Damian Markham

Bell non-locality is a powerful framework to distinguish classical, quantum, and post-quantum resources, which relies on non-communicating players. Under which restriction can we have the same separations, if we allow for communication? Non-signalling state assemblages, and the fact that they can always be simultaneously purified, turned out to be the key element to restrict the simplest bipartite communication scenario, the prepare-and-measure, to the standard bipartite Bell scenario. Yet, many distinctive features of quantum theory are genuinely multipartite and cannot be reduced to two-party behaviour. In this work we are interested in extending this simultaneous purification inspired result to all multipartite communication schemes. As a first step, we unify and extend the simultaneous purification result from states to instruments and super-instruments, which are composable structures, and open up the possibility to explore more complex communication scenarios. Our main contribution is to establish that arbitrary compositions of non-signalling assemblages cannot escape the standard spatial quantum Bell correlations set. As a consequence, any interactive quantum realization of correlations outside of this set must involve at least one signalling assemblage of quantum operations, even when the resulting correlations are non-signalling.

Quantum sensors are powerful tools for measuring physical quantities with high sensitivity, enabling, for instance, the mapping of Earth’s gravitational field , detecting very small changes of magnetic fields, or the passage of time. The underlying principle is to use a quantum state as a probe that interacts with the physical quantity of interest, thereby encoding relevant information into the state. Although individual quantum sensors may exhibit remarkable sensitivity, the precision of a certain measurement can be significantly enhanced when multiple probes are entangled. Distributed quantum sensing extends this further and leverages entanglement among spatially separated sensors, allowing them to function as a single, coherent system. This approach enables measurements across extended spatial regions, while surpassing the precision achievable by independent sensors. However, a significant challenge in a network setting is ensuring that sensors deployed across different parties serve as the necessary resources for the correct functioning of the target sensing task. This challenge has motivated the combination of quantum cryptography with quantum sensing. In this context, Shettell et al. introduced the notion of privacy for sensor networks, ensuring that, beyond the metrological advantage of cooperative estimation of a global function, parties can also maintain the privacy of their local information and control what data is accessible to others. In this work, we adopt this protocol and focus on a multi-user quantum sensor network framework to analyze the privacy aspects of this parameter estimation task, leveraging a high-quality four-party GHZ state source.

Authentication of quantum resources is a critical tool in the development of quantum information processing protocols. In particular, the verification of quantum states is often used as a building block for communication tasks, determining whether the communicating parties can trust the resources at hand to exchange information or whether the protocol should be aborted. Self-testing methods have been used to tackle such verification tasks in a device-independent (DI) scenario. However, these approaches commonly consider the limit of large, identically and independently distributed (IID) samples, which weakens the DI claim and poses serious challenges to their experimental implementation. To address these issues, Gocanin et al. [1] developed a protocol to certify quantum states in the few-copies and non-IID regime. In this work, we adopt their protocol to experimentally demonstrate the device-independent verification of a four-photon GHZ state, produced with our compact and high-fidelity multipartite entangled photon source.

Graph state verification protocols allow multiple parties to share a graph state while checking that the state is honestly prepared, even in the presence of malicious parties. Since graph states are the starting point of numerous quantum protocols, it is crucial to ensure that graph state verification protocols can safely be composed with other protocols, this property being known as composable security. Previous works conjectured that such a property could not be proven within the abstract cryptography framework: we disprove this conjecture by showing that all graph state verification protocols can be turned into a composably secure protocol with respect to the natural functionality for graph state preparation. Moreover, we show that any unchanged graph state verification protocol can also be considered as composably secure for a slightly different, yet useful, functionality. Finally, we show that these two results are optimal, in the sense that any such generic result, considering arbitrary black-box protocols, must either modify the protocol or consider a different functionality. Along the way, we show a protocol to generalize entanglement swapping to arbitrary graph states that might be of independent interest.

Quantum transmission links are central elements in essentially all implementations of quantum information protocols. Emerging progress in quantum technologies involving such links needs to be accompanied by appropriate certification tools. In adversarial scenarios, a certification method can be vulnerable to attacks if too much trust is placed on the underlying system. Here, we propose a protocol in a device independent framework, which allows for the certification of practical quantum transmission links in scenarios where minimal assumptions are made about the functioning of the certification setup. We take in particular unavoidable transmission losses into account by modeling the link as a completely-positive trace-decreasing map. We also crucially remove the assumption of independent and identically distributed samples, which is known to be incompatible with adversarial settings. Finally, in view of the use of the certified transmitted states for follow-up applications, our protocol allows to estimate the quality of the state and does not certify the channel only. To illustrate the practical relevance and the feasibility of our protocol with currently available technology we provide an experimental implementation based on a state-of-the-art polarization entangled photon pair source in a Sagnac configuration and analyse its robustness for realistic losses and errors.

In this work we develop new methods for the characterisation of continuous variable quantum states using heterodyne measurement in both the trusted and untrusted settings. First, building on quantum state tomography with heterodyne detection, we introduce a reliable method for continuous variable quantum state certication, which directly yields the elements of the density matrix of the state considered and analytical condence intervals. This method neither needs mathematical reconstruction of the data, nor discrete binning of the sample space, and uses a single Gaussian measurement setting. Second, beyond quantum state tomography and without its identical copies assumption, we promote our reliable tomography method to a general efficient protocol for verifying continuous variable pure quantum states with Gaussian measurements against fully malicious adversaries, i.e. making no assumptions whatsoever on the state generated by the adversary. These results are obtained using a new analytical estimator for the expected value of any operator acting on a continuous variable quantum state with bounded support over the Fock basis, computed with samples from heterodyne detection of the state.

Analytical and algebraic geometry are valuable tools for dealing with problems involving analytical functions and polynomials. In what we connote as spatial quantum sensing the goal is, given an underlying field and a set of quantum sensors interrogating the field in a set of positions, to find an estimator for some property the field. This property can have multiple forms, be it distinguishing the source of a target signal, or evaluating the field (or a derivative thereof) in an arbitrary position. In this work we also link this problem to the development of networks of quantum sensors, and the role and usefulness of entangling these sensors. We find that the estimators that come out as a solution to the problem are such that a non-local entangled strategy provides maximum precision. We start by working under the assumption of polynomial fields, which relates to the interpolation problem, and then generalize for any signal that is modeled via analytical functions, giving rise to any general least-squares estimator. We discuss the effects of the placement of the sensors in the estimation, namely, how to find well defined, construction error-free placements for the sensors. In the case of interpolation we provide concrete examples and proofs in a $m$-dimensional array of sensors, and discuss necessary and sufficient conditions for the more general cases. We provide clear examples of the possible use-cases and statements, and compare a non-local entangled strategy with the best local strategy for an interpolation problem, showing the benefit in terms of precision in a distributed sensing scenario. This is a key tool for a wide-range of problem in sensing problems, ranging from large-scale such as earth-sized experiments, to local-scale, such has biological experiments.

Quantum networks have recently generated significant interest due to enhanced functionalities and security, including offering the capability to securely calculate a linear function of several parameters which themselves remain private. This allows joint estimation of a parameter using the precision advantage of quantum sensing. In this work, we extend the functionality of previously considered schemes to allow for some subset of the network, without sharing their own private network, to carry out parameter estimation together without revealing the identities of participants, either to each other or to the rest of the network, while being guaranteed that only the relevant parties have inputted their parameter.

We derive a general framework for a quantum metrology scheme where the quantum probes are exchanged via an unsecured quantum channel. We construct two protocols for this task which offer a trade-off between difficulty of implementation and efficiency. We show that, for both protocols, a malicious eavesdropper cannot access any information regarding the unknown parameter. We further derive general inequalities regarding how the uncertainty in a resource state for quantum metrology can bias the estimate and the precision. From this, we link the effectiveness of the cryptographic part of the protocol to the effectiveness of the metrology scheme with a (potentially) malicious probe resource state.