© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2110.01479

Reducing the detection of genuine entanglement of n qubits to two qubits

Dafa Li

Published Oct 4, 2021• 0 citations

Abstract

We propose a criterion for the detection of genuine entanglement of pure multiqubit states. To this aim, we define an operator called the losing one qubit operator, which is different from the reduced density operator. The states obtained from a multiqubit state by applying the losing one qubit operator are referred to as its projected states. We show that all of the projected states of a pure product n-qubit state are pure product states provided that it cannot be written as a product of a single qubit state and a genuinely entangled (n-1)-qubit state. We also show that a pure n-qubit state is genuinely entangled provided that the state has at least two genuinely entangled (n-1)-qubit projected states. By repeating the losing process, we reduce the detection of entanglement of pure n-qubit states to the one of pure two-qubit states. Also we write a LISP program for the reduction process.

DOI: 10.48550/arxiv.2110.01479

Related papers

Multiqubit Entanglement Witness

Shiqi Zhang

With an aim to detect the genuine entanglement of a mixed state at the nearby pure state, we reflect a practicable approach concerning the construction of witness and express expectations to detect separable, bipartite states, and multiqubit entangled states. We introduce the related concept of the density matrix, multiqubit state, entangled state entanglement witness, etc. In addition, we give unambiguous definitions of separable states, entangled states, and genuinely entangled states. Therefore, we are able to detect the genuine entanglement of a mixed state at the nearby pure state employing the witness that is constructed for the multiqubit states.

Advances in transdisciplinary engineering•Mar 21, 2024•0 citations

Information-theoretic measure of genuine multiqubit entanglement

Jianming Cai, Zheng-Wei Zhou, Xingxiang Zhou +1 more

We consider pure quantum states of $N$ qubits and study the genuine $N$-qubit entanglement that is shared among all the $N$ qubits. We introduce an information-theoretic measure of genuine $N$-qubit entanglement based on bipartite partitions. When $N$ is an even number, this measure is presented in a simple formula, which depends only on the purities of the partially reduced density matrices. It can be easily computed theoretically and measured experimentally. When $N$ is an odd number, the measure can also be obtained in principle.

arXiv:quant-ph/0609027•Physical Review A•Oct 27, 2006•23 citations

Criterion for Genuine Multipartite Entanglement Quantum Channels

Nian-Quan Jiang, Wangyu-Jian

We introduce a character matrix for the N -qubit subsystem of a 2 N -qubit state and show the criterion for genuine entanglement channel existing between two N -qubit subsystems in the state. The criterion allows us to check conveniently whether genuine quantum channels exist or not in the 2 N -qubit state without calculating its N -qubit reduced density matrices.

Chinese Physics Letters•Jan 1, 2010•9 citations

Multiqubit entanglement witness

Lin Chen, Yi-Xin Chen

We introduce a feasible method of constructing the entanglement witness that detects genuine multiqubit entanglement in the vicinity of a given pure multiqubit state. We illustrate our method in the scenario of constructing the witnesses for the multiqubit states that are most often investigated theoretically and experimentally. It is shown that our method can construct the effective witnesses for experiments. We also investigate the entanglement detection of symmetric states and mixed states.

arXiv:0705.2665•Physical Review A•Aug 24, 2007•22 citations

Package of facts and theorems for efficiently generating entanglement criteria for many qubits

Marcin Wieśniak, Koji Maruyama

We present a package of mathematical theorems that allows us to construct multipartite-entanglement criteria. Importantly, establishing bounds for certain classes of entanglement does not take an optimization over continuous sets of states. These bonds are found from the properties of commutativity graphs of operators used in the criterion. We present two examples of criteria constructed according to our method. One of them detects genuine five-qubit entanglement without ever referring to correlations between all five qubits.

arXiv:1204.2722•Physical Review A•Jun 19, 2012•6 citations

Genuine entanglement detection via projection map in multipartite systems

Bivas Mallick, Sumit Nandi

Abstract We present a formalism to detect genuine multipartite entanglement by considering projection map which is a positive but not completely positive map. Projection map has been motivated by the no-pancake theorem which repudiates the existence of a quantum operation that maps the Bloch sphere onto a disk along its equator. The not-complete positivity feature of projection map is explored to investigate genuine multipartite entanglement in arbitrary N-qubit quantum systems. Our proposed framework can detect some important classes of genuinely entangled states in tripartite and quadripartite scenarios. We provide illustrative example to show the efficacy of our formalism to detect a class of tripartite PPT bound entangled states. Finally, we construct a suitable witness operator based on projection map to certify genuine tripartite entanglement, which is likely to be feasible experimentally.

arXiv:2401.03052•Physica Scripta•Aug 21, 2024•4 citations

We propose a criterion for the detection of genuine entanglement of pure multiqubit states. To this aim, we define an operator called the losing one qubit operator, which is different from the reduced density operator. The states obtained from a multiqubit state by applying the losing one qubit operator are referred to as its projected states. We show that all of the projected states of a pure product n-qubit state are pure product states provided that it cannot be written as a product of a single qubit state and a genuinely entangled (n-1)-qubit state. We also show that a pure n-qubit state is genuinely entangled provided that the state has at least two genuinely entangled (n-1)-qubit projected states. By repeating the losing process, we reduce the detection of entanglement of pure n-qubit states to the one of pure two-qubit states. Also we write a LISP program for the reduction process.

With an aim to detect the genuine entanglement of a mixed state at the nearby pure state, we reflect a practicable approach concerning the construction of witness and express expectations to detect separable, bipartite states, and multiqubit entangled states. We introduce the related concept of the density matrix, multiqubit state, entangled state entanglement witness, etc. In addition, we give unambiguous definitions of separable states, entangled states, and genuinely entangled states. Therefore, we are able to detect the genuine entanglement of a mixed state at the nearby pure state employing the witness that is constructed for the multiqubit states.

We consider pure quantum states of

N

qubits and study the genuine

N

-qubit entanglement that is shared among all the

N

qubits. We introduce an information-theoretic measure of genuine

N

-qubit entanglement based on bipartite partitions. When

N

is an even number, this measure is presented in a simple formula, which depends only on the purities of the partially reduced density matrices. It can be easily computed theoretically and measured experimentally. When

N

is an odd number, the measure can also be obtained in principle.

We present a package of mathematical theorems that allows us to construct multipartite-entanglement criteria. Importantly, establishing bounds for certain classes of entanglement does not take an optimization over continuous sets of states. These bonds are found from the properties of commutativity graphs of operators used in the criterion. We present two examples of criteria constructed according to our method. One of them detects genuine five-qubit entanglement without ever referring to correlations between all five qubits.

Abstract We present a formalism to detect genuine multipartite entanglement by considering projection map which is a positive but not completely positive map. Projection map has been motivated by the no-pancake theorem which repudiates the existence of a quantum operation that maps the Bloch sphere onto a disk along its equator. The not-complete positivity feature of projection map is explored to investigate genuine multipartite entanglement in arbitrary N-qubit quantum systems. Our proposed framework can detect some important classes of genuinely entangled states in tripartite and quadripartite scenarios. We provide illustrative example to show the efficacy of our formalism to detect a class of tripartite PPT bound entangled states. Finally, we construct a suitable witness operator based on projection map to certify genuine tripartite entanglement, which is likely to be feasible experimentally.