Related papers: Fractal Properties of Magic State Distillation
We theoretically and numerically demonstrate that completely integrable scattering processes may exhibit fractal transmission fluctuations, due to typical spectral properties of integrable systems. Similar properties also occur with…
Magic state distillation, which is a probabilistic process used to generate magic states, plays an important role in universal fault-tolerant quantum computers. On the other hand, to solve interesting problems, we need to run complex…
We find a minimal set of necessary and sufficient conditions for the existence of a local procedure that converts a finite pure state into one of a set of possible final states. This result provides a powerful method for obtaining optimal…
The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a…
Distillation protocols enable generation of high quality entanglement even in the presence of noise. Existing protocols ignore the presence of local information in mixed states produced from some noise sources such as photon loss, amplitude…
We show that the physical consistency of magic state distillation imposes new constraints on the weight enumerators of classical error-correcting codes. We establish that for $|T\rangle$-state distillation protocols based on linear…
Fault-tolerant implementation of non-Clifford gates is a major challenge for achieving universal fault-tolerant quantum computing with quantum error-correcting codes. Magic state distillation is the most well-studied method for this but…
Entanglement distillation is a key step in quantum information, both theoretically and practically. It has been proven that non-positive-partial transpose (NPT) entangled states of rank at most four is 1-distillable under local operation…
Motivated by the mathematical definition of entanglement we undertake a rigorous analysis of the separability and non-distillability properties in the neighborhood of those three-qubit mixed states which are entangled and completely…
Quantum technologies rely on high-quality resource states, such as maximally entangled or private states, which are indispensable for quantum communication and cryptography. In practice, however, these states are inevitably degraded by…
It is well known that any entangled mixed state in $2\otimes 2$ systems can be purified via infinite copies of the mixed state. But can one distill a pure maximally entangled state from finite copies of a mixed state in any bipartite system…
A mixed quantum state shared between two parties is said to be distillable if, by means of a protocol involving only local quantum operations and classical communication, the two parties can transform some number of copies of that state…
The reduction criterion is a well known necessary condition for separable states, and states violating this condition are entangled and also 1-distillable. In this paper we introduce a new set of necessary conditions for separability of…
We show that all quantum states that do not have a positive partial transpose are distillable via channels, which preserve the positivity of the partial transpose. The question whether NPT bound entanglement exist is therefore closely…
We consider distillation of entanglement from two qubit states which are mixtures of three mutually orthogonal states: two pure entangled states and one pure product state. We distill entanglement from such states by projecting n copies of…
States of sufficiently low purity are separable and cannot be entangled by unital (purity-non-generating) operations. Since high-purity states are experimentally demanding, it is natural to ask how much purity a state must possess to enable…
Frontier models that generate extended reasoning traces inadvertently produce rich token sequences that can facilitate model distillation. Recognizing this vulnerability, model owners may seek sampling strategies that limit the…
Repeated measurements on a part of a bipartite system strongly affect the other part not measured, whose dynamics is regulated by an effective contracted evolution operator. When the spectrum of this operator is discrete, the latter system…
Magic state distillation plays an important role in universal fault-tolerant quantum computing, and its overhead is one of the major obstacles to realizing fault-tolerant quantum computers. Hence, many studies have been conducted to reduce…
We present an optimal probabilistic protocol to distill quantum coherence. Inspired by a specific entanglement distillation protocol, our main result yields a strictly incoherent operation that produces one of a family of maximally coherent…