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Mateus Araújo

Publications and source records attributed to Mateus Araújo.

At least 37 records · Page 2Linked to original sources
arXiv2022

Semi-device-independent certification of indefinite causal order

When transforming pairs of independent quantum operations according to the fundamental rules of quantum theory, an intriguing phenomenon emerges: some such higher-order operations may act on the input operations in an indefinite causal order. Recently, the formalism of process matrices has been developed to investigate these noncausal properties of higher-order operations. This formalism predicts, in principle, statistics that ensure indefinite causal order even in a device-independent scenario, where the involved operations are not characterised. Nevertheless, all physical implementations of process matrices proposed so far require full characterisation of the involved operations in order to certify such phenomena. Here we consider a semi-device-independent scenario, which does not require all operations to be characterised. We introduce a framework for certifying noncausal properties of process matrices in this intermediate regime and use it to analyse the quantum switch, a well-known higher-order operation, to show that, although it can only lead to causal statistics in a device-independent scenario, it can exhibit noncausal properties in semi-device-independent scenarios. This proves that the quantum switch generates stronger noncausal correlations than it was previously known.

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arXiv2021

Experimental entanglement of temporal order

The study of causal relations has recently been applied to the quantum realm, leading to the discovery that not all physical processes have a definite causal structure. While indefinite causal processes have previously been experimentally shown, these proofs relied on the quantum description of the experiments. Yet, the same experimental data could also be compatible with definite causal structures within different descriptions. Here, we present the first demonstration of indefinite temporal order outside of quantum formalism. We show that our experimental outcomes are incompatible with a class of generalised probabilistic theories satisfying the assumptions of locality and definite temporal order. To this end, we derive physical constraints (in the form of a Bell-like inequality) on experimental outcomes within such a class of theories. We then experimentally invalidate these theories by violating the inequality using entangled temporal order. This provides experimental evidence that there exist correlations in nature which are incompatible with the assumptions of locality and definite temporal order.

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arXiv2021

Computational advantage from quantum superposition of multiple temporal orders of photonic gates

Models for quantum computation with circuit connections subject to the quantum superposition principle have been recently proposed. There, a control quantum system can coherently determine the order in which a target quantum system undergoes $N$ gate operations. This process, known as the quantum $N$-switch, is a resource for several information-processing tasks. In particular, it provides a computational advantage -- over fixed-gate-order quantum circuits -- for phase-estimation problems involving $N$ unknown unitary gates. However, the corresponding algorithm requires an experimentally unfeasible target-system dimension (super)exponential in $N$. Here, we introduce a promise problem for which the quantum $N$-switch gives an equivalent computational speed-up with target-system dimension as small as 2 regardless of $N$. We use state-of-the-art multi-core optical-fiber technology to experimentally demonstrate the quantum $N$-switch with $N=4$ gates acting on a photonic-polarization qubit. This is the first observation of a quantum superposition of more than $N=2$ temporal orders, demonstrating its usefulness for efficient phase-estimation.

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arXiv2020

Computational advantage from quantum-controlled ordering of gates

It is usually assumed that a quantum computation is performed by applying gates in a specific order. One can relax this assumption by allowing a control quantum system to switch the order in which the gates are applied. This provides a more general kind of quantum computing, that allows transformations on blackbox quantum gates that are impossible in a circuit with fixed order. Here we show that this model of quantum computing is physically realizable, by proposing an interferometric setup that can implement such a quantum control of the order between the gates. We show that this new resource provides a reduction in computational complexity: we propose a problem that can be solved using $O(n)$ blackbox queries, whereas the best known quantum algorithm with fixed order between the gates requires $O(n^2)$ queries. Furthermore, we conjecture that solving this problem in a classical computer takes exponential time, which may be of independent interest.

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arXiv2020

A purification postulate for quantum mechanics with indefinite causal order

To study which are the most general causal structures which are compatible with local quantum mechanics, Oreshkov et al. introduced the notion of a process: a resource shared between some parties that allows for quantum communication between them without a predetermined causal order. These processes can be used to perform several tasks that are impossible in standard quantum mechanics: they allow for the violation of causal inequalities, and provide an advantage for computational and communication complexity. Nonetheless, no process that can be used to violate a causal inequality is known to be physically implementable. There is therefore considerable interest in determining which processes are physical and which are just mathematical artefacts of the framework. Here we make the first step in this direction, by proposing a purification postulate: processes are physical only if they are purifiable. We derive necessary conditions for a process to be purifiable, and show that several known processes do not satisfy them.

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arXiv2019

Probability in two deterministic universes

How can probabilities make sense in a deterministic many-worlds theory? We address two facets of this problem: why should rational agents assign subjective probabilities to branching events, and why should branching events happen with relative frequencies matching their objective probabilities. To address the first question, we generalise the Deutsch-Wallace theorem to a wide class of many-world theories, and show that the subjective probabilities are given by a norm that depends on the dynamics of the theory: the 2-norm in the usual Many-Worlds interpretation of quantum mechanics, and the 1-norm in a classical many-worlds theory known as Kent's universe. To address the second question, we show that if one takes the objective probability of an event to be the proportion of worlds in which this event is realised, then in most worlds the relative frequencies will approximate well the objective probabilities. This suggests that the task of determining the objective probabilities in a many-worlds theory reduces to the task of determining how to assign a measure to the worlds.

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arXiv2016

Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication

In communication complexity, a number of distant parties have the task of calculating a distributed function of their inputs, while minimizing the amount of communication between them. It is known that with quantum resources, such as entanglement and quantum channels, one can obtain significant reductions in the communication complexity of some tasks. In this work, we study the role of the quantum superposition of the direction of communication as a resource for communication complexity. We present a tripartite communication task for which such a superposition allows for an exponential saving in communication, compared to one-way quantum (or classical) communication; the advantage also holds when we allow for protocols with bounded error probability.

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arXiv2016

Experimental Verification of an Indefinite Causal Order

Investigating the role of causal order in quantum mechanics has recently revealed that the causal distribution of events may not be a-priori well-defined in quantum theory. While this has triggered a growing interest on the theoretical side, creating processes without a causal order is an experimental task. Here we report the first decisive demonstration of a process with an indefinite causal order. To do this, we quantify how incompatible our set-up is with a definite causal order by measuring a 'causal witness'. This mathematical object incorporates a series of measurements which are designed to yield a certain outcome only if the process under examination is not consistent with any well-defined causal order. In our experiment we perform a measurement in a superposition of causal orders - without destroying the coherence - to acquire information both inside and outside of a 'causally non-ordered process'. Using this information, we experimentally determine a causal witness, demonstrating by almost seven standard deviations that the experimentally implemented process does not have a definite causal order.

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arXiv2016

Causally nonseparable processes admitting a causal model

A recent framework of quantum theory with no global causal order predicts the existence of "causally nonseparable" processes. Some of these processes produce correlations incompatible with any causal order (they violate so-called "causal inequalities" analogous to Bell inequalities) while others do not (they admit a "causal model" analogous to a local model). Here we show for the first time that bipartite causally nonseparable processes with a causal model exist, and give evidence that they have no clear physical interpretation. We also provide an algorithm to generate processes of this kind and show that they have nonzero measure in the set of all processes. We demonstrate the existence of processes which stop violating causal inequalities but are still causally nonseparable when mixed with a certain amount of "white noise". This is reminiscent of the behavior of Werner states in the context of entanglement and nonlocality. Finally, we provide numerical evidence for the existence of causally nonseparable processes which have a causal model even when extended with an entangled state shared among the parties.

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arXiv2015

Quantum superposition of the order of parties as a communication resource

In a variant of communication complexity tasks, two or more separated parties cooperate to compute a function of their local data, using a limited amount of communication. It is known that communication of quantum systems and shared entanglement can increase the probability for the parties to arrive at the correct value of the function, compared to classical resources. Here we show that quantum superpositions of the direction of communication between parties can also serve as a resource to improve the probability of success. We present a tripartite task for which such a superposition provides an advantage compared to the case where the parties communicate in a fixed order. In a more general context, our result also provides the first semi-device-independent certification of the absence of a definite order of communication.

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arXiv2015

Witnessing causal nonseparability

Our common understanding of the physical world deeply relies on the notion that events are ordered with respect to some time parameter, with past events serving as causes for future ones. Nonetheless, it was recently found that it is possible to formulate quantum mechanics without any reference to a global time or causal structure. The resulting framework includes new kinds of quantum resources that allow performing tasks - in particular, the violation of causal inequalities - which are impossible for events ordered according to a global causal order. However, no physical implementation of such resources is known. Here we show that a recently demonstrated resource for quantum computation - the quantum switch - is a genuine example of "indefinite causal order". We do this by introducing a new tool - the causal witness - which can detect the causal nonseparability of any quantum resource that is incompatible with a definite causal order. We show however that the quantum switch does not violate any causal nequality.

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arXiv2015

The simplest causal inequalities and their violation

In a scenario where two parties share, act on and exchange some physical resource, the assumption that the parties' actions are ordered according to a definite causal structure yields constraints on the possible correlations that can be established. We show that the set of correlations that are compatible with a definite causal order forms a polytope, whose facets define causal inequalities. We fully characterize this causal polytope in the simplest case of bipartite correlations with binary inputs and outputs. We find two families of nonequivalent causal inequalities; both can be violated in the recently introduced framework of process matrices, which extends the standard quantum formalism by relaxing the implicit assumption of a fixed causal structure. Our work paves the way to a more systematic investigation of causal inequalities in a theory-independent way, and of their violation within the framework of process matrices.

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arXiv2014

Experimental Superposition of Orders of Quantum Gates

In a quantum computer, creating superpositions of quantum bits (qubits) in different states can lead to a speed-up over classical computers [1], but quantum mechanics also allows for the superposition of quantum circuits [2]. In fact, it has recently been theoretically predicted that superimposing quantum circuits, each with a different gate order, could provide quantum computers with an even further computational advantage [3-5]. Here, we experimentally demonstrate this enhancement by applying two quantum gates in a superposition of both possible orders to determine whether the two gates commute or anti-commute. We are able to make this determination with only a single use (or query) of each gate, while all quantum circuits with a fixed order of gates would require at least two uses of one of the gates [3]. Remarkably, when the problem is scaled to N gates, creating a superposition of quantum circuits is likely to provide an exponential advantage over classical algorithms, and a linear advantage over quantum algorithms with fixed gate order [4]. The new resource that we exploit in our experiment can be interpreted as a "superposition of causal orders". We demonstrate such a superposition could allow some quantum algorithms to be implemented with an efficiency that is unlikely to be achieved on a quantum computer with a fixed gate order.

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arXiv2014

Quantum realism and quantum surrealism

In this thesis we explore the questions of what should be considered a "classical" theory, and which aspects of quantum theory cannot be captured by any theory that respects our intuition of classicality. This exploration is divided in two parts: in the first we review classical results of the literature, such as the Kochen-Specker theorem, von Neumann's theorem, Gleason's theorem, as well as more recent ideas, such as the distinction between $ψ$-ontic and $ψ$-epistemic ontological models, Spekkens' definition of contextuality, Hardy's ontological excess baggage theorem and the PBR theorem. The second part is concerned with pinning down what should be the "correct" definition of contextuality. We settle down on the definition advocated by Abramsky and Branderburger, motivated by the Fine theorem, and show the connection of this definition with the work of George Boole. This definition allows us to unify the notions of locality and noncontextuality, and use largely the same tools to characterize how quantum mechanics violates these notions of classicality. Exploring this formalism, we find a new family of noncontextuality inequalities. We conclude by reviewing the notion of state-independent contextuality.

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arXiv2014

Quantum circuits cannot control unknown operations

One of the essential building blocks of classical computer programs is the "if" clause, which executes a subroutine depending on the value of a control variable. Similarly, several quantum algorithms rely on applying a unitary operation conditioned on the state of a control system. Here we show that this control cannot be performed by a quantum circuit if the unitary is completely unknown. However, this no-go theorem does not prevent implementing quantum control of unknown unitaries in practice, as any physical implementation of an unknown unitary provides additional information that makes the control possible. We then argue that one should extend the quantum circuit formalism to capture this possibility in a straightforward way. This is done by allowing unknown unitaries to be applied to subspaces and not only to subsystems.

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arXiv2013

All noncontextuality inequalities for the n-cycle scenario

The problem of separating classical from quantum correlations is in general intractable and has been solved explicitly only in few cases. In particular, known methods cannot provide general solutions for an arbitrary number of settings. We provide the complete characterization of the classical correlations and the corresponding maximal quantum violations for the case of n >= 4 observables X_0, ...,X_{n-1}, where each consecutive pair {X_i,X_{i+1}}, sum modulo n, is jointly measurable. This generalizes both the Clauser-Horne-Shimony-Holt and the Klyachko-Can-Binicioglu-Shumovsky scenarios, which are the simplest ones for, respectively, locality and noncontextuality. In addition, we provide explicit quantum states and settings with maximal quantum violation and minimal quantum dimension.

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arXiv2013

Realistic loophole-free Bell test with atom-photon entanglement

The establishment of nonlocal correlations, obtained through the violation of a Bell inequality, is not only important from a fundamental point of view, but constitutes the basis for device-independent quantum information technologies. Although several nonlocality tests have been performed so far, all of them suffered from either the locality or the detection loopholes. Recent studies have suggested that the use of atom-photon entanglement can lead to Bell inequality violations with moderate transmission and detection efficiencies. In this paper we propose an experimental setup realizing a simple atom-photon entangled state that, under realistic experimental parameters available to date, achieves a significant violation of the Clauser-Horn-Shimony-Holt inequality. Most importantly, the violation remains when considering typical detection efficiencies and losses due to required propagation distances.

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