Related papers: Numerical ranges of Bargmann invariants
Sensing and imaging are among the most important applications of quantum information science. To investigate their fundamental limits and the possibility of quantum enhancements, researchers have for decades relied on the quantum…
We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the…
We identify five selected open problems in the theory of quantum information, which are rather simple to formulate, were well-studied in the literature, but are technically not easy. As these problems enjoy diverse mathematical connections,…
Gram matrix approach to an entanglement analysis of pure states describing $(d,\infty)$ -- quantum systems is being introduced. In particular, maximally entangled states are described as those having a special forms of the corresponding…
Separation bounds are a fundamental measure of the complexity of solving a zero-dimensional system as it measures how difficult it is to separate its zeroes. In the positive dimensional case, the notion of reach takes its place. In this…
The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations…
Let $\ket{\0}$ and $\ket{\1}$ be two states that are promised to come from known subsets of orthogonal subspaces, but are otherwise unknown. Our paper probes the question of what can be achieved with respect to the basis…
We propose quantum devices that can realize probabilistically different projective measurements on a qubit. The desired measurement basis is selected by the quantum state of a program register. First we analyze the phase-covariant…
The accurate and reliable description of measurement devices is a central problem in both observing uniquely non-classical behaviors and realizing quantum technologies from powerful computing to precision metrology. To date quantum…
It is shown that the finite size corrections to the spectrum of the giant magnon solution of classical string theory, computed using the uniform light-cone gauge, are gauge invariant and have physical meaning. This is seen in two ways: from…
Invariants are a set of properties over program attributes that are expected to be true during the execution of a program. Since developing those invariants manually can be costly and challenging, there are a myriad of approaches that…
Several concrete examples in quantum information are discussed to demonstrate the importance of proper modeling that relates the mathematical description to real-world applications. In particular, it is shown that some commonly accepted…
The manipulation of neutral atoms by light is at the heart of countless scientific discoveries in the field of quantum physics in the last three decades. The level of control that has been achieved at the single particle level within arrays…
We address the framework of analysing quantum metrology in the information-theoretic picture. Firstly we show how to extract the maximum amount of information in general via suitable state initialization of the probes at the beginning and a…
We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation…
This paper deals with the entanglement, as quantified by the negativity, of pure quantum states chosen at random from the invariant Haar measure. We show that it is a constant (0.72037) multiple of the maximum possible entanglement. In line…
Continuous-variable quantum computing utilizes continuous parameters of a quantum system to encode information, promising efficient solutions to complex problems. Trapped-ion systems provide a robust platform with long coherence times and…
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 metrology based on quantum entanglement and quantum coherence improves the accuracy of measurement. In this paper, we briefly review the schemes of quantum metrology in various complex systems, including non-Markovian noise,…
We propose new algebraic invariants that distinguish and classify entangled states. Considering qubits as well as higher spin systems, we obtained complete entanglement classifications for cases that were either unsolved or only conjectured…