultaneous measurement on the input system. For complementary observables, this joint measurement gives the system's state, just as in the classical case. We demonstrate this experimentally using polarized single photons.
Projectors are a simple but powerful tool for manipulating and probing quantum systems. For instance, projecting two-qubit systems onto maximally entangled states can enable quantum teleportation. ...While such projectors have been extensively studied, partially-entangling projectors have been largely overlooked, especially experimentally, despite their important role in quantum foundations and quantum information. Here, we propose a way to project two polarized photons onto any state with a single experimental setup. Our scheme does not require optical nonlinearities or additional photons. Instead, the entangling operation is provided by Hong-Ou-Mandel interference and post-selection. The efficiency of the scheme is between 50% and 100%, depending on the projector. We perform an experimental demonstration and reconstruct the operator describing our measurement using detector tomography. Finally, we flip the usual role of measurement and state in Hardy's test by performing a partially-entangling projector on separable states. The results verify the entangling nature of our measurement with six standard deviations of confidence.
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