Related papers: A semidefinite programming upper bound of quantum …
We investigate the classical communication over quantum channels when assisted by no-signaling (NS) and positive-partial-transpose-preserving (PPT) codes, for which both the optimal success probability of a given transmission rate and the…
We derive several efficiently computable converse bounds for quantum communication over quantum channels in both the one-shot and asymptotic regime. First, we derive one-shot semidefinite programming (SDP) converse bounds on the amount of…
We derive one-shot upper bounds for quantum noisy channel codes. We do so by regarding a channel code as a bipartite operation with an encoder belonging to the sender and a decoder belonging to the receiver, and imposing constraints on the…
Determining the optimal fidelity for the transmission of quantum information over noisy quantum channels is one of the central problems in quantum information theory. Recently, [Berta-Borderi-Fawzi-Scholz, Mathematical Programming, 2021]…
Recently, a lot of attention has been devoted to finding physically realisable operations that realise as closely as possible certain desired transformations between quantum states, e.g. quantum cloning, teleportation, quantum gates, etc.…
Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing…
Quantum capacity, as the ultimate transmission rate of quantum communication, is characterized by regularized coherent information. In this work, we reformulate approximations of the quantum capacity by operator space norms and give both…
This paper presents a comprehensive exploration of semi-definite programming (SDP) techniques within the context of quantum information. It examines the mathematical foundations of convex optimization, duality, and SDP formulations,…
A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…
We analyze the quantum capacity of a unital quantum channel, using ideas from the proof of near-optimality of Petz recovery map [Barnum and Knill 2000] and give an upper bound on the quantum capacity in terms of regularized output $2$-norm…
This work is concerned with the issue of applications of the semi-definite programming (SDP) in the field of quantum information science. Our results of the analysis of certain quantum information protocols using this optimization technique…
We present a class of numerical algorithms which adapt a quantum error correction scheme to a channel model. Given an encoding and a channel model, it was previously shown that the quantum operation that maximizes the average entanglement…
Semidefinite programs (SDPs) are a framework for exact or approximate optimization that have widespread application in quantum information theory. We introduce a new method for using reductions to construct integrality gaps for SDPs. These…
A fundamental problem in quantum coding theory is to determine the maximum size of quantum codes of given block length and distance. A recent work introduced bounds based on semidefinite programming, strengthening the well-known quantum…
We investigate the generation of EPR pairs between three observers in a general causally structured setting, where communication occurs via a noisy quantum broadcast channel. The most general quantum codes for this setup take the form of…
Gaussian loss channels are of particular importance since they model realistic optical communication channels. Except for special cases, quantum capacity of Gaussian loss channels is not yet known completely. In this paper, we provide…
We study the one-shot zero-error classical capacity of a quantum channel assisted by quantum no-signalling correlations, and the reverse problem of exact simulation of a prescribed channel by a noiseless classical one. Quantum no-signalling…
Superactivation of quantum capacity is the phenomenon whereby two quantum channels, each with zero quantum capacity, can exhibit a strictly positive capacity when used in tandem. In this work, we explore superactivation in the previously…
Tradeoffs between the information rate and fidelity of quantum error-correcting codes are discussed. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a general completely…
Semidefinite programs (SDPs) are a class of optimisation problems that find application in numerous areas of physics, engineering and mathematics. Semidefinite programming is particularly suited to problems in quantum physics and quantum…