Detection of entanglement for multipartite quantum states
- URL: http://arxiv.org/abs/2302.08655v2
- Date: Fri, 11 Aug 2023 06:34:55 GMT
- Title: Detection of entanglement for multipartite quantum states
- Authors: Hui Zhao, Yu-Qiu Liu, Naihuan Jing, Zhi-Xi Wang
- Abstract summary: We study genuine tripartite entanglement and multipartite entanglement of arbitrary $n$-partite quantum states.
We derive useful and operational criteria to detect genuine tripartite entanglement.
We also obtain a sufficient criterion to detect entanglement for multipartite quantum states in arbitrary dimensions.
- Score: 1.4550422197805504
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study genuine tripartite entanglement and multipartite entanglement of
arbitrary $n$-partite quantum states by using the representations with
generalized Pauli operators of a density matrices. While the usual Bloch
representation of a density matrix uses three types of generators in the
special unitary Lie algebra $\mathfrak{su}(d)$, the representation with
generalized Pauli operators has one uniformed type of generators and it
simplifies computation. In this paper, we take the advantage of this simplicity
to derive useful and operational criteria to detect genuine tripartite
entanglement. We also obtain a sufficient criterion to detect entanglement for
multipartite quantum states in arbitrary dimensions. The new method can detect
more entangled states than previous methods as backed by detailed examples.
Related papers
- Geometric structure and transversal logic of quantum Reed-Muller codes [51.11215560140181]
In this paper, we aim to characterize the gates of quantum Reed-Muller (RM) codes by exploiting the well-studied properties of their classical counterparts.
A set of stabilizer generators for a RM code can be described via $X$ and $Z$ operators acting on subcubes of particular dimensions.
arXiv Detail & Related papers (2024-10-10T04:07:24Z) - Detecting multipartite entanglement via complete orthogonal basis [4.421825850868445]
We derive useful and operational criteria to detect genuine tripartite entanglement and multipartite entanglement.
We study multipartite entanglement in arbitrary dimensional multipartite systems.
arXiv Detail & Related papers (2023-10-10T08:54:16Z) - Detection of Genuine Multipartite Entanglement in Arbitrary Multipartite
systems [5.759560029580599]
We study the genuine multipartite entanglement of arbitrary $n$-partite quantum states.
We introduce a general framework for detecting genuine multipartite entanglement and non full-separability of multipartite quantum states.
arXiv Detail & Related papers (2023-08-07T01:44:48Z) - Vectorization of the density matrix and quantum simulation of the von
Neumann equation of time-dependent Hamiltonians [65.268245109828]
We develop a general framework to linearize the von-Neumann equation rendering it in a suitable form for quantum simulations.
We show that one of these linearizations of the von-Neumann equation corresponds to the standard case in which the state vector becomes the column stacked elements of the density matrix.
A quantum algorithm to simulate the dynamics of the density matrix is proposed.
arXiv Detail & Related papers (2023-06-14T23:08:51Z) - Calculating the many-body density of states on a digital quantum
computer [58.720142291102135]
We implement a quantum algorithm to perform an estimation of the density of states on a digital quantum computer.
We use our algorithm to estimate the density of states of a non-integrable Hamiltonian on the Quantinuum H1-1 trapped ion chip for a controlled register of 18bits.
arXiv Detail & Related papers (2023-03-23T17:46:28Z) - Sparse random Hamiltonians are quantumly easy [105.6788971265845]
A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems.
This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state.
Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
arXiv Detail & Related papers (2023-02-07T10:57:36Z) - Criteria of genuine multipartite entanglement based on correlation
tensors [0.0]
We revisit the genuine multipartite entanglement by a simplified method, which only involves the Schmidt decomposition and local unitary transformation.
We construct a local unitary equivalent class of the tri-qubit quantum state, then use the trace norm of the whole correlation tensor as a measurement to detect genuine multipartite entanglement.
arXiv Detail & Related papers (2023-01-16T15:08:33Z) - Detection of genuine tripartite entanglement based on Bloch
representation of densitymatrices [1.3319340093980596]
We study the genuine multipartite entanglement in tripartite quantum systems.
By using the Schmidt decomposition and local unitary transformation, we convert the general states to simpler forms.
Using these special matrices, we obtain new criteria for genuine multipartite entanglement.
arXiv Detail & Related papers (2022-03-27T02:07:23Z) - General expressions for the quantum Fisher information matrix with
applications to discrete quantum imaging [0.28675177318965034]
We derive general expressions for the quantum Fisher information matrix which bypass matrix diagonalization and do not require the expansion of operators on an orthonormal set of states.
We demonstrate the power of our approach by deriving novel results in the timely field of discrete quantum imaging.
arXiv Detail & Related papers (2020-12-02T22:18:22Z) - Quantum Gram-Schmidt Processes and Their Application to Efficient State
Read-out for Quantum Algorithms [87.04438831673063]
We present an efficient read-out protocol that yields the classical vector form of the generated state.
Our protocol suits the case that the output state lies in the row space of the input matrix.
One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
arXiv Detail & Related papers (2020-04-14T11:05:26Z) - Genuine Network Multipartite Entanglement [62.997667081978825]
We argue that a source capable of distributing bipartite entanglement can, by itself, generate genuine $k$-partite entangled states for any $k$.
We provide analytic and numerical witnesses of genuine network entanglement, and we reinterpret many past quantum experiments as demonstrations of this feature.
arXiv Detail & Related papers (2020-02-07T13:26:00Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.