Related papers: Continuous-Variable Quantum MacWilliams Identities
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…
Gottesman-Kitaev-Preskill (GKP) encoding holds promise for continuous-variable fault-tolerant quantum computing. While an ideal GKP encoding is abstract and impractical due to its nonphysical nature, approximate versions provide viable…
We provide a sphere-packing lower bound for the optimal error probability in finite blocklengths when coding over a symmetric classical-quantum channel. Our result shows that the pre-factor can be significantly improved from the order of…
An important part of the information theory folklore had been about the output statistics of codes that achieve the capacity and how the empirical distributions compare to the output distributions induced by the optimal input in the channel…
Quantum error correction is capable of digitizing quantum noise and increasing the robustness of qubits. Typically, error correction is designed with the target of eliminating all errors - making an error so unlikely it can be assumed that…
Quantum Cram\'er--Rao theory is intrinsically local: it bounds precision near a specified parameter value, and its saturating measurement generally depends on that value. Barankin-type bounds use finite parameter displacements, but remain…
Encoding quantum information into a set of harmonic oscillators is considered a hardware efficient approach to mitigate noise for reliable quantum information processing. Various codes have been proposed to encode a qubit into an oscillator…
In this article, we establish a general covariance identity for infinitely divisible distributions (IDD). Using this result, we derive Cacoullos type variance bounds for the IDD. Applications to some important distributions are discussed,…
The speed of light $c$ sets a strict upper bound on the speed of information transfer in both classical and quantum systems. In nonrelativistic quantum systems, the Lieb-Robinson Theorem imposes an emergent speed limit $v \hspace{-0.2mm}…
A curve attaining the Hasse-Weil bound is called a maximal curve. Usually classical error-correcting codes obtained from a maximal curve have good parameters. However, the quantum stabilizer codes obtained from such classical…
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…
Coherent control errors, for which ideal Hamiltonians are perturbed by unknown multiplicative noise terms, are a major obstacle for reliable quantum computing. In this paper, we present a framework for analyzing the robustness of quantum…
We treat a quantum walk (QW) on the line whose quantum coin at each vertex tends to be the identity as the distance goes to infinity. We obtain a limit theorem that this QW exhibits localization with not an exponential but a "power-law"…
Constrained devices, such as smart sensors, wearable devices, and Internet of Things nodes, are increasingly prevalent in society and rely on secure communications to function properly. These devices often operate autonomously, exchanging…
Continuous-variable quantum key distribution (CVQKD) enables remote users to share high-rate and unconditionally secure secret keys while maintaining compatibility with classical optical communication networks and effective resistance…
We provide a stochastic interpretation of non-commutative Dirichlet forms in the context of quantum filtering. For stochastic processes motivated by quantum optics experiments, we derive an optimal finite time deviation bound expressed in…
There are various approaches to long-range quantum communication based on conceptually different forms of quantum repeaters. Here we explore a quantum repeater scheme that employs quantum error correction (QEC) both on the flying (light)…
Quantum repeaters are a promising platform for realizing long-distance quantum communication and thus could form the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. Repeater protocols…
We consider the rate-limited quantum-to-classical optimal transport in terms of output-constrained rate-distortion coding for both finite-dimensional and continuous-variable quantum-to-classical systems with limited classical common…
We show how to use properties of the quantum conditional mutual information to obtain continuity bounds for information characteristics of quantum channels depending on their input dimension. First we prove tight estimates for variation of…