Through the generalization of Khinchin's classical axiomatic foundation, a basis is developed for nonadditive information theory. The classical nonadditive conditional entropy indexed by the positive parameter q is introduced and then translated into quantum information. This quantity is nonnegative for classically correlated states but can take negative values for entangled mixed states. This property is used to study quantum entanglement in the parametrized Werner-Popescu-like state of an N^n-system, that is, an n-partite N-level system. It is shown how the strongest limitation on validity of local realism (i.e., separability of the state) can be obtained in a novel manner.
Experimental observation of entropic-singularity-induced nonadditive quantum communication in a qutrit platypus channel
University of Science and Technology of China（中国科学技术大学）；CAS Center for Excellence in Quantum Information and Quantum Physics（中国科学院量子信息与量子物理前沿卓越中心）；Hefei National Laboratory（合肥国家实验室）
Collective Quantum State Preparation Is Nonadditive
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；Quantum Science Center of Guangdong–Hong Kong–Macao Greater Bay Area（粤港澳大湾区量子科学中心）
Quantum entanglement as an extremal Kirkwood-Dirac nonreality
Research Center for Quantum Physics, National Research and Innovation Agency（量子物理研究中心，国家研究与创新局）；Research Center for Nanoscience and Nanotechnology, Bandung Institute of Technology（纳米科学与纳米技术中心，万隆理工学院）；Department of Engineering Physics, Bandung Institute of Technology（工程物理系，万隆理工学院）
We present a numerical strategy to efficiently estimate bipartite entanglement measures, and in particular the Entanglement of Formation, for many-body quantum systems on a lattice. Our approach exploits the Tree Tensor Operator tensor network ansatz, a positive loopless representation for density matrices which, as we demonstrate, efficiently encodes information on bipartite entanglement, enabling the up-scaling of entanglement estimation. Employing this technique, we observe a finite-size scaling law for the entanglement of formation in 1D critical lattice models at finite temperature for up…
We present a full definition of mixed maximally entangled (MME) states for multipartite systems, generalizing their existing definition for bipartite systems by using multipartite Schmidt decomposition. MME states are a special kind of maximally entangled mixed state (MEMS) for which every pure decomposition state in all decompositions is maximally entangled. Thus, MME states have entanglement 1 by all valid unit-normalized entanglement measures, whereas general MEMS can have entanglement less than 1. Multipartite MME states likely have important applications such as remote state preparation, …
We study mixed anomaly between $G_1$ and $G_2$ of one-form finite symmetry $G_1\times G_2$ in $3d$ Chern-Simons theories. We assign a quantum entanglement structure to two linked $G$-symmetry lines (Wilson loops) and compute the entanglement entropy $S[G]$. We find a measure of the mixed anomaly by computing $S[G_1\times G_2]-S[G_1]-S[G_2]$.
Entanglement verification and measurement is essential for experimental tests of quantum mechanics and also for quantum communication and information science. Standard methods of verifying entanglement in a bipartite mixed state require detection of both particles and involve coincidence measurement. We present a method that enables us to verify and measure entanglement in a two-photon mixed state without detecting one of the photons, i.e., without performing any coincidence measurement or postselection. We consider two identical sources, each of which can generate the same two-photon mixed st…
We study the entanglement between a certain qubit and the remaining system in rank- 2 mixed states prepared on the quantum computer. The protocol, which we propose for this purpose, is based on the relation of geometric measure of entanglement with correlations between qubits. As a special case, we consider a two-qubit rank-2 mixed state and find the relation of concurrence with the geometric measure of entanglement. On the ibmq-melbourne quantum computer we measure the geometric measure of entanglement in the cases of 2- and 4-qubit mixed quantum states which consist of Schrödinger cat states…
It has been showed that two entangle pure states can violate the bilocal inequality in the entanglement-swapping network, vice versa. What happens for mixed states? Whether or not are there separable mixed states violating the bilocal inequality? In the work, we devote to finding the mixed Werner states which violate the bilocal inequality by Particle Swarm Optimization (PSO) algorithms. Finally, we shows that there are pairs of states, where one is separable and the other is entangled, can violate the bilocal inequality.
We propose an entanglement criterion, specially designed for mixed states, based on uncertainty relation and the Wigner-Yanase skew information. The variances in this uncertainty relation does not involve any classical mixing uncertainty, and thus turns out to be purely of quantum mechanical nature. We show that any mixed entangled state can be characterized by our criterion. We demonstrate its utility for several generalized mixed entangled state including Werner states and it turns out to be stronger than any other known criterion in identifying the correct domain of relevant parameters for …
In the general framework of $d\times d$ mixed states, we derive an explicit bound for bipartite NPT entanglement based on the mixedness characterization of the physical system. The result derived is very general, being based only on the assumption of finite dimensionality. In addition it turns out to be of experimental interest since some purity measuring protocols are known. Exploiting the bound in the particular case of thermal entanglement, a way to connect thermodynamic features to monogamy of quantum correlations is suggested, and some recent results on the subject are given a physically …
