楊麗麗，閆棟華，王銀珠

多體復(fù)合量子態(tài)基于可觀測(cè)量算子的糾纏測(cè)度

楊麗麗，閆棟華，*王銀珠

（太原科技大學(xué)應(yīng)用科學(xué)學(xué)院，山西，太原 030024）

近些年，人們對(duì)量子糾纏的量化已經(jīng)有了許多深入的研究，但是，許多已有的糾纏度量還是難以計(jì)算的。LuoShunlong基于互信息提出了兩體量子態(tài)的可觀測(cè)量關(guān)聯(lián)，并得到了兩體量子態(tài)的一類糾纏測(cè)度。本文將兩體系統(tǒng)的糾纏測(cè)度推廣到多體復(fù)合量子系統(tǒng)，并證明了其滿足糾纏測(cè)度的必要物理?xiàng)l件。

多體量子系統(tǒng)；量子態(tài)；可觀測(cè)量關(guān)聯(lián)；互信息；糾纏測(cè)度

0 引言

量子糾纏作為量子系統(tǒng)之間的一種非經(jīng)典關(guān)聯(lián)，越來越受到人們的關(guān)注。量化糾纏的目的最初來自量子通信[1-2]。近年來，糾纏被認(rèn)為是量子信息理論中的一種資源，并被廣泛應(yīng)用于量子通信和信息處理任務(wù)中[3-4]。目前已經(jīng)有許多比較成熟的糾纏測(cè)度，比如Concurrence糾纏測(cè)度[5-10]，形成糾纏測(cè)度[11-12]，Negativity 糾纏測(cè)度[13]等。一般來說，糾纏度量應(yīng)該滿足以下幾個(gè)公理[14]：

產(chǎn)生的聯(lián)合概率分布為：

Luo Shunlong基于互信息提出了兩體量子態(tài)的可觀測(cè)量關(guān)聯(lián)，并得到了兩體量子態(tài)的一類糾纏測(cè)度[16]。本文將兩體系統(tǒng)的糾纏測(cè)度推廣到多體復(fù)合量子系統(tǒng)，并證明了其滿足糾纏測(cè)度的必要物理性質(zhì)。

1 主要結(jié)果

為了證明引理2，引入以下引理3。

引理2證明 先證必要性成立。

等號(hào)左邊可化簡(jiǎn)為

同時(shí)等號(hào)右邊可化簡(jiǎn)為

下面證明充分性成立。

性質(zhì)1 （糾纏測(cè)度的非負(fù)性）

證明 由引理1有

性質(zhì)2 （糾纏測(cè)度的局部酉不變性）

而對(duì)混合態(tài)來說,根據(jù)凸組合的結(jié)構(gòu),顯然成立。

性質(zhì)3 （糾纏測(cè)度的LOCC單調(diào)性）

證明 根據(jù)文獻(xiàn)[20]，有

因此

所以

2 結(jié)論

本研究，定義了多體復(fù)合量子態(tài)基于可觀測(cè)量算子的糾纏測(cè)度，并證明了該糾纏測(cè)度滿足非負(fù)性，局部酉不變性，LOCC單調(diào)性等性質(zhì)。

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THE ENTANGLEMENT MEASURE OF THE MULTIPARTITE COMPOSITE QUANTUM STATES BASED ON OBSERVABLE OPERATOR

YANG Li-li，YAN Dong-hua，*WANG Yin-zhu

（School of Applied Sciences, Taiyuan University of Science and Technology, Taiyuan, Shanxi 030024, China）

In recent years, there are many research results on the quantization of quantum entanglement, but many of the existing entanglement measures are still difficult to calculate. In the paper “Entanglement measures based on observable correlations”, LUO Shun-long proposed an observable correlation measure of bipartite quantum states based on mutual information, and obtained a class of entanglement measures of bipartite quantum states. In this paper, we generalize the entanglement measure of the bipartite system to the multipartite composite quantum system, and prove that it satisfies the necessary physical conditions of entanglement measure.

multipartite quantum system; quantum states; observable correlations; mutual information; entanglement measure

1674-8085（2022）03-0001-05

O413.1

A

10.3969/j.issn.1674-8085.2022.03.001

2021-11-29；

2022-01-12

國家自然科學(xué)基金項(xiàng)目(11901421)；山西省自然科學(xué)基金面上項(xiàng)目(201901D111254)

楊麗麗(1997-)，女，山西臨汾人，碩士生，主要從事量子信息與量子計(jì)算方面的研究(E-mail:1043177300@qq.com)；

*王銀珠(1977-)，男，山西朔州人，副教授，博士，主要從事量子信息與量子計(jì)算方面的研究(E-mail:2006wang.yinzhu@163.com).