相关论文: Lattice structures for quantum channels

A quantum communication channel can be put to many uses: it can transmit classical information, private classical information, or quantum information. It can be used alone, with shared entanglement, or together with other channels. For each…

We present a framework to treat quantum networks and all possible transformations thereof, including as special cases all possible manipulations of quantum states, measurements, and channels, such as, e.g., cloning, discrimination,…

Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum…

This paper focuses on analyzing and differentiating between lattice linear problems and algorithms. It introduces a new class of algorithms called \textit{(fully) lattice linear algorithms}. A property of these algorithms is that they…

Linear maps preserving pure states of a quantum system of any dimension are characterized. This is then used to establish a structure theorem for linear maps that preserve separable pure states in multipartite systems. As an application, a…

These lectures (given at TASI 2000) provide an introduction to lattice methods for nonperturbative studies of Quantum Chromodynamics. Lecture 1 (Ch. 2) is a very vanilla introduction to lattice QCD. Lecture 2 (Ch. 3) describes examples of…

Quantum operations, or quantum channels cannot be inverted in general. An arbitrary state passing through a quantum channel looses its fidelity with the input. Given a quantum channel ${\cal E}$, we introduce the concept of its…

We present a novel method to perform quantum state tomography for many-particle systems which are particularly suitable for estimating states in lattice systems such as of ultra-cold atoms in optical lattices. We show that the need for…

We apply random matrix and free probability techniques to the study of linear maps of interest in quantum information theory. Random quantum channels have already been widely investigated with spectacular success. Here, we are interested in…

Modern quantum chemistry can make quantitative predictions on an immense array of chemical systems. However, the interpretation of those predictions is often complicated by the complex wave function expansions used. Here we show that an…

We study the landscape of solutions of the coherent quantum states in a ring shaped lattice potential in the context of ultracold atoms with an effective positive nonlinearity induced by interatomic interactions. The exact analytical…

We provide a new class of positive maps in matrix algebras. The construction is based on the family of balls living in the space of density matrices of n-level quantum system. This class generalizes the celebrated Choi map and provide a…

Pauli channels are fundamental in the context of quantum computing as they model the simplest kind of noise in quantum devices. We propose a quantum algorithm for simulating Pauli channels and extend it to encompass Pauli dynamical maps…

Quantum simulation is of great importance in quantum information science. Here, we report an experimental quantum channel simulator imbued with an algorithm for imitating the behavior of a general class of quantum systems. The reported…

We consider compound multi-input multi-output (MIMO) wiretap channels where minimal channel state information at the transmitter (CSIT) is assumed. Code construction is given for the special case of isotropic mutual information, which…

A linear map $L$ from ${\mathbb C}^{n \times n}$ into ${\mathbb C}^{n \times n}$ is called a quantum channel if it is completely positive and trace preserving. The set ${\cal L}_n$ of all such quantum channels is known to be a compact…

Let C be the set of all possible quantum states. We study the convex subsets of C with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of…

Quantum communication holds a promise for absolutely secure transmission of secret messages and faithful transfer of unknown quantum states. Photonic channels appear to be very attractive for physical implementation of quantum…

We investigate the set of quantum channels acting on a single qubit. We provide an alternative, compact generalization of the Fujiwara-Algoet conditions for complete positivity to non-unital qubit channels, which we then use to characterize…

A necessary condition for reversibility (sufficiency) of a quantum channel with respect to complete families of states with bounded rank is obtained. A full description (up to isometrical equivalence) of all quantum channels reversible with…