Lucas Emanuel Antunes Porto | LIP6 - Équipe QI

Can every set of incompatible measurements lead to genuine multipartite steering?

Fri, 03 Jul 2026 00:00:00 +0000

Measurement incompatibility and bipartite quantum steering are known to display a strong connection: a set of measurements is incompatible if and only if it can lead to bipartite steering. Despite such a close link between these concepts in bipartite scenarios, little is known in the multipartite setting, where notions of genuine multipartite correlations play major roles. In this work we prove that, as in the bipartite case, incompatibility is also necessary and sufficient for genuine multipartite steering in any multipartite scenario with a single uncharacterised party. Interestingly, genuine multipartite steering can be extracted from any set of incompatible measurements using states which are not SLOCC equivalent, such as GHZ and W states. In contrast, we prove that this result does not hold in scenarios with more than one uncharacterised party, by presenting a set of incompatible measurements that can never lead to genuine multipartite steering in these cases. In order to obtain our main results, we introduce methods tailored for multipartite correlations, paving the way to understanding the role of measurement incompatibility beyond bipartite scenarios.

Non-signaling assistance in prepare-and-measure scenarios with classical communication

Fri, 03 Jul 2026 00:00:00 +0000

Extracting the full power of non-local correlations in prepare-and-measure (PM) scenarios requires precise control over the timing and structure of the receiver’s measurements. Indeed, recent developments in entanglement-assisted classical communication scenarios have shown that adaptive strategies-where the receiver uses the transmitted message to guide their measurement choice-can outperform standard non-adaptive protocols. Moving beyond quantum theory, however, the ultimate limits of such advantages remain largely unexplored. In this work, we thoroughly study adaptive and non-adaptive non-signaling (NS) assistance in PM scenarios with classical communication. We provide simple characterizations of the sets of behaviors that can be realized using both non-adaptive and adaptive NS assistance in arbitrary PM scenarios. As a consequence, we show that non-adaptive NS assistance is already strong enough to reproduce quantum communication with the same message dimension: the transmission of a qudit can be simulated by a classical dit assisted non-adaptively by NS correlations. We then compare adaptive and non-adaptive NS assistance. We prove that any adaptive NS advantage can be traced back to scenarios in which the receiver has no measurement choice, ruling out the genuinely multi-setting advantages found in entanglement-assisted quantum protocols. Finally, we identify all PM scenarios where adaptive NS strategies provide a strict advantage over non-adaptive ones.

Can outcome communication explain Bell nonlocality?

Wed, 01 Jan 2025 00:00:00 +0000

A central aspect of quantum information is that correlations between spacelike separated observers sharing entangled states cannot be reproduced by local hidden variable (LHV) models, a phenomenon known as Bell nonlocality. If one wishes to explain such correlations by classical means, a natural possibility is to allow communication between the parties. In particular, LHV models augmented with two bits of classical communication can explain the correlations of any two-qubit state. Would this still hold if communication is restricted to measurement outcomes? While in certain scenarios with a finite number of inputs the answer is yes, we prove that if a model must reproduce all projective measurements, then for any qubit-qudit state the answer is no. In fact, a qubit-qudit under projective measurements admits an LHV model with outcome communication if and only if it already admits an LHV model without communication. On the other hand, we also show that when restricted sets of measurements are considered (for instance, when the qubit measurements are in the upper hemisphere of the Bloch ball), outcome communication does offer an advantage. This exemplifies that trivial properties in standard LHV scenarios, such as deterministic measurements and outcome-relabelling, play a crucial role in the outcome communication scenario.

Measurement incompatibility and quantum steering via linear programming

Wed, 01 Jan 2025 00:00:00 +0000

The problem of deciding whether a set of quantum measurements is jointly measurable is known to be equivalent to determining whether a quantum assemblage is unsteerable. This problem can be formulated as a semidefinite program (SDP). However, the number of variables and constraints in such a formulation grows exponentially with the number of measurements, rendering it intractable for large measurement sets. In this work, we circumvent this problem by transforming the SDP into a hierarchy of linear programs that compute upper and lower bounds on the incompatibility robustness with a complexity that grows polynomially in the number of measurements. The hierarchy is guaranteed to converge and it can be applied to arbitrary measurements – including non-projective POVMs – in arbitrary dimensions. While convergence becomes impractical in high dimensions, in the case of qubits our method reliably provides accurate upper and lower bounds for the incompatibility robustness of sets with several hundred measurements in a short time using a standard laptop. We also apply our methods to qutrits, obtaining non-trivial upper and lower bounds in scenarios that are otherwise intractable using the standard SDP approach. Finally, we show how our methods can be used to construct local hidden state models for states, or conversely, to certify that a given state exhibits steering; for two-qubit quantum states, our approach is comparable to, and in some cases outperforms, the current best methods.