量子纠缠问题的最小Hartree值
量子物理
2012-02-15 v1
摘要
复合量子系统的一般 n n n ∣ Ψ > | \Psi> ∣Ψ > \HH = ⊗ k = 1 n \HH k \HH = \otimes_{k=1}^n \HH_k \HH = ⊗ k = 1 n \HH k \HH k \HH_k \HH k d k d_k d k k = 1 , . . . , n k = 1,..., n k = 1 , ... , n d 1 ≤ . . . ≤ d n d_1 \le...\le d_n d 1 ≤ ... ≤ d n n n n ∣ ϕ > | \phi> ∣ ϕ > ∣ ϕ > = ⊗ k = 1 n ∣ ϕ ( k ) > | \phi> = \otimes_{k=1}^n | \phi^{(k)}> ∣ ϕ >= ⊗ k = 1 n ∣ ϕ ( k ) > ∣ ϕ ( k ) > ∈ \HH k | \phi^{(k)}> \in \HH_k ∣ ϕ ( k ) >∈ \HH k σ : = min { < Ψ ∣ ϕ Ψ > : ∣ Ψ > ∈ \HH , < Ψ ∣ Ψ > = 1 } \sigma := \min \{< \Psi | \phi_\Psi> : | \Psi> \in \HH, < \Psi | \Psi > = 1\} σ := min { < Ψ∣ ϕ Ψ >: ∣Ψ >∈ \HH , < Ψ∣Ψ >= 1 } ∣ ϕ Ψ > | \phi_\Psi > ∣ ϕ Ψ > ∣ Ψ > | \Psi > ∣Ψ > σ \sigma σ \HH \HH \HH σ ≥ 1 / d 1 . . . d n − 1 \sigma \ge 1/{\sqrt{d_1... d_{n-1}}} σ ≥ 1/ d 1 ... d n − 1 Ψ \Psi Ψ ∥ ∣ Ψ > − ∣ ϕ Ψ > ∥ ≤ 2 − 2 σ ≤ 2 − 2 ( 1 / d 1 . . . d n − 1 ) \| | \Psi > - | \phi_\Psi > \| \le \sqrt{2-2\sigma} \le \sqrt{2-2(1/{\sqrt{d_1...d_{n-1}}})} ∥∣Ψ > − ∣ ϕ Ψ > ∥ ≤ 2 − 2 σ ≤ 2 − 2 ( 1/ d 1 ... d n − 1 )
引用
@article{arxiv.1202.2983,
title = {The Minimum Hartree Value for the Quantum Entanglement Problem},
author = {Liqun Qi},
journal= {arXiv preprint arXiv:1202.2983},
year = {2012}
}