The light produced by parametric down-conversion shows strong spatial entanglement that leads to violations of EPR criteria for separability. Historically, such studies have been performed by scanning a single-element, single-photon detector across a detection plane. Here we show that modern electron-multiplying charge-coupled device cameras can measure correlations in both position and momentum across a multi-pixel field of view. This capability allows us to observe entanglement of around 2,500 spatial states and demonstrate Einstein–Podolsky–Rosen type correlations by more than two orders of magnitude. More generally, our work shows that cameras can lead to important new capabilities in quantum optics and quantum information science.

Ascertaining the physical state of a system is vital in order to understand and predict its behaviour. However, due to their fragile nature, the direct observation of quantum states has been elusive until recently. Historically, determination of the quantum state has been performed indirectly, through use of tomography. We report on two experiments showing that an alternative approach can be used to determine the polarisation quantum state in a simple, fast, and general manner. The first experiment entails the direct measurement of the probability amplitudes describing pure polarisation states of light, the first such measurement on a two-level system. The second experiment entails the direct measurement of the Dirac distribution (a phase-space quasi-probability distribution informationally equivalent to the density matrix), demonstrating that the direct measurement procedure is applicable to general (i.e., potentially mixed) quantum states. Our work has applications to measurements in foundational quantum mechanics, quantum information, and quantum metrology.Measurement plays a vital role in the practice of science. This is especially so in the case of quantum mechanics, where the measurement process is fundamental to the formulation of the theory. A crucial feature of quantum mechanics is that a measurement of one variable of a system erases information about the corresponding conjugate variable. The classic example is that determining the position of a particle disturbs its momentum, and vice versa. These measurements, known as strong measurements, collapse the wavefunction such that no additional information can be obtained.In order to completely determine a quantum state, which is described in general by complex numbers, one must perform multiple measurements on many identical copies of the system. Quantum tomography 1 is one method of quantum state determination that uses strong measurements 2-6 . Tomographic reconstruction entails estimating the complex numbers that describe the state

The problem of inferring causal relations from observed correlations is relevant to a wide variety of scientific disciplines. Yet given the correlations between just two classical variables, it is impossible to determine whether they arose from a causal influence of one on the other or a common cause influencing both. Only a randomized trial can settle the issue. Here we consider the problem of causal inference for quantum variables. We show that the analogue of a randomized trial, causal tomography, yields a complete solution. We also show that, in contrast to the classical case, one can sometimes infer the causal structure from observations alone. We implement a quantum-optical experiment wherein we control the causal relation between two optical modes, and two measurement schemes-with and without randomization-that extract this relation from the observed correlations. Our results show that entanglement and quantum coherence provide an advantage for causal inference.T he slogan 'correlation does not imply causation' is meant to capture the fact that any joint probability distribution over two variables can be explained not only by a causal influence of one variable on the other, but also by a common cause acting on both 1 . We here investigate whether a similar ambiguity holds for quantum systems, and we show that, surprisingly, it does not.Finding causal explanations of observed correlations is a fundamental problem in science, with applications ranging from medicine and genetics to economics 2,3 . As a practical illustration, consider a drug trial. Naively, a correlation between the variables treatment and recovery may suggest a causal influence of the former on the latter. But suppose men are more likely than women to seek treatment, and also more likely to recover spontaneously, regardless of treatment. In this case, gender is a common cause, inducing correlations between treatment and recovery even if there is no cause-effect relation between them.Unless one can make strong assumptions about the nature of the causal mechanisms 4 , the only way to distinguish between the two possibilities is to replace observation of the early variable with an intervention on it. For instance, pharmaceutical companies do not leave the choice of treatment to the subjects of their trials, but carefully randomize the assignment of drug or placebo. This ensures that the administered treatment is statistically independent of any potential common causes with recovery. Consequently, any correlations with recovery that persist herald a directed causal influence. The question of whether there were in fact common causes can be answered by tracking whether recovery correlates with the subjects' intent to treat. Thus, the ability to intervene allows a complete solution of the causal inference problem: it reveals both which variables are causes of which others and, via the strength of the correlations, the precise mathematical form of the causal dependencies.In this article, we consider the quantum version of this causal inference probl...

Systems entangled in high dimensions have recently been proposed as important tools for various quantum information protocols, such as multibit quantum key distribution and loophole-free tests of nonlocality. It is therefore important to have precise knowledge of the nature of such entangled quantum states. We tomographically reconstruct the quantum state of the two photons produced by parametric downconversion that are entangled in a d-dimensional orbital angular momentum basis. We determine exactly the density matrix of the entangled two-qudit state with d ranging from 2 to 8. The recording of higher-dimensional states is limited only by the number of data points required and therefore the length of time needed to complete the measurements. We find all the measured states to have fidelities and linear entropies that satisfy the criteria required for a violation of the appropriate high-dimensional Bell inequality. Our results therefore precisely characterize the nature of the entanglement, thus establishing the suitability of such states for applications in quantum information science.

A simple approach to preparing high-dimensional entangled states by quantum interference.