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

TL;DR

This paper investigates the differences in multipartite entangling and disentangling powers of unitaries, revealing disparities between even and odd qubit systems, and demonstrating how these can be simulated with specific Hamiltonians and random circuits.

Contribution

It extends the understanding of entanglement dynamics by analyzing the disparity between entangling and disentangling powers in multipartite systems, highlighting differences between even and odd qubit configurations.

Findings

Diagonal unitaries can have equal entangling and disentangling powers.

Non-diagonal unitaries show imbalance in entanglement capabilities.

Asymmetry can be simulated with specific Hamiltonians for even and odd qubits.

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.