相关论文: A Schmidt number for density matrices

Understanding the nature of multipartite entanglement is a central mission of quantum information theory. To this end, we investigate the question of tripartite entanglement convertibility. We find that there exists no easy criterion to…

Higher-dimensional entanglement is a valuable resource for several quantum information processing tasks, and is often characterized by the Schmidt number and specific classes of entangled states beyond qubit-qubit and qubit-qutrit systems.…

We introduce a general bipartite-like representation and Schmidt decomposition of an arbitrary pure state of $N$ indistinguishable fermions, based on states of $M<N$ and $(N-M)$ fermions. It is directly connected with the reduced $M$- and…

We investigate the entanglement of the ground state in the quantum networks that their nodes are considered as quantum harmonic oscillators. To this aim, the Schmidt numbers and entanglement entropy between two arbitrary partitions of a…

We prove that for many ranks r<2m-2, random rank r mixed states in bipartite mxm systems have relatively high Schmidt numbers, which is based on algebraic-geometric separability criterion proved in [1]. This also means that the…

We show that pure states of multipartite quantum systems are multiseparable (i.e. give separable density matrices on tracing any party) if and only if they have a generalized Schmidt decomposition. Implications of this result for the…

We show that a mixed state $\rho=\sum_{mn}a_{mn}|m> < n|$ can be realized by an ensemble of pure states $\{p_{k}, |\phi_{k} > \}$ where $|\phi_{k}>=\sum_{m}\sqrt{a_{mm}}e^{i\theta_{m}^{k}}|m>$. Employing this form, we discuss the relative…

Entanglement of any pure state of an N times N bi-partite quantum system may be characterized by the vector of coefficients arising by its Schmidt decomposition. We analyze various measures of entanglement derived from the generalized…

Optimized, necessary and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure…

The class of local invertible operations is defined and the invariance of entanglement under such operations is established. For the quantification of entanglement, universal entanglement measures are defined, which are invariant under…

For many completely positive maps repeated compositions will eventually become entanglement breaking. To quantify this behaviour we develop a technique based on the Schmidt number: If a completely positive map breaks the entanglement with…

High-dimensional entanglement has been identified as an important resource in quantum information processing, and also as a main obstacle for simulating quantum systems. Its certification is often difficult, and most widely used methods for…

Entangled states with a positive partial transpose (so-called PPT states) are central to many interesting problems in quantum theory. On one hand, they are considered to be weakly entangled, since no pure state entanglement can be distilled…

We compute analytically the density $\varrho_{N,M}(\lambda)$ of Schmidt eigenvalues, distributed according to a fixed-trace Wishart-Laguerre measure, and the average R\'enyi entropy $\langle\mathcal{S}_q\rangle$ for reduced density matrices…

We point out that density matrices can only be used to describe quantum states, so the entanglement contained in a density matrix is just quantum entanglement. This means a bipartite state described by a density matrix contains quantum…

Three-dimensional entanglement of orbital angular momentum states of an atomic qutrit and a single photon qutrit has been observed. Their full state was reconstructed using quantum state tomography. The fidelity to the maximally entangled…

We analyze features of mixed biphoton polarization states which arise from pure states of polarization-frequency biphoton ququarts after averaging over frequencies of photons. For mixed states we find their concurrence C, Schmidt parameter…

We introduce an experimental procedure for the detection of quantum entanglement of an unknown quantum state with as few measurements as possible. The method requires neither a priori knowledge of the state nor a shared reference frame…

The Schmidt measure was introduced by Eisert and Briegel for quantifying the degree of entanglement of multipartite quantum systems [Phys. Rev. A 64, 022306 (2001)]. Although generally intractable, it turns out that there is a bound on the…

There is an ongoing effort to quantify entanglement of quantum pure states for systems with more than two subsystems. We consider three approaches to this problem for three-qubit states: choosing a basis which puts the state into a standard…