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Tradeoffs between the information rate and fidelity of quantum error-correcting codes are discussed. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a general completely…
A pure-loss bosonic channel is a simple model for communication over free-space or fiber-optic links. More generally, phase-insensitive bosonic channels model other kinds of noise, such as thermalizing or amplifying processes. Recent work…
In the low-energy high-energy-efficiency regime of classical optical communications---relevant to deep-space optical channels---there is a big gap between reliable communication rates achievable via conventional optical receivers and the…
We prove a one-shot "minimax" converse bound for quantum channel coding assisted by positive partial transpose channels between sender and receiver. The bound is similar in spirit to the converse by Polyanskiy, Poor, and Verdu [IEEE Trans.…
We solve the fundamental quantum error correction problem for bi-unitary channels on two-qubit Hilbert space. By solving an algebraic compression problem, we construct qubit codes for such channels on arbitrary dimension Hilbert space, and…
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…
The classical coding theorem in Kolmogorov complexity states that if an $n$-bit string $x$ is sampled with probability $\delta$ by an algorithm with prefix-free domain then K$(x) \leq \log(1/\delta) + O(1)$. In a recent work, Lu and…
We show that any classical two-way communication protocol with shared randomness that can approximately simulate the result of applying an arbitrary measurement (held by one party) to a quantum state of $n$ qubits (held by another), up to…
Given a classical channel---a stochastic map from inputs to outputs---the input can often be transformed to an intermediate variable that is informationally smaller than the input. The new channel accurately simulates the original but at a…
In this article we show that the Holevo capacity of a classical quantum channel, can be reached not only by a POVM but by von Neumann measurement too. Furthermore we show two use of this fact 1) We can generalize the classical compound…
We analyze a task in which classical and quantum messages are simultaneously communicated via a noisy quantum channel, assisted with a limited amount of shared entanglement. We derive direct and converse bounds for the one-shot capacity…
Bidirectional teleportation is a fundamental protocol for exchanging quantum information between two parties by means of a shared resource state and local operations and classical communication (LOCC). Here we develop two seemingly…
We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This…
Following initial work by Gregoratti and Werner [J. Mod. Optics 50, 913-933, 2003 and quant-ph/0403092] and Hayden and King [quant-ph/0409026], we study the problem of the capacity of a quantum channel assisted by a "friendly (channel)…
We propose a quantum-resistant quantum teleportation (QRQT) framework protected by post-quantum cryptography (PQC) to secure the classical correction channel, which is vulnerable to quantum adversaries. By applying PQC to the classical…
We use the smooth entropy approach to treat the problems of binary quantum hypothesis testing and the transmission of classical information through a quantum channel. We provide lower and upper bounds on the optimal type II error of quantum…
A formalism for quantum error correction based on operator algebras was introduced in [1] via consideration of the Heisenberg picture for quantum dynamics. The resulting theory allows for the correction of hybrid quantum-classical…
In our previous work, we presented the \emph{Hypothesis Testing Lemma}, a key tool that establishes sufficient conditions for the existence of good deterministic identification (DI) codes for memoryless channels with finite output, but…
We derive a sphere-packing error exponent for coded transmission over discrete memoryless channels with a fixed decoding metric. By studying the error probability of the code over an auxiliary channel, we find a lower bound to the…
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated…