Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0403163 · Physical Review A

Entanglement-changing power of two-qubit unitary operations

Ming-Yong Ye, Dong Sun, Yong-Sheng Zhang, Guang‐Can Guo

Published Aug 30, 2004• 21 citations
arXivHTMLPDF

Abstract

Entanglement-changing power of an arbitrary two-qubit operation, including increasing and decreasing power, is investigated in this paper. We consider the maximal entanglement ${C}_{\mathrm{max}}$ and the minimal entanglement ${C}_{\mathrm{min}}$ of the states obtained by a given two-qubit unitary operation ${U}_{d}$ acting on arbitrary pure states with fixed entanglement ${C}_{0}$. We give the condition that the maximal entanglement ${C}_{\mathrm{max}}$ of the obtained states can be $1$ and the minimal entanglement ${C}_{\mathrm{min}}$ can be $0$. When the maximal entanglement ${C}_{\mathrm{max}}$ cannot be $1$, we give the maximal value it can reach. When the minimal entanglement ${C}_{\mathrm{min}}$ cannot be $0$, we give the minimal value it can reach. We think ${C}_{\mathrm{max}}$ and ${C}_{\mathrm{min}}$ represent the entanglement-changing power of two-qubit unitary operations.

DOI
10.1103/physreva.70.022326

Related papers

Entangling power of two-qubit gates on mixed states

Zhe Guan, Huan He, Yong-Jian Han +3 more

The ability to reach a maximally entangled state from a separable one through the use of a two-qubit unitary operator is analyzed for mixed states. This extension from the known case of pure states shows that there are at least two families of gates which are able to give maximum entangling power for all values of purity. It is notable that one of this gates coincides with a maximum discording one. We give analytical proof that such gate is indeed a perfect entangler at all purities and give numerical evidence for the existence of the second one. Furthermore, we find that there are other gates, many in fact, which are perfect entanglers for a restricted range of purities. This highlights the fact that many perfect entangler gates could in principle be found if a thorough analysis of the full parameter space is performed.

arXiv:1311.5809•Physical Review A•Jan 23, 2014•14 citations

Entangling and assisted entangling power of bipartite unitary operations

Lin Chen, Li Zhi Yu

Nonlocal unitary operations can create quantum entanglement between distributed particles, and the quantification of created entanglement is a hard problem. It corresponds to the concepts of entangling and assisted entangling power when the input states are, respectively, product and arbitrary pure states. We analytically derive them for Schmidt-rank-two bipartite unitary and some complex bipartite permutation unitaries. In particular, the entangling power of permutation unitary of Schmidt rank three can take only one of two values: ${log}_{2}9\ensuremath{-}16/9$ or ${log}_{2}3$ ebits. The entangling power, assisted entangling power, and disentangling power of $2\ifmmode\times\else\texttimes\fi{}{d}_{B}$ permutation unitaries of Schmidt rank four are all 2 ebits. These quantities are also derived for generalized Clifford operators. We further show that any bipartite permutation unitary of Schmidt rank greater than two has entangling power greater than 1.223 ebits. We construct the generalized controlled-not (cnot) gates whose assisted entangling power reaches the maximum. We quantitatively compare the entangling power and assisted entangling power for general bipartite unitaries and their connection to the disentangling power by proposing a probabilistic protocol for implementing bipartite unitaries.

arXiv:1604.05788•Physical Review A•Aug 8, 2016•16 citations

Multipartite entangling power by von Neumann entropy

Xinyu Qiu, Zhiwei Song, Lin Chen

Quantifying the entanglement generation of a multipartite unitary operation is a key problem in quantum information processing. We introduce the definition of multipartite entangling, assisted entangling, and disentangling power, which is a natural generalization of the bipartite ones. We show that they are assumed at a specified quantum state. We analytically derive the entangling power of Schmidt-rank-two multiqubit unitary operations by the minimal convex sum of modulo-one complex numbers. Besides we show the necessary and sufficient condition that the assisted entangling power of Schmidt-rank-two unitary operations reaches the maximum. We investigate the widely used multiqubit gates, for example, the entangling power of CCZS gate, the entangling and assisted entangling power of the $n$-qubit Toffoli gate. The entangling power of the three-qubit Fredkin gate is two ebits, and that of the four-qubit Fredkin gate is in two to ${log}_{2}5$ ebits. Further we investigate the entangling power during the noisy implementation of operations.

arXiv:2410.15253•Physical Review A•Feb 7, 2025•1 citation

Entangling power of two-qubit unitary operations

Yi Shen, Lin Chen

Abstract The entangling power of a bipartite unitary operation shows the maximum created entanglement with the product input states. For an arbitrary two-qubit unitary operation, it is sufficient to consider its normalized operation U with parameters and c 3 . We show how to compute the entangling power of U when . In particular we construct the analytical expressions of entangling power of such U for two examples. We also formulate the entangling power of bipartite unitary operations of Schmidt rank two for any dimensions.

arXiv:1804.01222•Journal of Physics A Mathematical and Theoretical•Aug 3, 2018•8 citations

Optimal creation of entanglement using a two-qubit gate

Barbara Kraus, J. I. Cirac

We consider a general unitary operator acting on two qubits in a product state. We find the conditions such that the state of the qubits after the action is as entangled as possible. We also consider the possibility of using ancilla qubits to increase the entanglement.

arXiv:quant-ph/0011050•Physical Review A•May 17, 2001•432 citations

Inequality relation between entanglement and Bell nonlocality for arbitrary two-qubit states

Xiao‐Gang Fan, Zhiyong Ding, Fei Ming +3 more

Entanglement and Bell nonlocality are used to describe quantum inseparabilities. Bell-nonlocal states form a strict subset of entangled states. A natural question arises concerning how much territory Bell nonlocality occupies entanglement for a general two-qubit entangled state. In this work, we investigate the relation between entanglement and Bell nonlocality by using lots of randomly generated two-qubit states, and give out a constraint inequality relation between the two quantum resources. For studying the upper or lower boundary of the inequality relation, we discover maximally (minimally) nonlocal entangled states, which maximize (minimize) the value of the Bell nonlocality for a given value of the entanglement. Futhermore, we consider a special kind of mixed state transformed by performing an arbitrary unitary operation on werner state. It is found that the special mixed state's entanglement and Bell nonlocality are related to ones of a pure state transformed by the unitary operation performed on the Bell state.

arXiv:1909.00346•Sep 1, 2019•1 citation
Entanglement-changing power of an arbitrary two-qubit operation, including increasing and decreasing power, is investigated in this paper. We consider the maximal entanglement Cmax{C}_{\mathrm{max}}Cmax​ and the minimal entanglement Cmin{C}_{\mathrm{min}}Cmin​ of the states obtained by a given two-qubit unitary operation Ud{U}_{d}Ud​ acting on arbitrary pure states with fixed entanglement C0{C}_{0}C0​. We give the condition that the maximal entanglement Cmax{C}_{\mathrm{max}}Cmax​ of the obtained states can be 111 and the minimal entanglement Cmin{C}_{\mathrm{min}}Cmin​ can be 000. When the maximal entanglement Cmax{C}_{\mathrm{max}}Cmax​ cannot be 111, we give the maximal value it can reach. When the minimal entanglement Cmin{C}_{\mathrm{min}}Cmin​ cannot be 000, we give the minimal value it can reach. We think Cmax{C}_{\mathrm{max}}Cmax​ and Cmin{C}_{\mathrm{min}}Cmin​ represent the entanglement-changing power of two-qubit unitary operations.
The ability to reach a maximally entangled state from a separable one through the use of a two-qubit unitary operator is analyzed for mixed states. This extension from the known case of pure states shows that there are at least two families of gates which are able to give maximum entangling power for all values of purity. It is notable that one of this gates coincides with a maximum discording one. We give analytical proof that such gate is indeed a perfect entangler at all purities and give numerical evidence for the existence of the second one. Furthermore, we find that there are other gates, many in fact, which are perfect entanglers for a restricted range of purities. This highlights the fact that many perfect entangler gates could in principle be found if a thorough analysis of the full parameter space is performed.
Nonlocal unitary operations can create quantum entanglement between distributed particles, and the quantification of created entanglement is a hard problem. It corresponds to the concepts of entangling and assisted entangling power when the input states are, respectively, product and arbitrary pure states. We analytically derive them for Schmidt-rank-two bipartite unitary and some complex bipartite permutation unitaries. In particular, the entangling power of permutation unitary of Schmidt rank three can take only one of two values: ${log}_{2}9\ensuremath{-}16/9$ or log23{log}_{2}3log2​3 ebits. The entangling power, assisted entangling power, and disentangling power of $2\ifmmode\times\else\texttimes\fi{}{d}_{B}$ permutation unitaries of Schmidt rank four are all 2 ebits. These quantities are also derived for generalized Clifford operators. We further show that any bipartite permutation unitary of Schmidt rank greater than two has entangling power greater than 1.223 ebits. We construct the generalized controlled-not (cnot) gates whose assisted entangling power reaches the maximum. We quantitatively compare the entangling power and assisted entangling power for general bipartite unitaries and their connection to the disentangling power by proposing a probabilistic protocol for implementing bipartite unitaries.
Quantifying the entanglement generation of a multipartite unitary operation is a key problem in quantum information processing. We introduce the definition of multipartite entangling, assisted entangling, and disentangling power, which is a natural generalization of the bipartite ones. We show that they are assumed at a specified quantum state. We analytically derive the entangling power of Schmidt-rank-two multiqubit unitary operations by the minimal convex sum of modulo-one complex numbers. Besides we show the necessary and sufficient condition that the assisted entangling power of Schmidt-rank-two unitary operations reaches the maximum. We investigate the widely used multiqubit gates, for example, the entangling power of CCZS gate, the entangling and assisted entangling power of the nnn-qubit Toffoli gate. The entangling power of the three-qubit Fredkin gate is two ebits, and that of the four-qubit Fredkin gate is in two to log25{log}_{2}5log2​5 ebits. Further we investigate the entangling power during the noisy implementation of operations.
Abstract The entangling power of a bipartite unitary operation shows the maximum created entanglement with the product input states. For an arbitrary two-qubit unitary operation, it is sufficient to consider its normalized operation U with parameters and c 3 . We show how to compute the entangling power of U when . In particular we construct the analytical expressions of entangling power of such U for two examples. We also formulate the entangling power of bipartite unitary operations of Schmidt rank two for any dimensions.
Entanglement and Bell nonlocality are used to describe quantum inseparabilities. Bell-nonlocal states form a strict subset of entangled states. A natural question arises concerning how much territory Bell nonlocality occupies entanglement for a general two-qubit entangled state. In this work, we investigate the relation between entanglement and Bell nonlocality by using lots of randomly generated two-qubit states, and give out a constraint inequality relation between the two quantum resources. For studying the upper or lower boundary of the inequality relation, we discover maximally (minimally) nonlocal entangled states, which maximize (minimize) the value of the Bell nonlocality for a given value of the entanglement. Futhermore, we consider a special kind of mixed state transformed by performing an arbitrary unitary operation on werner state. It is found that the special mixed state's entanglement and Bell nonlocality are related to ones of a pure state transformed by the unitary operation performed on the Bell state.