PHYSICAL REVIEW A 86, 052121 (2012)
Time-resolved measurement of Bell inequalities and the coincidence loophole
M´ onica B. Ag ¨ uero,
*
Alejandro A. Hnilo, and Marcelo G. Kovalsky
CEILAP, Centro de Investigaciones en L´ aseres y Aplicaciones, UNIDEF (MINDEF-CONICET), J.B. de La Salle 4397,
(1603) Villa Martelli, Argentina
(Received 10 May 2012; revised manuscript received 18 September 2012; published 30 November 2012)
We report an Einstein-Podolsky-Rosen-Bohm experiment with a pulsed source of entangled pairs of photons,
recording the time of arrival of the pulses and of the detection of each single photon. This allows varying the
parameters of the analysis (as the size of the time coincidence window) at will after the experiment has ended.
Among other results, we present the measurement of the time variation of the Clauser-Horne-Shimony-Holt
parameter during the pulse. The obtained results close (or at least impose new and tight restrictions to) the
last loophole that remains open in the tests of quantum mechanics vs local realism (the so-called coincidence
loophole).
DOI: 10.1103/PhysRevA.86.052121 PACS number(s): 03.65.Ud, 42.50.Dv, 42.50.Xa, 42.65.Lm
I. INTRODUCTION
Local realism (LR) is, roughly speaking, the intuitive belief
that the results of an experiment are generally unaffected by
events occurring at remote places and that the physical world
is independent of observation. Some predictions of quantum
mechanics (QM) are incompatible with this belief [1]. A large
number of experiments have been performed with the aim
to determine whether QM or LR is valid in nature. Most of
them are of the Einstein-Podolsky-Rosen-Bohm (EPRB) type,
where for a state of two photons entangled in polarization, the
rate of coincident detections is measured after analyzers are
set at certain angles. The correlation between the results of the
measurements according to QM is larger than allowed by any
theory holding to LR. The correlation is usually quantified with
an experimentally accessible parameter such as the Clauser-
Horne-Shimony-Holt (S
CHSH
) parameter [1]. The inequality
S
CHSH
2 holds for LR while, according to QM, S
CHSH
= 2
√
2.
The violation of this often-called Bell-CHSH inequality has
been observed and, consequently, QM has been confirmed
against LR. However, practical limitations in the experiments
leave space to alternative LR theories to survive by exploiting
the so-called logical loopholes. It is therefore essential to the
foundations of QM to close all the loopholes.
The loopholes can be classified as follows: (i) the detection
or efficiency loophole, which exploits the imperfect efficiency
of detection; (ii) the contextual, locality, or timing loophole,
which exploits the possibility that the source of photon pairs
is somehow affected by the setting of the analyzers; and
(iii) the coincidence [2], trapping [3], or memory loophole [4],
which exploits the ambiguity in the definition of a coincident
detection due to the arbitrary (but usually fixed) value T
w
of
the time coincidence window. The LR theories exploiting this
loophole (coincidence-loophole theories, CLHT) assume that
the analyzer’s setting influences the time at which the photon
detection occurs. Then, a local detection may be coincident
with a remote detection, or not, depending on the angle setting
and the size of T
w
. The result is that the number of coincidences
depends on both settings and that it can be adjusted to fit the
*
Corresponding author: maguero@citedef.gob.ar
QM values, even though the process is completely local. Not
a single photon is lost; all that happens is that its detection is
shifted in time, in or out the coincidence window. Most CLHT
are able to fit the QM values even in ideal setups with 100%
efficient optics and detectors, and with random variation of the
analyzers’ settings.
An experiment using an ion trap closed the detection
loophole by reaching nearly 100% efficiency [5], and EPRB
experiments using random varying analyzers placed in remote
stations closed the contextual loophole [6,7]. The simplest
of the CLHT [8] was disproved by recording the time of
detection (“time stamping”) of the photons produced with a
continuous-wave (CW) source [9]. A general test of CLHT
requires, in addition, the definition of the time interval where
it is expected to detect photons if there is no shifting effect.
This time interval is named here the “natural time” for photon
detection. As it is detailed later, the statistical properties of
the photons detected outside the natural time provide a test
of the coincidence loophole. Two setups have been proposed
for this purpose [3]: one uses an event-ready source [10],
and the other one uses a pulsed spontaneous parametric
down-conversion (SPDC) source. Here we choose the second
alternative, closely following [3]: “In the case of pulsed optical
experiments...if the pulse is short in comparison with the pulse
spacing...(it) will provide a well-defined, pre-determined
coincidence window and this will remove the coincidence
loophole” and [4]: “...one selects just those measurements
within an appropriate time interval after a saved “alert”
message... It is practically extremely important that this
selection may be done after the experiment has run its course.”
Finally, some LR theories suppose that the setup (or some
hypothetical ether) “learns” how to reproduce the QM values as
photons cross it [11–13]. To test this supposition, it is necessary
to measure the time evolution of the correlation.
In this paper, we report the main results of an experiment
using a nanosecond-pulsed SPDC source. The “alert” or
“trigger” signal is provided by a fast photodiode detecting
the pump pulse. The time values of the triggers of all the pump
pulses, as well as the time of detection of each single photon,
are recorded and saved for further analysis (see Fig. 1). To
our knowledge, the realization of an experiment with these
features has not been done before.
052121-1 1050-2947/2012/86(5)/052121(5) ©2012 American Physical Society