Quantifying quantum coherence of optical cat states

Miao Zhang; Haijun Kang; Meihong Wang; Fengyi Xu; Xiaolong Su; Kunchi Peng

doi:10.1364/PRJ.418417

Journals >Photonics Research >Volume 9 >Issue 5 >Page 887 > Article

Photonics Research
Vol. 9, Issue 5, 887 (2021)

Quantifying quantum coherence of optical cat states

Miao Zhang^1、†, Haijun Kang^1、†, Meihong Wang^1、2, Fengyi Xu¹, Xiaolong Su^1、2、*, and Kunchi Peng^1、2

Author Affiliations

¹State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China

²Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

show less

DOI: 10.1364/PRJ.418417 Cite this Article Set citation alerts

Miao Zhang, Haijun Kang, Meihong Wang, Fengyi Xu, Xiaolong Su, Kunchi Peng. Quantifying quantum coherence of optical cat states[J]. Photonics Research, 2021, 9(5): 887 Copy Citation Text

EndNote(RIS)

BibTex

Plain Text

show less

Abstract

The optical cat state plays an essential role in quantum computation and quantum metrology. Here, we experimentally quantify quantum coherence of an optical cat state by means of relative entropy and the

l_{1}

norm of coherence in a Fock basis based on the prepared optical cat state at the rubidium D1 line. By transmitting the optical cat state through a lossy channel, we also demonstrate the robustness of quantum coherence of the optical cat state in the presence of loss, which is different from the decoherence properties of fidelity and Wigner function negativity of the optical cat state. Our results confirm that quantum coherence of optical cat states is robust against loss and pave the way for the application of optical cat states.

C_{rel.ent.} (\hat{ρ}) = S ({\hat{ρ}}_{diag}) - S (\hat{ρ}),

(1)

View in Article

C_{l_{1}} (\hat{ρ}) = \sum_{\binom{m, n}{m \neq n}} | ρ_{m, n} | .

(2)

View in Article

\hat{ρ} (α, η) = (1 - P_{\pm}) {\hat{ρ}}_{\pm} (\sqrt{η} α) + P_{\pm} {\hat{ρ}}_{\mp} (\sqrt{η} α),

(3)

View in Article

C_{rel.ent.} (α, η) = (1 - P_{-}) C_{rel.ent.}^{odd} (\sqrt{η} α) + P_{-} C_{rel.ent.}^{even} (\sqrt{η} α),

(4)

View in Article

C_{l_{1}} (α, η) = (1 - P_{-}) C_{l_{1}}^{odd} (\sqrt{η} α) + P_{-} C_{l_{1}}^{even} (\sqrt{η} α),

(5)

View in Article

F = \cosh [- α^{2} (1 - η)] \frac{\sinh η α^{2}}{\sinh α^{2}},

(6)

View in Article

W_{N} = \min {0, W (0,0)},

(7)

View in Article

| Ψ ⟩ = \frac{1}{\sqrt{N \pm}} (| α ⟩ \pm | - α ⟩),

(B1)

View in Article

| Ψ_{+} ⟩ = \frac{1}{\sqrt{\cosh {| α |}^{2}}} \sum_{n = 0}^{\infty} \frac{α^{n}}{\sqrt{n!}} δ_{0 n}^{[2]} | n ⟩,

(B2)

View in Article

| Ψ_{-} ⟩ = \frac{1}{\sqrt{\sinh {| α |}^{2}}} \sum_{n = 0}^{\infty} \frac{α^{n}}{\sqrt{n!}} δ_{1 n}^{[2]} | n ⟩,

(B3)

View in Article

C_{rel.ent.}^{even} (α) = \frac{1}{\cosh {| α |}^{2}} (\sum_{n = 0}^{d - 1} \frac{α^{2 n}}{n!} δ_{0 n}^{[2]} \log_{2} \cosh {| α |}^{2} - \sum_{n = 0}^{d - 1} \frac{α^{2 n}}{n!} δ_{0 n}^{[2]} \log_{2} \frac{α^{2 n}}{n!}),

(B4)

View in Article

C_{rel.ent.}^{odd} (α) = \frac{1}{\sinh {| α |}^{2}} (\sum_{n = 0}^{d - 1} \frac{α^{2 n}}{n!} δ_{1 n}^{[2]} \log_{2} \sinh {| α |}^{2} - \sum_{n = 0}^{d - 1} \frac{α^{2 n}}{n!} δ_{1 n}^{[2]} \log_{2} \frac{α^{2 n}}{n!}) .

(B5)

View in Article

C_{l_{1}}^{even} (α) = \frac{1}{\cosh {| α |}^{2}} \sum_{\binom{m, n = 0}{m \neq n}}^{d - 1} \frac{α^{m + n}}{\sqrt{m! n!}} δ_{0 m}^{[2]} δ_{0 n}^{[2]},

(B6)

View in Article

C_{l_{1}}^{odd} (α) = \frac{1}{\sinh {| α |}^{2}} \sum_{\binom{m, n = 0}{m \neq n}}^{d - 1} \frac{α^{m + n}}{\sqrt{m! n!}} δ_{1 m}^{[2]} δ_{1 n}^{[2]} .

(B7)

View in Article

Miao Zhang, Haijun Kang, Meihong Wang, Fengyi Xu, Xiaolong Su, Kunchi Peng. Quantifying quantum coherence of optical cat states[J]. Photonics Research, 2021, 9(5): 887

Download Citation

EndNote(RIS)

BibTex

Plain Text

Set citation alerts for the article

Tools

Set citation alerts for the article

Save the article for my favorites

Paper Information