Jessica Bavaresco | LIP6 - Équipe QI

Strategy optimization for Bayesian quantum parameter estimation with finite copies: Adaptive greedy, parallel, sequential, and general strategies

Fri, 20 Mar 2026 00:00:00 +0000

In this work, we study Bayesian quantum parameter estimation given a finite number of uses of the process encoding one or more unknown physical quantities. For multiple uses, it is conventional to classify quantum metrological protocols as parallel, sequential, or indefinite causal order. Within each class, the central question is to determine the optimal strategy – namely, the choice of optimal input state, control operations, measurement, and estimator(s) – to perform the estimation task. Using the formalism of higher-order operations, we develop an algorithm that looks for the optimal solution, and we provide an efficient numerical implementation based on semidefinite programming. Our benchmark examples, specifically those against existing analytical solutions, demonstrate how powerful and precise our method is. We further explore the potential of greedy adaptive strategies, which are based on classical feedforward to design the optimal protocol for the next round. Using this framework, we compare the optimal achievable Bayesian score across classes. We demonstrate the strength of our algorithm in several examples, from single to multiparameter estimation and with various prior distributions. Particularly, we find examples in which there is a strict hierarchy between different classes. Nonetheless, the performance of the different quantum memory-assisted classes are not significantly different, while they may significantly outperform the adaptive greedy strategy.

Exponential separation in quantum query complexity of the quantum switch with respect to simulations with standard quantum circuits

Wed, 10 Dec 2025 00:00:00 +0000

Quantum theory is consistent with a computational model permitting black-box operations to be applied in an indefinite causal order, going beyond the standard circuit model of computation. The quantum switch – the simplest such example – has been shown to provide numerous information-processing advantages. Here, we prove that the action of the quantum switch on two $n$-qubit quantum channels cannot be simulated deterministically and exactly by any causally ordered quantum circuit that uses $M$ calls to one channel and one call to the other, if $M \leq \max(2, 2^n-1)$. This demonstrates an exponential separation in quantum query complexity of indefinite causal order compared to standard quantum circuits.

Catalytic Activation of Bell Nonlocality

Tue, 25 Nov 2025 00:00:00 +0000

The correlations of certain entangled states can be perfectly simulated classically via a local model. Hence such states are termed Bell local, as they cannot lead to Bell inequality violation. Here, we show that Bell nonlocality can nevertheless be activated for certain Bell-local states via a catalytic process. Specifically, we present a protocol where a Bell-local state, combined with a catalyst, is transformed into a Bell-nonlocal state while the catalyst is returned exactly in its initial state. Importantly, this transformation is deterministic and based only on local operations. Moreover, this procedure is possible even when the state of the catalyst is itself Bell local, demonstrating a new form of superactivation of Bell nonlocality, as well as an interesting form of quantum catalysis. On the technical level, our main tool is a formal connection between catalytic activation and many-copy activation, which is of independent interest.

Simulating the quantum switch with quantum circuits is computationally hard

Thu, 20 Nov 2025 00:00:00 +0000

Higher-order transformations acting on input quantum channels in an indefinite causal order—such as the quantum switch—cannot be described by quantum circuits using the same number of calls to the input channels. A natural question is whether they can be simulated, i.e., whether their action can be exactly and deterministically reproduced by a quantum circuit with more calls to the input channels. Here, we prove that the quantum switch acting on two n-qubit channels cannot be simulated by any quantum circuit using k calls to one channel and one to the other, if k < 2^n. This establishes an exponential separation in quantum query complexity between processes with indefinite causal order and quantum circuits. Moreover, even with one extra call to both input channels, such a simulation remains impossible. We further demonstrate the robustness of this separation by extending the result to probabilistic and approximate simulations scenarios.

The power of quantum catalytic local operations

Mon, 13 Oct 2025 00:00:00 +0000

A key result in entanglement theory is that the addition of a catalyst dramatically enlarges the set of possible state transformations via local operations and classical communication (LOCC). However, it remains unclear what is the interplay between classical communication and quantum catalysis. Here our aim is to disentangle the effect of the catalyst from that of classical communication. To do so, we explore a class of state transformations termed catalytic local operations (CLO) and compare it to LOCC and to stochastic LOCC augmented by bounded quantum communication. We show that these classes are incomparable and capture different facets of quantum state transformations.

Can the quantum switch be deterministically simulated?

Sun, 06 Oct 2024 00:00:00 +0000

Higher-order transformations that act on a certain number of input quantum channels in an indefinite causal order - such as the quantum switch - cannot be described by standard quantum circuits that use the same number of calls of the input quantum channels. However, the question remains whether they can be simulated, i.e., whether their action on their input channels can be deterministically reproduced, for all arbitrary inputs, by a quantum circuit that uses a larger number of calls of the input channels. Here, we prove that when only one extra call of each input channel is available, the quantum switch cannot be simulated by any quantum circuit. We demonstrate that this result is robust by showing that, even when probabilistic and approximate simulations are considered, higher-order transformations that are close to the quantum switch can be at best simulated with a probability strictly less than one. This result stands in stark contrast with the known fact that, when the quantum switch acts exclusively on unitary channels, its action can be simulated.

Exponential separation in quantum query complexity of the quantum switch with respect to simulations with standard quantum circuits

Sun, 06 Oct 2024 00:00:00 +0000