Related papers: Measuring relational information between quantum s…
Bargmann invariants, a class of gauge-invariant quantities arising from the overlaps of quantum state vectors, provide a profound and unifying framework for understanding the geometric structure of quantum mechanics. This survey offers a…
Bargmann invariants, multivariate traces of states, completely characterize any unitary-invariant property of a set of states. Unitary invariants enable the description of quantum resources such as basis-independent coherence and…
Research on quantum states often focuses on the correlation between nonlocal effects and local unitary invariants, among which local unitary equivalence plays a significant role in quantum state classification and resource theories. This…
Bargmann invariants have recently emerged as powerful tools in quantum information theory, with applications ranging from geometric phase characterization to quantum state distinguishability. Despite their widespread use, a complete…
Considerable effort has been devoted to developing techniques for witnessing and characterizing quantum resources that emerge from collective properties of a set of states. In this context, Bargmann invariants play a central role: they…
Efficient overlap estimation of high-dimensional quantum states is an important task in quantum information and a core element in computational speedups of quantum machine learning. Here we experimentally demonstrate the SWAP test that…
The imaginary in quantum theory plays a crucial role in describing quantum coherence and is widely applied in quantum information tasks such as state discrimination, pseudorandomness generation, and quantum metrology. A recent paper by…
We address the following state comparison problem: is it possible to design an experiment enabling us to unambiguously decide (based on the observed outcome statistics) on the sameness or difference of two unknown state preparations without…
Accurately estimating the overlap between quantum states is a fundamental task in quantum information processing. While various strategies using distinct quantum measurements have been proposed for overlap estimation, the lack of…
Certain unitary-invariants, known as Bargmann invariants or multivariate traces of quantum states, have recently gained attention due to their applications in quantum information theory. However, determining the boundaries of sets of…
Quantum theory is traditionally formulated using complex numbers. This imaginarity of quantum theory has been quantified as a resource with applications in discrimination tasks, pseudorandomness generation, and quantum metrology. Here we…
Quantum entanglement is essential to the development of quantum computation, communications, and technology. The controlled SWAP test, widely used for state comparison, can be adapted to an efficient and useful test for entanglement of a…
We study the estimation of the overlap between two unknown pure quantum states of a finite dimensional system, given $M$ and $N$ copies of each type. This is a fundamental primitive in quantum information processing that is commonly…
We investigate different geometries and invariant measures on the space of mixed Gaussian quan- tum states. We show that when the global purity of the state is held fixed, these measures coincide and it is possible, within this constraint,…
In the usual tomography of multipartite entangled quantum states one assumes that the measurement devices used in the laboratory are under perfect control of the experimenter. In this paper, using the so-called SWAP concept introduced…
The fact that quantum mechanics predicts stronger correlations than classical physics is an essential cornerstone of quantum information processing. Indeed, these quantum correlations are a valuable resource for various tasks, such as…
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…
Bargmann invariants, also known as multivariate traces of quantum states $\operatorname{Tr}(\rho_1 \rho_2 \cdots \rho_n)$, are unitary invariant quantities used to characterize weak values, Kirkwood-Dirac quasiprobabilities,…
Traditionally, the characterization of quantum resources has focused on individual quantum states. Recent literature, however, has increasingly explored the characterization of resources in multi-states (ordered collections of states…
Bargmann invariants of order $n$, defined as multivariate traces of quantum states $\text{Tr}[\rho_1\rho_2 \ldots \rho_n]$, are useful in applications ranging from quantum metrology to certification of nonclassicality. A standard quantum…