Stochastic behavior of outcome of Schur-Weyl duality measurement

Abstract

We focus on the measurement defined by the decomposition based on Schur-Weyl duality on $n$ qubits. As the first setting, we discuss the asymptotic behavior of the measurement outcome when the state is given as the permutation mixture ${\rho }_{mix,n,l}$ of the state $|1^l{0}^{n-l}⟩:=|1{⟩}^{\otimes l}\otimes |0{⟩}^{\otimes (n-l)}$. In contrast, when the state is given as the Dicke state $|{\Xi }_{n,l}⟩$, the measurement outcome takes one deterministic value. These two cases have completely different behaviors. As the second setting, we study the case when the state is given as the tensor product of the permutation mixture ${\rho }_{mix,k,l}$ and the Dicke state $|{\Xi }_{n-k,m-l}⟩$. We derive various types of asymptotic distribution including a kind of central limit theorem when $n$ goes to infinity.

The second part of the revised version. The first and third parts are submitted as new items. 45 pages, 5 figures

References in corpus (3)

• Coding Theorem and Strong Converse for Quantum Channels
• Experimental Observation of Four-Photon Entangled Dicke State with High Fidelity
• Relative entropy of entanglement for certain multipartite mixed states

Cited by in corpus (2)

• Global Heisenberg scaling in noisy and practical phase estimation
• Gelfand pairs and spherical functions for Iwahori-Hecke algebras