Experimental demonstration of a heralded entanglement source

Abstract

The heralded generation of entangled states is a long-standing goal in
quantum information processing, because it is indispensable for a number of
quantum protocols. Polarization entangled photon pairs are usually generated
through spontaneous parametric down-conversion, but the emission is
probabilistic. Their applications are generally accompanied by post-selection
and destructive photon detection. Here, we report a source of entanglement
generated in an event-ready manner by conditioned detection of auxiliary
photons. This scheme benefits from the stable and robust properties of
spontaneous parametric down-conversion and requires only modest experimental
efforts. It is flexible and allows the preparation efficiency to be
significantly improved by using beamsplitters with different transmission
ratios. We have achieved a fidelity better than 87% and a state preparation
efficiency of 45% for the source. This could offer promise in essential
photonics-based quantum information tasks, and particularly in enabling optical
quantum computing by reducing dramatically the computational overhead.

Full text

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arXiv:1007.2510v2 [quant-ph] 19 Jul 2010
Experimental Demonstration of a Heralded Entanglement
Source
ClaudiaWagenknecht1†, Che-MingLi1,2†, AndreasReingruber1, Xiao-HuiBao1,3, AlexanderGoebel1,
Yu-Ao Chen1,3, Qiang Zhang1, Kai Chen3⋆, and Jian-Wei Pan1,3⋆
1Physikalisches Institut, Ruprecht-Karls-Universit¨ at Heidelberg, Philosophenweg 12, 69120 Hei-
delberg, Germany
2Department of Physics and National Center for Theoretical Sciences, National Cheng Kung Uni-
versity, Tainan 701, Taiwan
3Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern
Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
†These authors contributed equally to this work.
⋆e-mail: kaichen@ustc.edu.cn; jian-wei.pan@physi.uni-heidelberg.de
The heralded generation of entangled states is a long-standing goal in quantum informa-
tion processing, since it is indispensable for a number of quantum protocols1,2. Polarization
entangled photon pairs are usually generated through spontaneous parametric down con-
version (SPDC)3whose emission, however, is probabilistic. Their applications are generally
accompanied with post-selection and destructive photon detection. Here, we report a source
of entanglement generated in an event-ready manner by conditioned detection of auxiliary
photons4. This scheme profits from the stable and robust properties of SPDC and requires
only modest experimental efforts. It is flexible and allows to significantly increase the prepa-
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ration efficiency by employing beam splitters with different transmission ratios. We have
achieved a fidelity better than 87% and a state preparation efficiency of 45% for the source.
This could offer promising applications in essential photonics-based quantum information
tasks, and particularly enables optical quantum computing by reducing dramatically the
computational overhead5,6.
Quantum entanglement is one of the key resources in quantum information and quantum
foundation. Besides its fundamental interest to reveal fascinating aspects of quantum mechanics,
they are also crucial for a variety of quantum information tasks1,2. In particular, photonic entan-
gled states are robust against decoherence, easy to manipulate and show little loss, both in fiber
and free-space transmission, and thus are exceptionally well suitable for long distance quantum
communication and linear optical quantum computing6,7. Consequently, an event-ready source for
entangled photonic states is of great importance, both from the fundamental and the practical point
of views. Entanglement sources based on the probabilistic generation process of SPDC allow for
demonstrations of a number of quantum protocols, but do not permit on-demand applications, de-
terministic quantum computing and significantly limit the efficiency of multi-photon experiments.
Alternative solutions, such as the controlled biexciton emission of a single quantum dot8–10or the
creation of heralded entanglement from atomic ensembles11, face severe experimental disadvan-
tages, such as liquid-helium temperature environment and large-volume setups.
There has been considerable progress towards the demonstration of heralded photonic Bell
pairs. The scheme by Knill, Laflamme and Milburn (KLM)12provides a theoretical breakthrough
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as proof that efficient quantum computing is possible with linear optics. Although the KLM
scheme allows the nearly non-probabilistic creation of entanglement, the method they use is still
intrinsically probabilistic. The fact that the KLM scheme uses a single photon source, perfect
photon-number-resolving detectors and moreover requires a large computational capacity makes it
barely accessible experimentally. The proposal of Browne and Rudolph5comprises a significant
advance in achieving experimental implementation by using photonic Bell pairs as the primary
resource and experimentally realistic detectors. Using their proposal, the number of optical op-
erations per logical two-qubit gate reduces to ∼ 100, in contrast to the original KLM scheme,
which would have ∼ 100,000 (refs 5,6,12). Central to such a dramatic improvement is the use of
a heralded entanglement source5,6.
Various ideas based on conditional detection of auxiliary photons or multi-photon interfer-
ence were recently proposed to overcome the probabilistic character of SPDC4,13–18. Following
this line, we demonstrate an experimental realization of a heralded entangled photon source by
adopting the proposal of´Sliwa and Banaszek4. This source provides a substantial advance over
the general methods by using linear optics12,13. In the experiment, we only use commercial thresh-
old single photon counting modules (SPCM) as detectors and passive linear optics. The source is
feasible to support on-demand applications, such as the controlled storage of photonic entangle-
ment in quantum memory19to realize the quantum repeater scheme20. Moreover, it is suitable to
serveon-chipwaveguidequantumcircuitapplicationswhichpromisenewtechnologiesinquantum
optics21.
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To demonstrate the basic principle of the heralded entangled photon source, we illustrate the
scheme of´Sliwa and Banaszek4in Fig. 1. With an input of SPDC source emitted from modes a,b,
theschemeherald an entangled photonpair in c,dmodes conditionedby triggers offour photonsin
e,f modes. As an input of the optical circuit, three-pair component of the down converted photons
entangled in polarizations is utilized. The quantum state of the three-pair photon term is given by22
|Ψ3? =
1
12(ˆ a†
xˆb†
y− ˆ a†
yˆb†
x)3|vac?,
(1)
where |vac? denotes the vacuum state, and ˆ a†andˆb†are the creation operators of photons in the
modes a and b. Horizontal and vertical polarization are represented by x and y, respectively. The
optical circuit (see the Methods section) transforms |Ψ3? into4:
|Ψ′
3? =
1
√2RT2|θ?t
??Φ+?
s+
?
1 −T4R2
2
|Γ?ts.
(2)
ThefirsttermofEq.(2)iscomposedofatensorproductoftwostates: thestate|θ?t= ˆ e†
xˆ e†
yˆf†
x′ˆf†
y′|vac?
denoting one photon in each of the four trigger modes, and the maximally entangled photon pair
in the output modes
??Φ+?
s=
1
√2(ˆ c†
xˆd†
x+ ˆ c†
yˆd†
y)|vac?.
(3)
The normalized state |Γ?tsis a superposition of all states that do not exactly have one photon in
each of the trigger mode ˆ ex, ˆ ey,ˆfx′ andˆfy′. Hence, the scheme for heralded entanglement source
is clearly based on the fact that when detecting a coincidence of four single photons in the trigger
modes (ˆ ex, ˆ ey;ˆfx′,ˆfy′), the two photons in the output modes (ˆ cx,ˆ cy) and (ˆdx,ˆdy) nondestructively
collapse to the maximally entangled state |Φ+?s.
In the experiment, we will generate the three-pair photon states (1) by a photon source (see
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the Methods section) and consequently implement the transformation of the linear optical circuit.
A schematic diagram of our experimental set-up is shown in Fig. 2, which is based on the proposal
of Ref. 4.
When taking all of experimental imperfections into account (see the Methods section), it is
crucial to evaluate the performance this source. Therefore, we have measured the state preparation
efficiency and its fidelity, where the efficiency is defined by the number of heralded photon pairs
created from the source per trigger signal. For an ideal case, one trigger signal of a fourfold single-
photon coincidence perfectly heralds one photon pair creation. In our experiment performed with
standard SPCMs, obviously, additional terms yielding triggers will thus result in a reduction of
the preparation efficiency. To overcome this obstacle, we limit their emergence by decreasing the
transmission coefficients of the beamsplitter. In this regime, the probability of transmitting more
than the minimum number of photons to the trigger becomes lower and as such, the danger of
under counting photons in the trigger detectors decreases. However, enhancing the preparation
efficiency in this way will lower the over all preparation rate.
In order to show the relation between the efficiency of state preparation and the transmission
coefficients of the partial reflecting beam splitters, we have chosen BS with three different reflec-
tion/transmission (R/T) ratios: 48.6/51.4, 57.0/43.0 and 68.5/31.5 in the experiment (Fig. 2). In
what follows we will denote them by 50/50, 60/40 and 70/30, respectively, for short. This relation
is shown in Fig. 3. The experimental efficiency can be straightforwardly represented as the follow-
ing relation by the number of triggers nt, the average detection efficiency ηsfor output states, the
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