Entanglement is a fundamental trait of many-body quantum systems and a key resource for quantum information processing. Yet, quantifying Entanglement is very hard! I have demonstrated universally valid, computable bounds to operationally meaningful measures of entanglement in terms of purity functionals. Then, experimentalists extracted these bounds by implementing two purity detection methods: shadow estimation and collective measurements. The experiments showed that quantum resources can be estimated, rather than just witnessed, with precision that does not scale with the rank of the state, conversely to state tomography. The scalability of the measurement network makes purity detection employable in testing the successful preparation of quantum superpositions in large computational registers, certifying that a complex device has run a truly quantum computation.
Fundamental limits to quantum correlations in many-body systems say so. Determining how a macroscopic classical world emerges from quantum building blocks is critical for our understanding of Nature. I have proven that when we perform physical measurements, we can only access and reach agreement about “classical” information. In particular, I have demonstrated tight bounds to quantum discord, the most general kind of quantum correlation, in terms of a new, well-motivated quantifier of classical objectivity. They limit the amount of quantum information that a system can simultaneously share with a network of independent observers, who access information via the system’s environment. While classical information is freely available to a multitude of agents, the very fact that they agree with each other about the properties of the quantum system of interest (what we call objectivity) inevitably suppresses quantum correlations.
References: Phys. Rev. Lett. 129, 010401 (2022) and Phys. Rev. Lett. 128, 010401 (2022)
The quantum state overlap, the textbook measure of the difference between two quantum states, is inadequate to compare the complex configurations of many-body systems. The problem is inherited by widely employed parent quantities, such as the quantum fidelity. I have introduced a new class of information-theoretic measures, the weighted distances, which overcome these limitations. They quantify the difference between quantum states of many particles, factoring in the size of the system dimension. Therefore, they can be used to evaluate both theoretical and experimental performance of many-body quantum devices. I have elucidated the operational interpretation of the weighted distances, uncovering a fundamental limit to quantum information processing: the computational resources of quantum systems are never greater than the experimental cost to create them.
Reference: Phys. Rev. Lett. 126, 170502 (2021)
Causal inference is one of the most fascinating and challenging problems across STEM disciplines. Unfortunately, given two or more interacting systems, there is no universally valid method for discriminating between different causal relations from same-looking input/output data, e.g. statistical analysis of measurement outcomes. I have introduced an information-theoretic measure of causation, capturing how much a quantum system influences the evolution of another system. The measure discriminates among different causal relations that generate same-looking data, with no information about the quantum channel. In particular, it determines whether correlation implies causation, and when causation manifests without correlation. In the classical scenario, the quantity evaluates the strength of causal links between random variables. Also, the measure is generalized to identify and rank concurrent sources of causal influence in many-body dynamics, enabling to reconstruct causal patterns in complex networks.
Reference: Phys. Lett. A, 126739 (2020)
I have found an analytical solution to this central question in quantum information processing. Consider a quantum system prepared in an input state. One wants to drive it into a target state. I have argued that incoherent states and classical stochastic maps as well-motivated sets of free states and operations, being the only ones which do not display quantum superpositions, i.e. coherence. Creating coherence should be never easy because it can be sufficient for outmatching classical devices. Then, I have introduced a design principle for quantum driving of general validity. The best preparation strategy is the input/target dynamics which minimizes a geometric index quantifying the quantum character of the transformation. The geometric measure, which overcomes the limitations of customary distance functions, lower bounds the operationally meaningful algorithmic cost to prepare a state via commuting operations. As a target state is expected to be computationally useful, it is also interesting to establish a link to the creation of quantum resources. I have derived quantitative relations between the quantumness of a process, a computable lower bound, and the coherence and quantum correlations created in the target.
Reference: Phys. Rev. Lett. 122, 010505 (2019), Editors' Suggestion
The very notion of genuine multipartite correlations still generates discussion. There is no consistent way to quantify dependencies which do not manifest bipartite correlations, encoding joint properties of k > 2 particles instead. A further problem is that computing correlations is not always sufficient to fully describe multipartite correlation patterns. Equally correlated networks of multivariate variables can display different structures and properties. Also, quantum states can be correlated in inherently inequivalent ways. I have identified measures of genuine multipartite correlations, i.e., statistical dependencies that cannot be ascribed to bipartite correlations, satisfying a set of desirable properties. Inspired by ideas developed in complexity science, I have then introduced the concept of weaving to classify states that display different correlation patterns, but cannot be distinguished by correlation measures. The weaving of a state is defined as the weighted sum of correlations of every order. Weaving measures are good descriptors of the complexity of correlation structures in multipartite systems.
Reference: Phys. Rev. Lett. 119, 140505 (2017)
It turns out that a few local measurements are sufficient! Important properties of a quantum system are not directly measurable, but they can be disclosed by how fast the system changes under controlled perturbations. In particular, asymmetry and entanglement can be verified by reconstructing the state of a quantum system. Yet, this usually requires experimental and computational resources which increase exponentially with the system size. I have showed how to detect metrologically useful asymmetry and entanglement by a limited number of measurements. This is achieved by studying how they affect the speed of evolution of a system under a unitary transformation. I have proved that the speed of multiqubit systems can be evaluated by measuring a set of local observables, providing exponential advantage with respect to state tomography. Indeed, the presented method requires neither the knowledge of the state and the parameter-encoding Hamiltonian nor global measurements performed on all the constituent subsystems. The detection scheme has been implemented in an all-optical experiment.
Reference: Phys. Rev. A 96, 042327 (2017)
Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology, and cryptography. Yet, there is no universally efficient method for quantifying coherence either in theoretical or in experimental practice. I have introduced a framework for measuring quantum coherence in finite dimensional systems. I have defined a theoretical measure which satisfies the reliability criteria established in the context of quantum resource theories. Then, I have designed an experimental scheme implementable with current technology which evaluates the quantum coherence of an unknown state of a d-dimensional system by performing two programmable measurements on an ancillary qubit, in place of the O(d^2) direct measurements required by full state reconstruction. The result yields a benchmark for monitoring quantum effects in complex systems, e.g., certifying nonclassicality in quantum protocols and probing the quantum behavior of biological complexes.
Reference: Phys. Rev. Lett. 113, 170401 (2014)
The answer is Yes! Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet seems to prevent a single physical quantity, such as one spin component, from being measured with arbitrary precision. I have showed that an intrinsic quantum uncertainty on a single observable is ineludible in a number of physical situations. When revealed on local observables of a bipartite system, such uncertainty defines an entire class of bona fide measures of nonclassical correlations. For the case of 2×d systems, I have found that a unique measure is defined, which we evaluate in closed form. I have then discussed the role that these correlations, which are of the “discord” type, can play in the context of quantum metrology. I have demonstrated, in particular, that the amount of discord present in a bipartite mixed probe state guarantees a minimum precision, as quantified by the quantum Fisher information, in the optimal phase estimation protocol.
Reference: Phys. Rev. Lett. 110, 240402 (2013), Editors' Suggestion
