Standard quantum computation is based on sequences of unitary quantum logic gates that process qubits. The one-way quantum computer proposed by Raussendorf and Briegel is entirely different. It has changed our understanding of the requirements for quantum computation and more generally how we think about quantum physics. This new model requires qubits to be initialized in a highly entangled cluster state. From this point, the quantum computation proceeds by a sequence of single-qubit measurements with classical feedforward of their outcomes. Because of the essential role of measurement, a one-way quantum computer is irreversible. In the one-way quantum computer, the order and choices of measurements determine the algorithm computed. We have experimentally realized four-qubit cluster states encoded into the polarization state of four photons. We characterize the quantum state fully by implementing experimental four-qubit quantum state tomography. Using this cluster state, we demonstrate the feasibility of one-way quantum computing through a universal set of one- and two-qubit operations. Finally, our implementation of Grover's search algorithm demonstrates that one-way quantum computation is ideally suited for such tasks.

Quantum computation promises to solve fundamental, yet otherwise intractable, problems across a range of active fields of research. Recently, universal quantum logic-gate sets-the elemental building blocks for a quantum computer-have been demonstrated in several physical architectures. A serious obstacle to a full-scale implementation is the large number of these gates required to build even small quantum circuits. Here, we present and demonstrate a general technique that harnesses multi-level information carriers to significantly reduce this number, enabling the construction of key quantum circuits with existing technology. We present implementations of two key quantum circuits: the three-qubit Toffoli gate and the general two-qubit controlled-unitary gate. Although our experiment is carried out in a photonic architecture, the technique is independent of the particular physical encoding of quantum information, and has the potential for wider application.T he realization of a full-scale quantum computer presents one of the most challenging problems facing modern science. Even implementing small-scale quantum algorithms requires a high level of control over multiple quantum systems. Recently, much progress has been made with demonstrations of universal quantum gate sets in a number of physical architectures including ion traps 1,2 , linear optics 3-6 , superconductors 7,8 and atoms 9,10 . In theory, these gates can now be put together to implement any quantum circuit and build a scalable quantum computer. In practice, there are many significant obstacles that will require both theoretical and technological developments to overcome. One is the sheer number of elemental gates required to build quantum logic circuits.Most approaches to quantum computing use qubits-the quantum version of bits. A qubit is a two-level quantum system that can be represented mathematically by a vector in a two-dimensional Hilbert space. Realizing qubits typically requires enforcing a twolevel structure on systems that are naturally far more complex and which have many readily accessible degrees of freedom, such as atoms, ions or photons. Here, we show how harnessing these extra levels during computation significantly reduces the number of elemental gates required to build key quantum circuits. Because the technique is independent of the physical encoding of quantum information and the way in which the elemental gates are themselves constructed, it has the potential to be used in conjunction with existing gate technology in a wide variety of architectures. Our technique extends a recent proposal 11 , and we use it to demonstrate two key quantum logic circuits: the Toffoli and controlled-unitary 12 gates. We first outline the technique in a general context, then present an experimental realization in a linear optic architecture: without our resource-saving technique, linear optic implementations of these gates are infeasible with current technology. Simplifying the Toffoli gateOne of the most important quantum logic gates is the Toffoli 1...

The simplest decomposition of a Toffoli gate acting on three qubits requires five 2-qubit gates. If we restrict ourselves to controlled-sign (or controlled-NOT) gates this number climbs to six. We show that the number of controlled-sign gates required to implement a Toffoli gate can be reduced to just three if one of the three quantum systems has a third state that is accessible during the computation, i.e. is actually a qutrit. Such a requirement is not unreasonable or even atypical since we often artificially enforce a qubit structure on multilevel quantums systems (eg. atoms, photonic polarization and spatial modes). We explore the implementation of these techniques in optical quantum processing and show that linear optical circuits could operate with much higher probabilities of success.

To make precise the sense in which nature fails to respect classical physics, one requires a formal notion of classicality. Ideally, such a notion should be defined operationally, so that it can be subject to direct experimental test, and it should be applicable in a wide variety of experimental scenarios so that it can cover the breadth of phenomena thought to defy classical understanding. Bell's notion of local causality fulfils the first criterion but not the second. The notion of noncontextuality fulfils the second criterion, but it is a long-standing question whether it can be made to fulfil the first. Previous attempts to test noncontextuality have all assumed idealizations that real experiments cannot achieve, namely noiseless measurements and exact operational equivalences. Here we show how to devise tests that are free of these idealizations. We perform a photonic implementation of one such test, ruling out noncontextual models with high confidence.

The three-box problem is a gedankenexperiment designed to elucidate some interesting features of quantum measurement and locality. A particle is prepared in a particular superposition of three boxes, and later found in a different (but nonorthogonal) superposition. It was predicted that appropriate "weak" measurements of particle position in the interval between preparation and post-selection would find the particle in two different places, each with certainty. We verify these predictions in an optical experiment and address the issues of locality and of negative probability.Weak measurements have been controversial ever since the concept was developed by Aharonov, Albert, and Vaidman (AAV) [1].In contrast to the usual, von Neumann, approach to measurement, weak measurement uses an apparatus whose pointer has a very large quantum mechanical uncertainty when compared with its typical shift. After the system-pointer interaction, the shift in the pointer position is much smaller than its initial uncertainty and almost no information is gained about the quantum system. Nevertheless, after a sufficiently large number of measurements on an ensemble of identically prepared quantum systems, the mean pointer position can be determined to any degree of precision. In such a measurement strategy, one sacrifices knowledge of the value of an observable on any given experimental run to avoid entanglement with the measurement device and the ensuing 'collapse' of the wavefunction. In particular, this makes it possible to contemplate the behavior of a system defined both by state preparation and by a later post-selection, without significant disturbance of the system in the intervening period.AAV [1] calculated the shift in the pointer of a measurement apparatus that weakly measured an observable A between two strong measurements. The initial strong measurement pre-selects (or prepares) the state, |ψ i , of the quantum system and the final strong measurement post-selects the quantum state, ψ f . In between, consider a von Neumann-style interaction Hamiltonian of the formwhere is the hermitian operator corresponding to an observable A of the quantum system, g is a (real) coupling constant, andP x is the momentum operator conjugate to the pointer positionX. In the absence of postselection, the effect of having this measurement interaction on for a time T (assumed short enough that A is constant during the measurement) shifts the pointer position by an amount ∆x = K  ≡ gT  ,such that one can infer a value for A by dividing the pointer shift by the interaction strength K. The main result of AAV's seminal work [1] is that for sufficiently weak coupling strength K and in the presence of postselection, the inferred value of

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...

Heisenberg's uncertainty principle provides a fundamental limitation on an observer's ability to simultaneously predict the outcome when one of two measurements is performed on a quantum system. However, if the observer has access to a particle (stored in a quantum memory) which is entangled with the system, his uncertainty is generally reduced. This effect has recently been quantified by Berta et al. [Nature Physics 6, 659 (2010)] in a new, more general uncertainty relation, formulated in terms of entropies. Using entangled photon pairs, an optical delay line serving as a quantum memory and fast, active feed-forward we experimentally probe the validity of this new relation. The behaviour we find agrees with the predictions of quantum theory and satisfies the new uncertainty relation. In particular, we find lower uncertainties about the measurement outcomes than would be possible without the entangled particle. This shows not only that the reduction in uncertainty enabled by entanglement can be significant in practice, but also demonstrates the use of the inequality to witness entanglement.Consider an experiment in which one of two measurements is made on a quantum system. In general, it is not possible to predict the outcomes of both measurements precisely, which leads to uncertainty relations constraining our ability to do so. Such relations lie at the heart of quantum theory and have profound fundamental and practical consequences. They set fundamental limits on precision technologies such as metrology and lithography, and also served as the intuition behind new types of technologies such as quantum cryptography [1,2].The first relation of this kind was formulated by Heisenberg for the case of position and momentum [3]. Subsequent work by Robertson [4] and Schrödinger [5] generalized this relation to arbitrary pairs of observables. In particular, Robertson showed thatwhere uncertainty is characterized in terms of the standard deviation ∆R for an observable R (and likewise for S) and the right-hand-side (RHS) of the inequality is expressed in terms of the expectation value of the commutator, [R, S] := RS − SR, of the two observables. More recently, driven by information theory, uncertainty relations have been developed in which the uncertainty is quantified using entropy [6,7], rather than the standard deviation. This links uncertainty relations more naturally to classical and quantum information and overcomes some pitfalls of equation (1) pointed out by Deutsch [7]. Most uncertainty relations apply only in the case where the uncertainty is measured for an observer holding only classical information about the system. One such relation, conjectured by Kraus [8] and subsequently proven by Maassen and Uffink [9], states that for any observables R and Swhere H(R) denotes the Shannon entropy [10] of the probability distribution of the outcomes when R is measured and the term 1/c quantifies the complementarity of the observables. For non-degenerate observables, it is defined by c := max r,s | Ψ r |Υ s | 2 , where ...

Non-classical states of light, such as entangled photon pairs and number states, are essential for fundamental tests of quantum mechanics and optical quantum technologies. The most widespread technique for creating these quantum resources is spontaneous parametric down-conversion of laser light into photon pairs. Conservation of energy and momentum in this process, known as phase-matching, gives rise to strong correlations that are used to produce two-photon entanglement in various degrees of freedom. It has been a longstanding goal in quantum optics to realize a source that can produce analogous correlations in photon triplets, but of the many approaches considered, none has been technically feasible. Here we report the observation of photon triplets generated by cascaded down-conversion. Each triplet originates from a single pump photon, and therefore quantum correlations will extend over all three photons in a way not achievable with independently created photon pairs. Our photon-triplet source will allow experimental interrogation of novel quantum correlations, the generation of tripartite entanglement without post-selection and the generation of heralded entangled photon pairs suitable for linear optical quantum computing. Two of the triplet photons have a wavelength matched for optimal transmission in optical fibres, suitable for three-party quantum communication. Furthermore, our results open interesting regimes of non-linear optics, as we observe spontaneous down-conversion pumped by single photons, an interaction also highly relevant to optical quantum computing.