Physics Letters A 315 (2003) 189–193
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Entanglement and interference
Shunlong Luo
a,∗
, Zhengmin Zhang
b
a
Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080 Beijing, PR China
b
School of Mathematics and Statistics, Carleton University, Ottawa, ON K1S 5B6, Canada
Received 26 April 2003; received in revised form 19 June 2003; accepted 1 July 2003
Communicated by P.R. Holland
Abstract
Entanglement is a manifestation of interference effect, which in turn arises from superposition. Bell’s inequalities have their
origin in entanglement. Motivated by these observations, we introduce a numerical measure which quantifies entanglement
from the interference perspective. It turns out that this measure coincides with Rényi’s α-entropy with index α = 1/2.
2003 Elsevier B.V. All rights reserved.
PACS: 03.65.Ud; 03.67.Mn
Keywords: Interference; Entanglement; Rényi’s entropy; Hidden variable model
1. Introduction
Entanglement, which exhibits correlations that can-
not be accounted for classically, is an intriguing fea-
ture and a wonderful resource of quantum mechan-
ics. It is associated with quantum nonseparability and
violation of Bell’s inequalities [1–4], and is the un-
derpinning of several quantum tasks such as telepor-
tation, quantum computation, quantum cryptography
and quantum communicationsthat would not be possi-
ble in a classical context[5,6].For boththeoreticaland
experimental purposes, it is desirable to quantify en-
tanglement, just as we quantify other physical notions
and resources such as force, energy, and information,
*
Corresponding author.
E-mail addresses: luosl@mail.amt.ac.cn (S. Luo),
zhangzm@math.carleton.ca (Z. Zhang).
so that we can manipulate and exploit entanglement
more precisely.
There are a lot of widely studied measures of en-
tanglement, such as entanglement of formation, distil-
lable entanglement, and relative entropy entanglement
[7–9]. Among them some are task-based, some are
information-based. There are many beautiful physical
implicationsandintriguingmathematicalproblemsas-
sociated with these entanglement measures, however,
none of them is simple and definitive, and we are still
lacking a general and satisfying mathematical theory
of entanglement.
In this Letter, we will derive a simple and intuitive
measure of entanglement motivated physically by
superposition principle and interference effect. It turns
out that this measure is a particular case of Rényi’s
α-entropy (with α = 1/2), a concept originated from
probability theory [10], and the case α 1 is already
used by Horodecki et al. to quantify entanglement
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doi:10.1016/S0375-9601(03)01036-3