Related papers: Complexity in algebraic QFT
We initiate a study of the complexity of quantum field theories (QFTs) by proposing a measure of information contained in a QFT and its observables. We show that from minimal assertions, one is naturally led to measure complexity by two…
We introduce a new framework for quantifying the complexity of quantum channels, grounded in a suitably chosen resource set. This class of convex functions is designed to analyze the complexity of both open and closed quantum systems. By…
Non-invertible symmetries of a quantum field theory (QFT) are a natural generalization of unitary symmetries, but in which the product of operators does not satisfy a group multiplication law. We show that such symmetry operations on states…
We analyze two ways to obtain distinguishability measures between quantum maps by employing the square root of the quantum Jensen-Shannon divergence, which forms a true distance in the space of density operators. The arising measures are…
The goal of quantum channel discrimination and estimation is to determine the identity of an unknown channel from a discrete or continuous set, respectively. The query complexity of these tasks is equal to the minimum number of times one…
We set up a general theory for a quantum Wasserstein distance of order 1 in an operator algebraic framework, extending recent work in finite dimensions. In addition, this theory applies not only to states, but also to channels, giving a…
Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the…
Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to…
Introducing contravariant trace-densities for quantum states, we restore one to one correspondence between quantum operations described by normal CP maps and their trace densities as Hermitian positive operator-valued contravariant kernels.…
The computational complexity of a quantum state quantifies how hard it is to make. `Complexity geometry', first proposed by Nielsen, is an approach to defining computational complexity using the tools of differential geometry. Here we…
Fidelity is crucial for characterizing transformations of quantum states under various quantum channels, which can be served as a fundamental tool in resource theories. Firstly, we define an $\alpha$-$z$-fidelity as a significant quantity…
In this work we analyze properties of generic quantum channels in the case of large system size. We use random matrix theory and free probability to show that the distance between two independent random channels converges to a constant…
We define and study a fidelity criterion for quantum channels, which we term the minimax fidelity, through a noncommutative generalization of maximal Hellinger distance between two positive kernels in classical probability theory. Like…
Quantum channel discrimination has been studied from an information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of unknown channel accesses. In this paper, we…
The statistical complexity of continuous-variable quantum states can be characterized with a quantifier defined in terms of information-theoretic quantities derived from the Husimi Q-function. In this work, we utilize this complexity…
We generalise some well-known graph parameters to operator systems by considering their underlying quantum channels. In particular, we introduce the quantum complexity as the dimension of the smallest co-domain Hilbert space a quantum…
The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be…
We study the question of how reliably one can distinguish two quantum field theories (QFTs). Each QFT defines a probability distribution on the space of fields. The relative entropy provides a notion of proximity between these distributions…
We study the complexity of testing properties of quantum channels. First, we show that testing identity to any channel $\mathcal N: \mathbb C^{d_{\mathrm{in}} \times d_{\mathrm{in}}} \to \mathbb C^{d_{\mathrm{out}} \times d_{\mathrm{out}}}$…
We define a new divergence of von Neumann algebras using a variational expression that is similar in nature to Kosaki's formula for the relative entropy. Our divergence satisfies the usual desirable properties, upper bounds the sandwiched…