It is known that beyond $2 \otimes 2$ and 3$ dimensional quantum systems, Peres-Hordecki criterion no longer sufficient as an entanglement detection there are entangled states with both positive negative partial transpose (PPT NPT). Further, it also true all PPT bound states. However, in the class of NPT states, can exist well free All free/useful/distillable a part In this article, we ask ques...

A quantum processor based on three-level ``qutrits,'' as opposed to two-level qubits, successfully runs a teleportation algorithm in proof-of-concept demonstration of resource-efficient systems.

Given a particular quantum computing architecture, how might one optimize its resources to maximize its computing power? We consider quantum computers with a number of distinguishable quantum states, and entangled particles shared between those states. Hilbert-space dimensionality is linked to nonclassicality and, hence, quantum computing power. We find that qutrit-based quantum computers optim...

In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schrödinger framework from this perspective and provide a description of the Weyl-Wigner construction. Finally, after reviewing the basics of the geometric formulation of quantum mechanics, we apply the methods presented to the most interesting cases of finite dimensional ...

We show that the no-disturbance principle imposes a tradeoff between locally contextual correlations violating the Klyachko-Can-Biniciogˇlu-Shumovski inequality and spatially separated correlations violating the Clauser-Horne-Shimony-Holt inequality. The violation of one inequality forbids the violation of the other. We also obtain the corresponding monogamy relation imposed by quantum theory f...

Contextuality is a foundational phenomenon underlying key differences between quantum theory and classical realistic descriptions of the world. Here we propose an experimental test which is capable of revealing contextuality in all qutrit systems, except the completely mixed state, provided we choose the measurement basis appropriately. The 3-level system is furnished by the polarization and sp...

We discuss properties of probabilistic coding of two qubits to one qutrit and generalize the scheme to higher dimensions. We show that the protocol preservers entanglement between qubits to be encoded and environment and can be also applied to mixed states. We present the protocol which enables encoding of n qudits to one qudit of dimension smaller than the Hilbert space of the original system ...