Related papers: Approximating quantum channels by completely posit…
We give a survey of the two remarkable analytical problems of quantum information theory. The main part is a detailed report of the recent (partial) solution of the quantum Gaussian optimizers problem which establishes an optimal property…
We consider quantum channels with one sender and two receivers, used in several different ways for the simultaneous transmission of independent messages. We begin by extending the technique of superposition coding to quantum channels with a…
Finding a high (or low) energy state of a given quantum Hamiltonian is a potential area to gain a provable and practical quantum advantage. A line of recent studies focuses on Quantum Max Cut, where one is asked to find a high energy state…
Entanglement and entanglement-assisted are useful resources to enhance the mutual information of the Pauli channels, when the noise on consecutive uses of the channel has some partial correlations. In this Paper, we study…
We consider a family of quantum channels characterized by the fact that certain (in general nonorthogonal) Pure states at the channel entrance are mapped to (tensor) Products of Pure states (PPP, hence "pcubed") at the complementary outputs…
We derive the effective channel for a logical qubit protected by an arbitrary quantum error-correcting code, and derive the map between channels induced by concatenation. For certain codes in the presence of single-bit Pauli errors, we…
To establish an entangled state of optimal fidelity between two distant observers when the available quantum channel is noisy, is a central problem in quantum information theory. We consider an instance of this problem for two-qubit systems…
We show that a quantum channel $\mathcal{N}$ constructed by averaging over $\mathcal{O}(\log d/\epsilon^2)$ randomly chosen unitaries gives a local $\epsilon$-randomizing map with non-negative probability. The idea comes from a small…
The quantum state space $\cal S$ over a $d$-dimensional Hilbert space is represented as a convex subset of a $D-1$-dimensional sphere $S_{D-1}\subset {\bf{R}}^D$, where $D=d^2-1.$ Quantum tranformations (CP-maps) are then associated with…
The approximate stabilizer rank of a quantum state is the minimum number of terms in any approximate decomposition of that state into stabilizer states. Bravyi and Gosset showed that the approximate stabilizer rank of a so-called "magic"…
Present-day quantum devices require precise implementation of desired quantum channels. To characterize the quality of implementation one uses the average operation fidelity $F$, defined as the fidelity between an initial pure state and its…
We study the measurement for the unambiguous discrimination of two mixed quantum states that are described by density operators $\rho_1$ and $\rho_2$ of rank d, the supports of which jointly span a 2d-dimensional Hilbert space. Based on two…
Birkhoff's Theorem states that doubly stochastic matrices are convex combinations of permutation matrices. Quantum mechanically these matrices are doubly stochastic channels, i.e. they are completely positive maps preserving both the trace…
We propose nearly-optimal control strategies for changing states of a quantum system. We argue that quantum control optimization can be studied analytically within some protocol families that depend on a small set of parameters for…
What is the ultimate performance for discriminating two arbitrary quantum channels acting on a finite-dimensional Hilbert space? Here we address this basic question by deriving a general and fundamental lower bound. More precisely, we…
We study the process of quantum telecloning of $d$-dimensional pure quantum states using partially entangled pure states as quantum channel. This process efficiently mixes optimal universal symmetric cloning with quantum teleportation. It…
We prove a necessary condition that a quantum channel on a multipartite system may be approximated arbitrarily closely using local operations and classical communication (LOCC). We then extend those arguments to obtain a condition that…
A state in a d-dimensional Hilbert space can be simulated by a state defined in a different dimension with high fidelity. We assess how faithfully such the approximated state can perform quantum protocols, using an example of the squeezed…
Underwater optical channels pose significant challenges to the security and reliability of quantum communication systems due to absorption and scattering. In this paper, we investigate the BBM92 entanglement-based quantum key distribution…
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…