Related papers: Quantum state testing beyond the polarizing regime…
Measurement for qubits plays a key role in quantum computation. Current methods for classifying states of single qubit in a superconducting multi-qubit system produce fidelities lower than expected due to the existence of crosstalk,…
In quantum optics, nonclassicality of quantum states is commonly associated with negativities of phase-space quasiprobability distributions. We argue that the impossibility of any classical simulations with phase-space functions is a…
We study the problem of discriminating between non-orthogonal quantum states with least probability of error. We demonstrate that this problem can be simplified if we solve for the error itself rather than solving directly for the optimal…
These notes introduce quantum computation and quantum error correction, emphasising the importance of stabilisers and the mathematical foundations in basic Lie theory. We begin by using the double cover map $\mathrm{SU}_2 \rightarrow…
Euclidean volume ratios between quantum states with positive partial transpose and all quantum states in bipartite systems are investigated. These ratios allow a quantitative exploration of the typicality of entanglement and of its…
Martingale concentration inequalities constitute a powerful mathematical tool in the analysis of problems in a wide variety of fields ranging from probability and statistics to information theory and machine learning. Here we apply…
The quantum state overlap is the textbook measure of the difference between two quantum states. Yet, it is inadequate to compare the complex configurations of many-body systems. The problem is inherited by the widely employed quantum state…
We consider the task of distinguishing whether a quantum system is prepared in a state from one of several sets of quantum states. Assuming their convexity and stability under tensor product, we prove that the optimal error exponent for…
Quantum information science has profoundly changed the ways we understand, store, and process information. A major challenge in this field is to look for an efficient means for classifying quantum state. For instance, one may want to…
We introduce a quantifier of phase-space complexity for discrete-variable (DV) quantum systems. Motivated by a recent framework developed for continuous-variable systems, we construct a complexity measure of quantum states based on the…
Quantum steering is a relatively simple test for quantumness of correlations, proving that the values of quantum-mechanical measurement outcomes come into being only in the act of measurement. By exploiting quantum correlations Alice can…
Recall the classical hypothesis testing setting with two convex sets of probability distributions P and Q. One receives either n i.i.d. samples from a distribution p in P or from a distribution q in Q and wants to decide from which set the…
Quantum channel discrimination is a fundamental task in quantum information processing. In the one-shot regime, discrimination between two candidate channels is characterized by the diamond norm. Beyond this basic setting, however, many…
The main result in this article shows that the quantum $f$-divergence of two states is equal to the classical $f$-divergence of the corresponding Nussbaum-Szko{\l}a distributions. This provides a general framework for studying certain…
We analyze the complexity of quantum state verification in the context of solving systems of linear equations of the form $A \vec x = \vec b$. We show that any quantum operation that verifies whether a given quantum state is within a…
Quantum speed limit (QSL) is the lower bound on the time required for a state to evolve to a desired final state under a given Hamiltonian evolution. Three well-known QSLs exist Mandelstam-Tamm (MT), Margolus-Levitin (ML), and dual ML…
Semidefinite programs (SDPs) are a framework for exact or approximate optimization that have widespread application in quantum information theory. We introduce a new method for using reductions to construct integrality gaps for SDPs. These…
We investigate whether paradigmatic measurements for quantum state tomography, namely mutually unbiased bases and symmetric informationally complete measurements, can be employed to certify quantum correlations. For this purpose, we…
The characterization of an infinite-order quantum phase transition (QPT) by entanglement measures is analyzed. To this aim, we consider two closely related solvable spin-1/2 chains, namely, the Ashkin-Teller and the staggered XXZ models.…
Quantum criticality often lies beyond the scope of the conventional Landau paradigm, and a unifying framework has yet to emerge, due in part to the wide variety of quantum orders. We propose a geometric approach to quantum phase transitions…