Entangling power of quantum evolutions

By Paolo Zanardi, Christof Zalka, Lara Faoro Isi Foundation, Torino Infm, P. Torino. 2000

322 citations recorded by the source corpus.

We analyze the entangling capabilities of unitary transformations U acting on a bipartite ${(d}_{1}\ifmmode\times\else\texttimes\fi{}{d}_{2})$-dimensional quantum system. To this aim we introduce an entangling power measure $e(U)$ given by the mean linear entropy produced acting with U on a given distribution of pure product states. This measure admits a natural interpretation in terms of quantum operations. For a uniform distribution explicit analytical results are obtained using group-theoretic arguments. The behavior of the features of $e(U)$ as the subsystem dimensions ${d}_{1}$ and ${d}_{2}$ are varied is studied both analytically and numerically. The two-qubit case ${d}_{1}{=d}_{2}=2$ is argued to be peculiar.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5d75425a60cdea3de37a6093990d079ba05000ce

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Citations in the corpus

Geometry of Quantum States: Index (2007, background): “A canonical form of a two-qubit gate is known [522, 558, 640], and various measures of entangling power of U have been proposed [995, 993, 210].”
Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1 + 1d (2016, background): “For integer values of α ≥ 2, the entanglement entropy can be rewritten as the expectation value of an operator, dubbed swap operator by Zanardi, Zalka and Faoro [26], in a replicated system.”
Aspects of Generic Entanglement (2004, background): “For example, the expected entropy [15, 33, 39, 42, 44] and purity [34, 56 , 59] of reduced states for random pure quantum states have been calculated.”
Quantum quenches in 1 + 1 dimensional conformal field theories (2016, methodology): “It is then clear [212] that the expectation value of Πn on the ground state of the n-copy model with Hamiltonian H (i.”
Emergent statistical mechanics of entanglement in random unitary circuits (2018, background): “[58] Paolo Zanardi, Christof Zalka, and Lara Faoro.”
Geometric (2019, background): “Thus, there were eight global patterns formed by local dot motion, with four patterns exhibiting a right-tilted contour ( No. 1 –”
Entanglement Membrane in Chaotic Many-Body Systems (2019, background): “These are referred to as operator entanglements [50–54], and have been studied in the context of quantifying the “entangling power” of unitary gates [50, 55].”