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We propose an ordered set of experimentally accessible conditions for detecting entanglement in mixed states. The $k$-th condition involves comparing moments of the partially transposed density operator up to order $k$. Remarkably, the…
Entanglement plays a crucial role in quantum information science and many-body physics, yet quantifying it in mixed quantum many-body systems has remained a notoriously difficult problem. Here, we introduce families of quantitative…
We formulate an entanglement criterion using Peres-Horodecki positive partial transpose operations combined with the Schr\"odinger-Robertson uncertainty relation. We show that any pure entangled bipartite and tripartite state can be…
We present a new set of inseparabilty inequalities to detect entanglement in $N$-spin states. These are based on negative partial transposition and involve collective spin-spin correlations of any two partitions of the entire system. They…
The correlation matrix (CM) criterion is a recently derived powerful sufficient condition for the presence of entanglement in bipartite quantum states of arbitrary dimensions. It has been shown that it can be stronger than the positive…
One of the main challenges of quantum information is the reliable verification of quantum entanglement. The conventional detection schemes require repeated measurement on a large number of identically prepared systems. This is hard to…
Entanglement plays a central role in quantum information processing, indicating the non-local correlation of quantum matters. However, few effective ways are known to detect the amount of entanglement of an unknown quantum state. In this…
Separability problem, to decide whether a given state is entangled or not, is a fundamental problem in quantum information theory. We propose a powerful and computationally simple separability criterion, which allows us to detect the…
We introduce the single-copy entanglement as a quantity to assess quantum correlations in the ground state in quantum many-body systems. We show for a large class of models that already on the level of single specimens of spin chains,…
Two electronic channels competing to screen a single impurity spin, as in the two-channel Kondo model, are expected to generate a ground state with nontrivial entanglement structure. We exploit a spin-chain representation of the two-channel…
For quantum systems with a total dimension greater than six, the positive partial transposition (PPT) criterion is sufficient but not necessary to decide the non-separability of quantum states. Here, we present an Automated Machine Learning…
We show how to design families of operational criteria that distinguish entangled from separable quantum states. The simplest of these tests corresponds to the well-known Peres-Horodecki positive partial transpose (PPT) criterion, and the…
Quantum entanglement plays a pivotal role in various quantum information processing tasks. However, there still lacks a universal and effective way to detecting entanglement structures, especially for high-dimensional and multipartite…
Quantum entanglement is essential to the development of quantum computation, communications, and technology. The controlled SWAP test, widely used for state comparison, can be adapted to an efficient and useful test for entanglement of a…
The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing, which is known to be an NP-hard problem in general. Despite the proposed many methods such as the positive partial…
Purification is a powerful technique in quantum physics whereby a mixed quantum state is extended to a pure state on a larger system. This process is not unique, and in systems composed of many degrees of freedom, one natural purification…
In recent years considerable progress has been made towards developing a general theory of quantum entanglement. In particular, criteria to decide whether a given quantum state is entangled are of high theoretical and practical interest.…
Although the realization of useful quantum computers poses significant challenges, swift progress in emerging quantum technologies is making this goal realistically approachable. In this context, one of the essential resources is quantum…
The scalar spin chirality is a three-body physical observable that plays an outstanding role both in classical magnetism, characterizing non-coplanar spin textures, and in quantum magnetism, as an order parameter for chiral spin liquids. In…
The nucleon is naturally viewed as a bipartite system of valence spin -- defined by its non-vanishing chiral charge -- and non-valence or sea spin. The sea spin can be traced over to give a reduced density matrix, and it is shown that the…