Related papers: Extremal equation for optimal completely-positive …
Non-local correlations between a fully characterised quantum system and an untrusted black box device are described by an assemblage of conditional quantum states. These assemblages form a convex set, whose extremal points are relevant in…
The striking differences between quantum and classical systems predicate disruptive quantum technologies. We peruse quantumness from a variety of viewpoints, concentrating on phase-space formulations because they can be applied beyond…
We explore the task of optimal quantum channel identification, and in particular the estimation of a general one parameter quantum process. We derive new characterizations of optimality and apply the results to several examples including…
The relation between completely positive maps and compound states is investigated in terms of the notion of quantum conditional probability.
The Quantum Approximate Optimisation Algorithm is a $p$ layer, time-variable split operator method executed on a quantum processor and driven to convergence by classical outer loop optimisation. The classical co-processor varies individual…
An exactly solvable model of a quantum spin interacting with a spin environment is considered. The interaction is chosen to be such that the state of the environment is conserved. The reduced density matrix of the spin is calculated for…
We propose a quantum algorithm for `extremal learning', which is the process of finding the input to a hidden function that extremizes the function output, without having direct access to the hidden function, given only partial input-output…
We analyze to what extent it is possible to copy arbitrary states of a two-level quantum system. We show that there exists a "universal quantum copying machine", which approximately copies quantum mechanical states in such a way that the…
We consider the general problem of the optimal transformation of N uses of (possibly different) unitary channels to a single use of another unitary channel in any finite dimension. We show how the optimal transformation can be fully…
Quantum metrology can achieve far better precision than classical metrology, and is one of the most important applications of quantum technologies in the real world. To attain the highest precision promised by quantum metrology, all steps…
We present a detailed account of quantum state estimation by joint maximization of the likelihood and the entropy. After establishing the algorithms for both perfect and imperfect measurements, we apply the procedure to data from simulated…
We address the problem of learning an unknown unitary transformation from a finite number of examples. The problem consists in finding the learning machine that optimally emulates the examples, thus reproducing the unknown unitary maximum…
The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…
In the study of quantum nonlocality, one obstacle is that the analytical criterion for identifying the boundaries between quantum and postquantum correlations has not yet been given, even in the simplest Bell scenario. We propose a…
We present a necessary and sufficient condition for a finite dimensional density matrix to be an extreme point of the convex set of density matrices with positive partial transpose with respect to a subsystem. We also give an algorithm for…
We show that quantum designs characterize the general structure of the optimal approximation of the transpose map on quantum states. Based on this characterization, we propose an implementation of the approximate transpose map by a…
This paper describes a data-driven framework for approximate global optimization in which precomputed solutions to a sample of problems are retrieved and adapted during online use to solve novel problems. This approach has promise for…
We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding…
A family of linear positive maps in the algebra of $3 \times 3$ complex matrices proposed recently in Bera et al. arXiv:2212.03807 is further analyzed. It provides a generalization of a seminal Choi nondecomposable extremal map in $M_3$. We…
A general method to derive the master equations for extremal models is established. These systems are shown to develop a peculiar kind of correlations between elements related to the characterization of extremal dynamics as an information…