Quantum discord characterizes "nonclassicality" of correlations in quantum mechanics. It has been proposed as the key resource present in certain quantum communication tasks and quantum computational models without containing much entanglement. We obtain a necessary and sufficient condition for the existence of nonzero quantum discord for any dimensional bipartite states. This condition is easily experimentally implementable. Based on this, we propose a geometrical way of quantifying quantum discord. For two qubits this results in a closed form of expression for discord. We apply our results to the model of deterministic quantum computation with one qubit, showing that quantum discord is unlikely to be the reason behind its speedup.

Universal quantum computers promise a dramatic speed-up over classical computers but a fullsize realization remains challenging. However, intermediate quantum computational models have been proposed that are not universal, but can solve problems that are strongly believed to be classically hard. Aaronson and Arkhipov have shown that interference of single photons in random optical networks can solve the hard problem of sampling the bosonic output distribution which is directly connected to computing matrix permanents. Remarkably, this computation does not require measurement-based interactions or adaptive feed-forward techniques. Here we demonstrate this model of computation using high-quality laser-written integrated quantum networks that were designed to implement random unitary matrix transformations. We experimentally characterize the integrated devices using an in-situ reconstruction method and observe three-photon interference that leads to the boson-sampling output distribution. Our results set a benchmark for quantum computers, that hold the potential of outperforming conventional ones using only a few dozen photons and linear-optical elements.

Quantum entanglement is widely recognized as one of the key resources for the advantages of quantum information processing, including universal quantum computation 1 , reduction of communication complexity 2,3 or secret key distribution 4 . However, computational models have been discovered, which consume very little or no entanglement and still can efficiently solve certain problems thought to be classically intractable 5,6 . The existence of these models suggests that separable or weakly entangled states could be extremely useful tools for quantum information processing as they are much easier to prepare and control even in dissipative environments. It has been proposed that a requirement for useful quantum states is the generation of so-called quantum discord 7,8 , a measure of non-classical correlations that includes entanglement as a subset. Although a link between quantum discord and few quantum information tasks has been studied, its role in computation speed-up is still open and its operational interpretation remains restricted to only few somewhat contrived situations 9-12 . Here we show that quantum discord is the optimal resource for the remote quantum state preparation 13 , a variant of the quantum teleportation protocol 14 . Using photonic quantum systems, we explicitly show that the geometric measure of quantum discord 15 is related to the fidelity of this task, which provides an operational meaning. Moreover, we demonstrate that separable states with non-zero quantum discord can outperform entangled states. Therefore, the role of quantum discord might provide fundamental insights for resource-efficient quantum information processing.Introduction.-Quantum computation and quantum communication is believed to allow for information processing with an efficiency that cannot be achieved by any classical device. It is usually assumed that a key resource for this enhanced performance is quantum entanglement 16 . The creation and manipulation of entanglement, however, is a very demanding task, as it requires extremely precise quantum control and isolation from the environment. Thus, current experimental achievements are limited to rather small scale entangled systems [17][18][19] . On the other hand there is no proof that quantum entanglement is necessary for quantum information processing (QIP) that can outperform its classical counterpart. The investigation of QIP protocols that allow for significant enhancements in the efficiency of data processing by only using separable states is of high interest. Obviously, such states have the benefit of being easier to prepare and more robust against losses and experimental imperfections. In fact, there are quantum computational models based on mixed, separable states, most notably the so-called deterministic quantum computation with one qubit (DQC1) 5 , which has recently been demonstrated experimentally [20][21][22] . In this context, quantum discord has been proposed as the resource that can provide the enhancement for the computation 23,24 , but its relation to...

Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some features with quantum theory, such as probabilistic predictions for individual outcomes (indeterminism), the impossibility of information transfer faster than speed of light (no-signaling) or the impossibility of copying of unknown states (no-cloning). A vast majority of attempts to find physical principles behind quantum theory either fall short of deriving the theory uniquely from the principles or are based on abstract mathematical assumptions that require themselves a more conclusive physical motivation. Here, we show that classical probability theory and quantum theory can be reconstructed from three reasonable axioms: (1) (Information capacity) All systems with information carrying capacity of one bit are equivalent. (2) (Locality) The state of a composite system is completely determined by measurements on its subsystems. (3) (Reversibility) Between any two pure states there exists a reversible transformation. If one requires the transformation from the last axiom to be continuous, one separates quantum theory from the classical probabilistic one. A remarkable result following from our reconstruction is that no probability theory other than quantum theory can exhibit entanglement without contradicting one or more axioms.

† These authors contributed equally to this work Quantum simulators are controllable quantum systems that can reproduce the dynamics of the system of interest, which are unfeasible for classical computers. Recent developments in quantum technology enable the precise control of individual quantum particles as required for studying complex quantum systems. Particularly, quantum simulators capable of simulating frustrated Heisenberg spin systems provide platforms for understanding exotic matter such as high-temperature superconductors. Here we report the analog quantum simulation of the ground-state wavefunction to probe arbitrary Heisenberg-type interactions among four spin-1/2 particles . Depending on the interaction strength, frustration within the system emerges such that the ground state evolves from a localized to a resonating valence-bond state. This spin-1/2 tetramer is created using the polarization states of four photons. The single-particle addressability and tunable measurement-induced interactions provide us insights into entanglement dynamics among individual particles. We directly extract ground-state energies and pair-wise quantum correlations to observe the monogamy of entanglement.During the past years, there has been an explosion of interest in quantum-enhanced technologies. The applications are many-fold and reach from quantum metrology[1] to quantum information processing [2]. In particular quantum computation has generated a lot of interest due to the discovery of quantum algorithms [3][4][5] which outperform classical ones. The first proposed application for which quantum computation can give an exponential enhancement over classical computation was suggested by Richard Feynman [6,7]. He considered a universal quantum mechanical simulator, which is a controllable quantum system that can be used to imitate other quantum systems, therefore being able to tackle problems that are intractable on classical computers. Since then the motivation to use a quantum simulator as a powerful tool to address the most important and difficult problems in multidisciplinary science has led to many theoretical proposals [8][9][10][11][12][13]. Vast technological developments allowed for recent realizations of such devices in atoms [14][15][16], trapped ions [17][18][19][20], single photons [21][22][23][24] and NMR [25,26]. The quantum simulation of strongly correlated quantum systems (e.g. frustrated spin systems) is of special interest and would provide new results that cannot be otherwise classically simulated [27].In order to manipulate and measure individual properties of microscopic quantum systems the complete control over all degrees of freedom for each particle is required. Typically, atoms in optical lattices [14] are used for realizing physical systems that can simulate various models in condensed-matter physics. The fact that the experimental addressability of single atoms in optical lattices remains very challenging [28][29][30] leads to the studies of bulk properties of the atomic ensemble (≈ 10 5 at...

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Can quantum theory be seen as a special case of a more general probabilistic theory, as classical theory is a special case of the quantum one? We study here the class of generalized probabilistic theories defined by the order of interference they exhibit as proposed by Sorkin. A simple operational argument shows that the theories require higher-order tensors as a representation of physical states. For the third-order interference we derive an explicit theory of 'density cubes' and show that quantum theory, i.e. theory of density matrices, is naturally embedded in it. We derive the genuine non-quantum class of states and nontrivial dynamics for the case of a three-level system and show how one can construct the states of higher dimensions. Additionally to genuine third-order interference, the density cubes are shown to violate the Leggett-Garg inequality beyond the quantum Tsirelson bound for temporal correlations.

One of the main challenges of quantum information is the reliable verification of quantum entanglement. The conventional detection schemes require repeated measurement on a large number of identically prepared systems. This is hard to achieve in practice when dealing with large-scale entangled quantum systems. In this letter we formulate verification as a decision procedure, i.e. entanglement is seen as the ability of quantum system to answer certain "yes-no questions". We show that for a variety of large quantum states even a single copy suffices to detect entanglement with a high probability by using local measurements. For example, a single copy of a 16-qubit k-producible state or one copy of 24-qubit linear cluster state suffices to verify entanglement with more than 95% confidence. Our method is applicable to many important classes of states, such as cluster states or ground states of local Hamiltonians in general.