Related papers: A Counterexample to the Optimality Conjecture in C…
Complete positivity is a ubiquitous assumption in the study of quantum systems interacting with the environment, but the lack of complete positivity of a quantum evolution (called the "negativity") can be used as a measure of the…
We investigate the problem of determining the parameters that describe a quantum channel. It is assumed that the users of the channel have at best only partial knowledge of it and make use of a finite amount of resources to estimate it. We…
In this paper, we consider a simplified error-correcting problem: for a fixed encoding process, to find a cascade connected quantum channel such that the worst fidelity between the input and the output becomes maximum. With the use of the…
We consider optimal state discrimination in a general convex operational framework, so-called generalized probabilistic theories (GPTs), and present a general method of optimal discrimination by applying the complementarity problem from…
We demonstrate that there exists a universal, near-optimal recovery map---the transpose channel---for approximate quantum error-correcting codes, where optimality is defined using the worst-case fidelity. Using the transpose channel, we…
Simulating quantum channels is a fundamental primitive in quantum computing, since quantum channels define general (trace-preserving) quantum operations. An arbitrary quantum channel cannot be exactly simulated using a finite-dimensional…
Abstracting neural networks with constraints they impose on their inputs and outputs can be very useful in the analysis of neural network classifiers and to derive optimization-based algorithms for certification of stability and robustness…
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…
A central problem in quantum resource theory is to give operational meaning to quantum resources that can provide clear advantages in certain physical tasks compared to the convex set of resource-free states. We propose to extend this basic…
We establish the optimal quantum teleportation protocol for the realistic scenario when both input state and quantum channel are afflicted by noise. In taking these effects into account higher fidelities are achieved. The optimality of the…
We show that approximating the trace norm contraction coefficient of a quantum channel within a constant factor is NP-hard. Equivalently, this shows that determining the optimal success probability for encoding a bit in a quantum system…
Quantum channels model many physical processes. For this reason, hypothesis testing between quantum channels is a fundamental task in quantum information theory. Here we consider the paradigmatic case of channel position finding, where the…
We investigate the possibility of dividing quantum channels into concatenations of other channels, thereby studying the semigroup structure of the set of completely-positive trace-preserving maps. We show the existence of 'indivisible'…
Using the convex structure of positive operator value measurements and of several quantities used in quantum metrology, such as quantum Fisher information or the quantum Van Trees information, we present an efficient numerical method to…
Inspired by the recent developments in the fields of quantum distributed computing, quantum systems are analyzed as networks of quantum nodes to reduce the complexity of the analysis. This gives rise to the distributed quantum consensus…
It has been argued that any test of quantum contextuality is nullified by the fact that perfect orthogonality and perfect compatibility cannot be achieved in finite precision experiments. We introduce experimentally testable two-qutrit…
We investigate the advantage of coherent superposition of two different coded channels in quantum metrology. In a continuous variable system, we show that the Heisenberg limit $1/N$ can be beaten by the coherent superposition without the…
The fragile nature of quantum information limits our ability to construct large quantities of quantum bits suitable for quantum computing. An important goal, therefore, is to minimize the amount of resources required to implement quantum…
The max-flow min-cut theorem is a cornerstone result in combinatorial optimization. Calegari et al. (arXiv:0802.3208) initialized the study of quantum max-flow min-cut conjecture, which connects the rank of a tensor network and the min-cut.…
In this paper, we consider the convex set of $d$ dimensional unital quantum channels. In particular, we parametrise a family of maps and through this parametrisation we provide a partial characterisation of the set of unital quantum maps…