Related papers: Optimality Condition for the Petz Map
The "noncommutative graphs" which arise in quantum error correction are a special case of the quantum relations introduced in [N. Weaver, Quantum relations, Mem. Amer. Math. Soc. 215 (2012), v-vi, 81-140]. We use this perspective to…
Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy of entanglement of a state is the minimum relative entropy to the set of separable…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…
The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…
Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization…
It is known that a necessary and sufficient condition for equality in the data processing inequality (DPI) for the quantum relative entropy is the existence of a recovery map. We show that equality in DPI for a sandwiched R\'enyi relative…
We find optimality conditions for testers in discrimination of quantum channels. These conditions are obtained using semidefinite programming and are similar to optimality conditions for POVMs obtained by Holevo for ensembles of quantum…
Uhlmann's theorem is a central result in quantum information theory, which associates the closeness of two quantum states with that of their purifications. The theorem also well characterizes a fundamental task: how close a pure quantum…
In adversarial settings, where attackers can deliberately and strategically corrupt quantum data, standard quantum error correction reaches its limits. It can only correct up to half the code distance and must output a unique answer.…
Models based on approximation capabilities have recently been studied in the context of Optimal Recovery. These models, however, are not compatible with overparametrization, since model- and data-consistent functions could then be…
We propose a novel optimization scheme designed to find optimally correctable subspace codes for a known quantum noise channel. To each candidate subspace code we first associate a universal recovery map, as if the code was perfectly…
We present analytic estimates of the performances of various approximate quantum error correction schemes for the generalized amplitude damping (GAD) qubit channel. Specifically, we consider both stabilizer and nonadditive quantum codes.…
We study the possibility of performing quantum state reconstruction from a measurement record that is obtained as a sequence of expectation values of a Hermitian operator evolving under repeated application of a single random unitary map,…
The relative entropy is a principal measure of distinguishability in quantum information theory, with its most important property being that it is non-increasing with respect to noisy quantum operations. Here, we establish a remainder term…
The ability of fully reconstructing quantum maps is a fundamental task of quantum information, in particular when coupling with the environment and experimental imperfections of devices are taken into account. In this context we carry out a…
Entanglement purification is essential for quantum technologies; yet, rigorous bounds on the success probability for universal protocols -- those requiring no prior knowledge about the input state -- have remained underexplored. We…
We investigate the problem of optimally approximating a desired state by the convex mixing of a set of available states. The problem is recasted as finding the optimal state with the minimum distance from target state in a convex set of…
After the appearance of the no-cloning theorem, approximate quantum cloning machines (QCMs) have become one of the most well-studied subject in quantum information theory. Among several measures to quantify the performance of a QCM,…
We show that quantum subdynamics of an open quantum system can always be described by a Hermitian map, irrespective of the form of the initial total system state. Since the theory of quantum error correction was developed based on the…
The success of quantum optimal control for both experimental and theoretical objectives is connected to the topology of the corresponding control landscapes, which are free from local traps if three conditions are met: (1) the quantum…