Related papers: Fractal Properties of Magic State Distillation
We study the distillability of a certain class of bipartite density operators which can be obtained via depolarization starting from an arbitrary one. Our results suggest that non-positivity of the partial transpose of a density operator is…
We describe new families of random fractals, referred to as "V-variable", which are intermediate between the notions of deterministic and of standard random fractals. The parameter V describes the degree of "variability" : at each…
Purification schemes for multi-particle entangled states cannot be treated as straightforward extensions of those for two particles because of the lack of symmetry they possess. We propose purification protocols for a wide range of mixed…
Magic state distillation is a crucial yet resource-intensive process in fault-tolerant quantum computation. The protocol's overhead, defined as the number of input magic states required per output magic state with an error rate below…
Criteria for distillability, and the property of having a positive partial transpose, are introduced for states of general bipartite quantum systems. The framework is sufficiently general to include systems with an infinite number of…
States with private correlations but little or no distillable entanglement were recently reported. Here, we consider the secure distribution of such states, i.e., the situation when an adversary gives two parties such states and they have…
The quantum states corresponding to a secret key are characterized using the so-called private states, where the key part consisting of a secret key is shielded by the additional systems. Based on the construction, it was shown that a…
Magic State Distillation is considered to be one of the promising methods for supplying the non-Clifford resources required to achieve universal fault tolerance. Conventional MSD protocols implemented in surface codes often require multiple…
This paper tries to probe the relation between the local distinguishability of orthogonal quantum states and the distillation of entanglement. An new interpretation for the distillation of entanglement and the distinguishability of…
The fractal property stipulates that the same physical laws apply for different scales of a given physics. This property is applied to particles and nuclei, in order to study the possibility to use it to help for determination of unknown…
The local structure of a fractal set is described by its dimension $D$, which is the exponent of a power-law relating the mass ${\cal N}$ in a ball to its radius $\epsilon$: ${\cal N}\sim \epsilon^D$. It is desirable to characterise the…
We address the crystallization of monodisperse hard spheres in terms of the properties of finite- size crystalline clusters. By means of large scale event-driven Molecular Dynamics simulations, we study systems at different packing…
Magic state distillation (MSD) is a quantum algorithm that enables performing logical non-Clifford gates with in principle arbitrarily low noise level. It is herein typically assumed that logical Clifford gates can be executed without…
Magic state distillation (MSD) is a cornerstone of fault-tolerant quantum computing, enabling non-Clifford gates via state injection into stabilizer circuits. However, the substantial overhead of current MSD protocols remains a major…
Learning a good state representation is a critical skill when dealing with multiple tasks in Reinforcement Learning as it allows for transfer and better generalization between tasks. However, defining what constitute a useful representation…
We consider entanglement distillation under the assumption that the input states are allowed to be correlated among each other. We hence replace the usually considered independent and identically-distributed hypothesis by the weaker…
Fractal AI is a theory for general artificial intelligence. It allows deriving new mathematical tools that constitute the foundations for a new kind of stochastic calculus, by modelling information using cellular automaton-like structures…
We look into multipartite quantum states on which quantum cryptographic protocols including quantum key distribution and quantum secret sharing can be perfectly performed, and define the quantum cryptographic resource distillable rate as…
Theoretical treatments of frictional granular matter often assume that it is legitimate to invoke classical elastic theory to describe its coarse-grained mechanical properties. Here we show, based on experiments and numerical simulations,…
A continuous-variable analog of the Deutsch's distillation protocol locally operating with two copies of the same Gaussian state is suggested. Irrespectively of the impossibility of Gaussian state distillation, we reveal that this protocol…