Related papers: Approximating quantum channels by completely posit…
In the theory of quantum information, the mixed-unitary quantum channels, for any positive integer dimension $n$, are those linear maps that can be expressed as a convex combination of conjugations by $n\times n$ complex unitary matrices.…
We show that the approximate quasiorthogonality of two operator algebras is equivalent to the algebras being approximately private relative to their conditional expectation quantum channels. Our analysis is based on a characterization of…
We study relaxations of entanglement-assisted quantum channel coding and establish that non-signaling assistance and a natural semi-definite programming relaxation\, -- \,termed meta-converse\, -- \,are equivalent in terms of success…
Quantum hypothesis testing is a central task in the entire field of quantum information theory. Understanding its ultimate limits will give insight into a wide range of quantum protocols and applications, from sensing to communication.…
Microscopic Hamiltonian models of the composite system "open system + environment" typically do not provide the operator-sum Kraus form of the open system's dynamical map. With the use of a recently de- veloped method [16], we derive the…
In quantum theory, there exist sets of operations that cannot be performed simultaneously. These sets of operations are referred to as incompatible. While this definition of incompatibility extends to general probabilistic theories (GPTs),…
We define a new family of codes for symmetric classical-quantum channels and establish their optimality. To this end, we extend the classical notion of generalized perfect and quasi-perfect codes to channels defined over some finite…
In this work, we investigate the possibility of compressing a quantum system to one of smaller dimension in a way that preserves the measurement statistics of a given set of observables. In this process, we allow for an arbitrary amount of…
We associate to every quantum channel $T$ acting on a Hilbert space $\mathcal{H}$ a pair of Hamiltonian operators over the symmetric subspace of $\mathcal{H}^{\otimes 2}$. The expectation values of these Hamiltonians over symmetric product…
In the problem of quantum channel certification, we have black box access to a quantum process and would like to decide if this process matches some predefined specification or is $\varepsilon$-far from this specification. The objective is…
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…
Several techniques of generating random quantum channels, which act on the set of $d$-dimensional quantum states, are investigated. We present three approaches to the problem of sampling of quantum channels and show under which conditions…
Concurrence and further entanglement quantifyers can be computed explicitly for channels of rank two if representable by just two Kraus operators. Almost all details are available for the subclass of rank two 1-qubit-channels. There is a…
Given a quantum channel and a state which satisfy a fixed point equation approximately (say, up to an error $\varepsilon$), can one find a new channel and a state, which are respectively close to the original ones, such that they satisfy an…
Just as any state of a single qubit or 2-level system can be obtained from any other state by a rotation operator parametrized by three real Euler angles, we show how any state of an n-qubit or 2^n-level system can be obtained from any…
Quantum process tomography is the task of reconstructing unknown quantum channels from measured data. In this work, we introduce compressed sensing-based methods that facilitate the reconstruction of quantum channels of low Kraus rank. Our…
We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In…
We consider a computational problem where the goal is to approximate the maximum eigenvalue of a two-local Hamiltonian that describes Heisenberg interactions between qubits located at the vertices of a graph. Previous work has shed light on…
The dynamics of quantum systems are generally described by a family of quantum channels (linear, completely positive and trace preserving maps). In this note, we mainly study the range of all possible values of…
We address the general problem of removing correlations from quantum states while preserving local quantum information as much as possible. We provide a complete solution in the case of two qubits, by evaluating the minimum amount of noise…