Related papers: Classical Coding and the Cauchy-Schwarz Inequality
State smoothing is a technique to estimate a state at a particular time, conditioned on information obtained both before (past) and after (future) that time. For a classical system, the smoothed state is a normalized product of the…
Sparse coding provides a versatile framework for efficiently capturing and representing crucial data (information) concisely, which plays an essential role in various computer science fields, including data compression, feature extraction,…
There exist diverse no-go theorems, ranging from no-cloning to monogamies of quantum correlations and Bell inequality violations, which restrict the processing of information in the quantum world. In a multipartite scenario, monogamy of…
This paper considers the problem of efficiently transmitting quantum states through a network. It has been known for some time that without additional assumptions it is impossible to achieve this task perfectly in general -- indeed, it is…
From its seemingly non-intuitive and puzzling nature, most evident in numerous EPR-like gedankenexperiments to its almost ubiquitous presence in quantum technologies, entanglement is at the heart of modern quantum physics. First introduced…
Transmission of classical information using quantum objects such as polarized photons is studied. The classical (Shannon) channel capacity and its relation to quantum (von Neumann) channel capacity is investigated for various receiver…
In classical statistical learning theory, one of the most well studied problems is that of binary classification. The information-theoretic sample complexity of this task is tightly characterized by the Vapnik-Chervonenkis (VC) dimension. A…
In 1926, Dirac stated that quantum mechanics can be obtained from classical theory through a change in the only rule. In his view, classical mechanics is formulated through commutative quantities (c-numbers) while quantum mechanics requires…
The divide-and-conquer framework, used extensively in classical algorithm design, recursively breaks a problem of size $n$ into smaller subproblems (say, $a$ copies of size $n/b$ each), along with some auxiliary work of cost…
We construct a universal code for stationary and memoryless classical-quantum channel as a quantum version of the universal coding by Csisz\'{a}r and K\"{o}rner. Our code is constructed by the combination of irreducible representation, the…
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard…
Optimal measurement is required to obtain the quantum and classical correlations of a quantum state, and the crucial difficulty is how to acquire the maximal information about one system by measuring the other part; in other words, getting…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
Since the beginning of quantum mechanics, many puzzling phenomena which distinguish the quantum from the classical world, have appeared such as complementarity, entanglement or contextuality. All of these phenomena are based on the…
We consider state redistribution of a "hybrid" information source that has both classical and quantum components. The sender transmits classical and quantum information at the same time to the receiver, in the presence of classical and…
The standard definition of quantum state randomization, which is the quantum analog of the classical one-time pad, consists in applying some transformation to the quantum message conditioned on a classical secret key $k$. We investigate…
A family of asymmetric cloning machines for $N$-dimensional quantum states is introduced. These machines produce two imperfect copies of a single state that emerge from two distinct Heisenberg channels. The tradeoff between the quality of…
Many quantum systems may have the same classical limit. We argue that in the classical limit their traces do not necessarily converge one to another. The trace formula allows to express quantum traces by means of classical quantities as…
In classical information theory one can, in principle, produce a perfect copy of any input state. In quantum information theory, the no cloning theorem prohibits exact copying of nonorthogonal states. Moreover, if we wish to copy…
Classical shadows are a computationally efficient approach to storing quantum states on a classical computer for the purposes of estimating expectation values of local observables, obtained by performing repeated random measurements. In…