arXiv subjects

Philippe Allard Guérin

Publications and source records attributed to Philippe Allard Guérin.

12 recordsLinked to original sources

arXiv2025

Quantum computation with indefinite causal structures

One way to study the physical plausibility of closed timelike curves (CTCs) is to examine their computational power. This has been done for Deutschian CTCs (D-CTCs) and post-selection CTCs (P-CTCs), with the result that they allow for the efficient solution of problems in PSPACE and PP, respectively. Since these are extremely powerful complexity classes, which are not expected to be solvable in reality, this can be taken as evidence that these models for CTCs are pathological. This problem is closely related to the nonlinearity of this models, which also allows for example cloning quantum states, in the case of D-CTCs, or distinguishing non-orthogonal quantum states, in the case of P-CTCs. In contrast, the process matrix formalism allows one to model indefinite causal structures in a linear way, getting rid of these effects, and raising the possibility that its computational power is rather tame. In this paper we show that process matrices correspond to a linear particular case of P-CTCs, and therefore that its computational power is upperbounded by that of PP. We show, furthermore, a family of processes that can violate causal inequalities but nevertheless can be simulated by a causally ordered quantum circuit with only a constant overhead, showing that indefinite causality is not necessarily hard to simulate.

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arXiv2022

Noncausal Page-Wootters circuits

One of the most fundamental open problems in physics is the unification of general relativity and quantum theory to a theory of quantum gravity. An aspect that might become relevant in such a theory is that the dynamical nature of causal structure present in general relativity displays quantum uncertainty. This may lead to a phenomenon known as indefinite or quantum causal structure, as captured by the process matrix formalism. Due to the generality of that framework, however, for many process matrices there is no clear physical interpretation. A popular approach towards a quantum theory of gravity is the Page-Wootters formalism, which associates to time a Hilbert space structure similar to spatial position. By explicitly introducing a quantum clock, it allows to describe time-evolution of systems via correlations between this clock and said systems encoded in history states. In this paper we combine the process matrix framework with a generalization of the Page-Wootters formalism in which one considers several agents, each with their own discrete quantum clock. We describe how to extract process matrices from scenarios involving such agents with quantum clocks, and analyze their properties. The description via a history state with multiple clocks imposes constraints on the implementation of process matrices and on the perspectives of the agents as described via causal reference frames. While it allows for scenarios where different definite causal orders are coherently controlled, we explain why certain noncausal processes might not be implementable within this setting.

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arXiv2022

Quantum teleportation of quantum causal structures

Quantum teleportation is a very helpful information-theoretic protocol that allows to transfer an unknown arbitrary quantum state from one location to another without having to transmit the quantum system through the intermediate region. Quantum states, quantum channels, and indefinite causal structures are all examples of quantum causal structures that not only enable advanced quantum information processing functions, but can also model causal structures in nonclassical spacetimes. In this letter, we develop quantum teleportation of arbitrary quantum causal structures, as formalized by the process matrix framework. Instead of teleporting all the physical degrees of freedom that implement the causal structure, the central idea is to just teleport the inputs to and outputs from the operations of agents. The communication of outcomes of Bell state measurements, which is necessary for deterministic quantum teleportation, is not possible for all causal structures that one might wish to investigate. To avoid this problem, we propose partially and fully post-selected teleportation protocols. We prove that our partially post-selected teleportation protocol is compatible with all quantum causal structures, including those that involve indefinite causal order.

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arXiv2021

Simple and maximally robust processes with no classical common-cause or direct-cause explanation

Guided by the intuition of coherent superposition of causal relations, recent works presented quantum processes without classical common-cause and direct-cause explanation, that is, processes which cannot be written as probabilistic mixtures of quantum common-cause and quantum direct-cause relations (CCDC). In this work, we analyze the minimum requirements for a quantum process to fail to admit a CCDC explanation and present "simple" processes, which we prove to be the most robust ones against general noise. These simple processes can be realized by preparing a maximally entangled state and applying the identity quantum channel, thus not requiring an explicit coherent mixture of common-cause and direct-cause, exploiting the possibility of a process to have both relations simultaneously. We then prove that, although all bipartite direct-cause processes are bipartite separable operators, there exist bipartite separable processes which are not direct-cause. This shows that the problem of deciding weather a process is direct-cause process is not equivalent to entanglement certification and points out the limitations of entanglement methods to detect non-classical CCDC processes. We also present a semi-definite programming hierarchy that can detect and quantify the non-classical CCDC robustnesses of every non-classical CCDC process. Among other results, our numerical methods allow us to show that the simple processes presented here are likely to be also the maximally robust against white noise. Finally, we explore the equivalence between bipartite direct-cause processes and bipartite processes without quantum memory, to present a separable process which cannot be realized as a process without quantum memory.

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arXiv2021

A no-go theorem for the persistent reality of Wigner's friend's perception

The notorious Wigner's friend thought experiment (and modifications thereof) has in recent years received renewed interest especially due to new arguments that force us to question some of the fundamental assumptions of quantum theory. In this paper, we formulate a no-go theorem for the persistent reality of Wigner's friend's perception, which allows us to conclude that the perceptions that the friend has of her own measurement outcomes at different times cannot "share the same reality", if seemingly natural quantum mechanical assumptions are met. More formally, this means that, in a Wigner's friend scenario, there is no joint probability distribution for the friend's perceived measurement outcomes at two different times, that depends linearly on the initial state of the measured system and whose marginals reproduce the predictions of unitary quantum theory. This theorem entails that one must either (1) propose a nonlinear modification of the Born rule for two-time predictions, (2) sometimes prohibit the use of present information to predict the future -- thereby reducing the predictive power of quantum theory -- or (3) deny that unitary quantum mechanics makes valid single-time predictions for all observers. We briefly discuss which of the theorem's assumptions are more likely to be dropped within various popular interpretations of quantum mechanics.

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arXiv2021

Experimental Quantum Communication Enhancement by Superposing Trajectories

In quantum communication networks, wires represent well-defined trajectories along which quantum systems are transmitted. In spite of this, trajectories can be used as a quantum control to govern the order of different noisy communication channels, and such a control has been shown to enable the transmission of information even when quantum communication protocols through well-defined trajectories fail. This result has motivated further investigations on the role of the superposition of trajectories in enhancing communication, which revealed that the use of quantum control of parallel communication channels, or of channels in series with quantum-controlled operations, can also lead to communication advantages. Building upon these findings, here we experimentally and numerically compare different ways in which two trajectories through a pair of noisy channels can be superposed. We observe that, within the framework of quantum interferometry, the use of channels in series with quantum-controlled operations generally yields the largest advantages. Our results contribute to clarify the nature of these advantages in experimental quantum-optical scenarios, and showcase the benefit of an extension of the quantum communication paradigm in which both the information exchanged and the trajectory of the information carriers are quantum.

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arXiv2020

Observer-dependent locality of quantum events

In general relativity, the causal structure between events is dynamical, but it is definite and observer-independent; events are point-like and the membership of an event A in the future or past light-cone of an event B is an observer-independent statement. When events are defined with respect to quantum systems however, nothing guarantees that the causal relationship between A and B is definite. We propose to associate a causal reference frame corresponding to each event, which can be interpreted as an observer-dependent time according to which an observer describes the evolution of quantum systems. In the causal reference frame of one event, this particular event is always localised, but other events can be "smeared out" in the future and in the past. We do not impose a predefined causal order between the events, but only require that descriptions from different reference frames obey a global consistency condition. We show that our new formalism is equivalent to the pure process matrix formalism. The latter is known to predict certain multipartite correlations, which are incompatible with the assumption of a causal ordering of the events -- these correlations violate causal inequalities. We show how the causal reference frame description can be used to gain insight into the question of realisability of such strongly non-causal processes in laboratory experiments. As another application, we use causal reference frames to revisit a thought experiment where the gravitational time dilation due to a massive object in a quantum superposition of positions leads to a superposition of the causal ordering of two events.

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arXiv2020

Uncertainty and Trade-offs in Quantum Multiparameter Estimation

Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum system. They quantify trade-offs in accuracy between complementary pieces of information about the system. In Quantum multiparameter estimation, such trade-offs occur for the precision achievable for different parameters characterizing a density matrix: an uncertainty relation emerges between the achievable variances of the different estimators. This is in contrast to classical multiparameter estimation, where simultaneous optimal precision is attainable in the asymptotic limit. We study trade-off relations that follow from known tight bounds in quantum multiparameter estimation. We compute trade-off curves and surfaces from Cramér--Rao type bounds which provide a compelling graphical representation of the information encoded in such bounds, and argue that bounds on simultaneously achievable precision in quantum multiparameter estimation should be regarded as measurement uncertainty relations. From the state-dependent bounds on the expected cost in parameter estimation, we derive a state independent uncertainty relation between the parameters of a qubit system.

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arXiv2019

A Spacetime Area Law Bound on Quantum Correlations

Area laws are a far-reaching consequence of the locality of physical interactions, and they are relevant in a range of systems, from black holes to quantum many-body systems. Typically, these laws concern the entanglement entropy or the quantum mutual information of a subsystem at a single time. However, when considering information propagating in spacetime, while carried by a physical system with local interactions, it is intuitive to expect area laws to hold for spacetime regions; in this work, we prove such a law in the case of quantum lattice systems. We consider a sequence of local quantum operations performed at discrete times on a spin-lattice, such that each operation is associated to a point in spacetime. In the time between operations, the time evolution of the spins is governed by a finite range Hamiltonian. By considering a purification of the quantum instruments and analyzing the quantum mutual information between the ancillas used in the purification, we obtain a spacetime area law bound for the correlations between the measurement outcomes inside a spacetime region, and those outside of it.

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arXiv2019

Communication through quantum-controlled noise

In a recent series of works [Ebler et al. Phys. Rev. Lett. 120, 120502 (2018); arXiv:1809.06655v2; arXiv:1810.10457v2], it has been proposed that the quantum superposition of causal order -- the quantum switch -- may offer an enhancement of classical and quantum channel capacity through noisy channels, a phenomena that was coined `causal activation'. In this paper we attempt to clarify the nature of the purported advantage, by comparing the quantum switch to a class of processes that can be interpreted as quantum superposition of processes with the same causal order. We show that some of these processes can match or even outperform the quantum switch at enhancing classical and quantum channel capacity, and argue that they require the same resources as the switch. We conclude, in agreement with Abbott et al. [arXiv:1810.09826v1], that the aforementioned advantages appear to be attributable to the ability to coherently control quantum operations, and not to indefinite causal order per se.

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arXiv2019

Composition rules for quantum processes: a no-go theorem

A quantum process encodes the causal structure that relates quantum operations performed in local laboratories. The process matrix formalism includes as special cases quantum mechanics on a fixed background space-time, but also allows for more general causal structures. Motivated by the interpretation of processes as a resource for quantum information processing shared by two (or more) parties, with advantages recently demonstrated both for computation and communication tasks, we investigate the notion of composition of processes. We show that under very basic assumptions such a composition rule does not exist. While the availability of multiple independent copies of a resource, e.g. quantum states or channels, is the starting point for defining information-theoretic notions such as entropy (both in classical and quantum Shannon theory), our no-go result means that a Shannon theory of general quantum processes will not possess a natural rule for the composition of resources.

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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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