Related papers: A note on quantum expanders
Quantum channels describe subsystem or open system evolution. Using the classical Koopman operator that evolves functions on phase space, 4 classical Koopman channels are identified that are analogs of the 4 possible quantum channels in a…
The ability to characterise and discern quantum channels is a crucial aspect of noisy quantum technologies. In this work, we explore the problem of distinguishing quantum channels when limited to sub-exponential resources, framed as von…
A minimal set of measurement operators for quantum state tomography has in the non-degenerate case ideally eigenbases which are mutually unbiased. This is different for the degenerate case. Here, we consider the situation where the…
The core of quantum tomography is the possibility of writing a generally unbounded complex operator in form of an expansion over operators that are generally nonlinear functions of a generally continuous set of spectral densities--the…
We show that there are well separated families of quantum expanders with asymptotically the maximal cardinality allowed by a known upper bound. This has applications to the "growth" of certain operator spaces: It implies asymptotically…
Simple, precise, and robust control is demanded for operating a large quantum information processor. However, existing routes to high-fidelity quantum control rely heavily on arbitrary waveform generators that are difficult to scale up.…
The development of techniques that reduce experimental complexity and minimize errors is an utmost importance for modeling quantum channels. In general, quantum simulators are focused on universal algorithms, whose practical implementation…
In this paper, we present a condition for the zero-error capacity of quantum channels. To achieve this result we first prove that the eigenvectors (or eigenstates) common to the Kraus operators representing the quantum channel are fixed…
We study the limiting spectral distribution of quantum channels whose Kraus operators are sampled as $n\times n$ random Hermitian matrices satisfying certain assumptions. We show that when the Kraus rank goes to infinity with n, the…
Gaussian quantum channels are well understood and have many applications, e.g., in Quantum Information Theory and in Quantum Optics. For more general quantum channels one can in general use semiclassical approximations or perturbation…
Entanglement is sometimes helpful in distinguishing between quantum operations, as differences between quantum operations can become magnified when their inputs are entangled with auxiliary systems. Bounds on the dimension of the auxiliary…
Many constructions of randomness extractors are known to work in the presence of quantum side information, but there also exist extractors which do not [Gavinsky {\it et al.}, STOC'07]. Here we find that spectral extractors $\psi$ with a…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
The purpose of this review article is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review,…
This work presents a differentiable geometric parameterization of quantum channels in Kraus representation, which can be efficiently probed to find an unknown quantum channel. We explore its feasibility in finding the quasi inverse…
Pseudo-random operators consist of sets of operators that exhibit many of the important statistical features of uniformly distributed random operators. Such pseudo-random sets of operators are most useful whey they may be parameterized and…
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…
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…
For large d, we study quantum channels on C^d obtained by selecting randomly N independent Kraus operators according to a probability measure mu on the unitary group U(d). When mu is the Haar measure, we show that for N>d/epsilon^2$, such a…
In this brief paper we present some results on creating and manipulating spectral gaps for a (regular) quantum graph by inserting appropriate internal structures into its vertices. Complete proofs and extensions of the results are planned…