Related papers: Symmetric extendibility for qudits and tolerable e…
The concept of symmetric extendibility has recently drawn attention in the context of tolerable error rates in quantum cryptography, where it can be used to decide whether quantum states shared between two parties can be purified by means…
Studies on symmetric extendibility of quantum states become especially important in a context of analysis of one-way quantum measures of entanglement, distilabillity and security of quantum protocols. In this paper we analyse composite…
We investigate the error tolerance of quantum cryptographic protocols using $d$-level systems. In particular, we focus on prepare-and-measure schemes that use two mutually unbiased bases and a key-distillation procedure with two-way…
We investigate which bipartite quantum states admit a symmetric extension and apply the results in the analysis of noise thresholds in quantum key distribution protocols with two-way postprocessing. We find that states that admit a…
The concept of asymptotic correctability of Bell-diagonal quantum states is generalised to elementary quantum systems of higher dimensions. Based on these results basic properties of quantum state purification protocols are investigated…
Current approaches for building quantum computing devices focus on two-level quantum systems which nicely mimic the concept of a classical bit, albeit enhanced with additional quantum properties. However, rather than artificially limiting…
We introduce symmetric extensions of bipartite quantum states as a tool for analyzing protocols that distill secret key from quantum correlations. Whether the correlations are coming from a prepare-and-measure quantum key distribution…
We investigate the security bounds of quantum cryptographic protocols using $d$-level systems. In particular, we focus on schemes that use two mutually unbiased bases, thus extending the BB84 quantum key distribution scheme to higher…
Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure…
Scalable quantum computing can only be achieved if qubits are manipulated fault-tolerantly. Topological error correction - a novel method which combines topological quantum computing and quantum error correction - possesses the highest…
Graph states have been used to construct quantum error correction codes for independent errors. Hypergraph states generalize graph states, and symmetric hypergraph states have been shown to allow for the correction of correlated errors. In…
We provide security bounds against coherent attacks for two families of quantum key distribution protocols that use $d$-dimensional quantum systems. In the asymptotic regime, both the secret key rate for fixed noise and the robustness to…
Quantum key distribution uses public discussion protocols to establish shared secret keys. In the exploration of ultimate limits to such protocols, the property of symmetric extendibility of underlying bipartite states $\rho_{AB}$ plays an…
We show that thresholds for fault-tolerant quantum computation are solely determined by the quality of single-system operations if one allows for d-dimensional systems with $8 \leq d \leq 32$. Each system serves to store one logical qubit…
We consider two quantum cryptographic schemes relying on encoding the key into qudits, i.e. quantum states in a d-dimensional Hilbert space. The first cryptosystem uses two mutually unbiased bases (thereby extending the BB84 scheme), while…
Encoding in a high-dimensional Hilbert space improves noise resilience in quantum information processing. This approach, however, may result in cross-mode coupling and detection complexities, thereby reducing quantum cryptography…
The general conditions are discussed which quantum state purification protocols have to fulfill in order to be capable of purifying Bell-diagonal qubit-pair states, provided they consist of steps that map Bell-diagonal states to…
We analyze bipartite quantum states that admit a symmetric extension. Any such state can be decomposed into a convex combination of states that allow a _pure_ symmetric extension. A necessary condition for a state to admit a pure symmetric…
Quantum computers face significant challenges from quantum deviations or coherent noise, particularly during gate operations, which pose a complex threat to the efficacy of quantum error correction (QEC) protocols. In this study, we…
It is commonly believed that logical states of quantum error-correcting codes have to be highly entangled such that codes capable of correcting more errors require more entanglement to encode a qubit. Here, we show that the validity of this…