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:2505.18539

Disparity between multipartite entangling and disentangling powers of unitaries: Even vs Odd

Samanta, Mrinmoy, Mondal, Sudipta, Aditi Sen De

Published May 24, 2025• 0 citations
arXivHTMLPDF

Abstract

We compare the multipartite entangling and disentangling powers of unitary operators by assessing their ability to generate or eliminate genuine multipartite entanglement. Our findings reveal that while diagonal unitary operators can exhibit equal entangling and disentangling powers, certain non-diagonal unitaries demonstrate an imbalance when acting on fully separable states, thereby extending the known disparity from bipartite systems to those with any number of parties. Counterintuitively, we construct classes of unitaries and their adjoints that display unequal entanglement generation capacities, behaving differently when applied to systems with an even number of qubits compared to those with an odd number. Further, we illustrate that this asymmetry can be simulated using physically realizable Hamiltonians: systems with an even number of qubits employ nearest-neighbor Dzyaloshinskii-Moriya (DM) interactions, while those with an odd number utilize a combination of Heisenberg and DM interactions. Additionally, we present a circuit composed of random noncommuting unitaries, constructed from alternating layers of two-qubit Haar-random gates, to illustrate the discrepancy in the entangling and disentangling capabilities of unitaries.

DOI
10.48550/arxiv.2505.18539

Related papers

Hierarchies among genuine multipartite entangling capabilities of quantum gates

Mrinmoy Samanta, Sudipta Mondal, Samir Kumar Hazra +1 more

We classify quantum gates according to their capability to generate genuine multipartite entanglement (GME), using a hierarchy based on multipartite separable states. In particular, when a fixed unitary operator acts on the set of k-separable states, the maximal genuine multipartite entanglement content produced via that particular unitary operator is determined after maximizing over the set of k-separable input states. We identify unitary operators that are beneficial for generating high GME when the input states are entangled in some bipartition, although the picture can also be reversed, where such initial entanglement offers no advantage. We investigate the maximum entangling power of a broad range of unitary operators, encompassing special classes of quantum gates, as well as diagonal, permutation, and Haar-uniformly generated unitaries by computing generalized geometric measure (GGM) as a GME quantifier. Additionally, we observe a notable distinction in entangling power based on the nature of the input states: when maximization is restricted to separable states with real coefficients, the entangling power is lower than when the optimization is carried out over arbitrary separable states with complex coefficients, thereby highlighting the role of complex amplitudes in entanglement creation. Furthermore, we determine which unitary operators, along with their corresponding optimal inputs, yield output states with the highest achievable GGM.

arXiv:2302.06574•Physical Review A•Dec 12, 2025•0 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

Entanglement and Nonlocality are Inequivalent for Any Number of Parties

Remigiusz Augusiak, Maciej Demianowicz, Jordi Tura +1 more

Understanding the relation between nonlocality and entanglement is one of the fundamental problems in quantum physics. In the bipartite case, it is known that these two phenomena are inequivalent, as there exist entangled states of two parties that do not violate any Bell inequality. However, except for a single example of an entangled three-qubit state that has a local model, almost nothing is known about such a relation in multipartite systems. We provide a general construction of genuinely multipartite entangled states that do not display genuinely multipartite nonlocality, thus proving that entanglement and nonlocality are inequivalent for any number of parties.

arXiv:1407.3114•Physical Review Letters•Jul 15, 2015•63 citations

Constructing genuinely entangled multipartite states with applications to local hidden variables and local hidden states models

Remigiusz Augusiak, Maciej Demianowicz, Jordi Tura

Building upon the results of R. Augusiak et al. [Phys. Rev. Lett. 115, 030404 (2015)] we develop a general approach to the generation of genuinely entangled multipartite states of any number of parties from genuinely entangled states of a fixed number of parties, in particular, the bipartite entangled ones. In our approach, certain isometries whose output subspaces are either symmetric or genuinely entangled in some multipartite Hilbert spaces are applied to local subsystems of bipartite entangled or multipartite genuinely entangled quantum states. To prove that entanglement of the resulting states is indeed genuine we then introduce criteria allowing us to decide it efficiently. The construction is then exploited to provide examples of multipartite states that are genuinely entangled but not genuinely nonlocal, giving further illustration for the inequivalence between entanglement and nonlocality in the multiparticle scenario. It is also shown how to construct genuinely entangled states which are unsteerable across certain bipartite cuts.

arXiv:1803.00279•Physical Review A•Jul 19, 2018•12 citations

Operator space entangling power of quantum dynamics and local operator entanglement growth in dual-unitary circuits

Faidon Andreadakis, Emanuel Dallas, Paolo Zanardi A

Operator entanglement is a well-established measure of operator complexity across a system bipartition. In this work, we introduce a measure of the ability of a unitary channel to generate operator entanglement, representing an operator-level generalization of the state-space entangling power. This operator space entangling power is demonstrated to be linked to the scrambling properties of the unitary channel via the recently introduced concept of mutual averaged noncommutativity of quantum operator algebras. An upper bound for the operator space entangling power is identified that corresponds to unitary channels with scrambling properties akin to those of typical unitaries. Additionally, for Hamiltonian dynamics, we find that the short-time growth rate of the operator space entangling power matches the Gaussian scrambling rate of the bipartite out-of-time-order correlator, establishing a direct link between information scrambling and operator entanglement generation for short timescales. Finally, we examine the average growth of local operator entanglement across a symmetric bipartition of a spin chain. For dual-unitary circuits, a combination of analytical and numerical investigations demonstrates that the average growth of local operator entanglement exhibits two distinct regimes in relation to the operator space entangling power of the building-block gate.

arXiv:2406.10206•Physical Review A•Nov 12, 2024•8 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
We compare the multipartite entangling and disentangling powers of unitary operators by assessing their ability to generate or eliminate genuine multipartite entanglement. Our findings reveal that while diagonal unitary operators can exhibit equal entangling and disentangling powers, certain non-diagonal unitaries demonstrate an imbalance when acting on fully separable states, thereby extending the known disparity from bipartite systems to those with any number of parties. Counterintuitively, we construct classes of unitaries and their adjoints that display unequal entanglement generation capacities, behaving differently when applied to systems with an even number of qubits compared to those with an odd number. Further, we illustrate that this asymmetry can be simulated using physically realizable Hamiltonians: systems with an even number of qubits employ nearest-neighbor Dzyaloshinskii-Moriya (DM) interactions, while those with an odd number utilize a combination of Heisenberg and DM interactions. Additionally, we present a circuit composed of random noncommuting unitaries, constructed from alternating layers of two-qubit Haar-random gates, to illustrate the discrepancy in the entangling and disentangling capabilities of unitaries.
We classify quantum gates according to their capability to generate genuine multipartite entanglement (GME), using a hierarchy based on multipartite separable states. In particular, when a fixed unitary operator acts on the set of k-separable states, the maximal genuine multipartite entanglement content produced via that particular unitary operator is determined after maximizing over the set of k-separable input states. We identify unitary operators that are beneficial for generating high GME when the input states are entangled in some bipartition, although the picture can also be reversed, where such initial entanglement offers no advantage. We investigate the maximum entangling power of a broad range of unitary operators, encompassing special classes of quantum gates, as well as diagonal, permutation, and Haar-uniformly generated unitaries by computing generalized geometric measure (GGM) as a GME quantifier. Additionally, we observe a notable distinction in entangling power based on the nature of the input states: when maximization is restricted to separable states with real coefficients, the entangling power is lower than when the optimization is carried out over arbitrary separable states with complex coefficients, thereby highlighting the role of complex amplitudes in entanglement creation. Furthermore, we determine which unitary operators, along with their corresponding optimal inputs, yield output states with the highest achievable GGM.
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.
Understanding the relation between nonlocality and entanglement is one of the fundamental problems in quantum physics. In the bipartite case, it is known that these two phenomena are inequivalent, as there exist entangled states of two parties that do not violate any Bell inequality. However, except for a single example of an entangled three-qubit state that has a local model, almost nothing is known about such a relation in multipartite systems. We provide a general construction of genuinely multipartite entangled states that do not display genuinely multipartite nonlocality, thus proving that entanglement and nonlocality are inequivalent for any number of parties.
Building upon the results of R. Augusiak et al. [Phys. Rev. Lett. 115, 030404 (2015)] we develop a general approach to the generation of genuinely entangled multipartite states of any number of parties from genuinely entangled states of a fixed number of parties, in particular, the bipartite entangled ones. In our approach, certain isometries whose output subspaces are either symmetric or genuinely entangled in some multipartite Hilbert spaces are applied to local subsystems of bipartite entangled or multipartite genuinely entangled quantum states. To prove that entanglement of the resulting states is indeed genuine we then introduce criteria allowing us to decide it efficiently. The construction is then exploited to provide examples of multipartite states that are genuinely entangled but not genuinely nonlocal, giving further illustration for the inequivalence between entanglement and nonlocality in the multiparticle scenario. It is also shown how to construct genuinely entangled states which are unsteerable across certain bipartite cuts.
Operator entanglement is a well-established measure of operator complexity across a system bipartition. In this work, we introduce a measure of the ability of a unitary channel to generate operator entanglement, representing an operator-level generalization of the state-space entangling power. This operator space entangling power is demonstrated to be linked to the scrambling properties of the unitary channel via the recently introduced concept of mutual averaged noncommutativity of quantum operator algebras. An upper bound for the operator space entangling power is identified that corresponds to unitary channels with scrambling properties akin to those of typical unitaries. Additionally, for Hamiltonian dynamics, we find that the short-time growth rate of the operator space entangling power matches the Gaussian scrambling rate of the bipartite out-of-time-order correlator, establishing a direct link between information scrambling and operator entanglement generation for short timescales. Finally, we examine the average growth of local operator entanglement across a symmetric bipartition of a spin chain. For dual-unitary circuits, a combination of analytical and numerical investigations demonstrates that the average growth of local operator entanglement exhibits two distinct regimes in relation to the operator space entangling power of the building-block gate.
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.