## Abstract

Plasmonics is a rapidly emerging platform for quantum state engineering with the potential for building ultra-compact and hybrid optoelectronic devices. Recent experiments have shown that despite the presence of decoherence and loss, photon statistics and entanglement can be preserved in single plasmonic systems. This preserving ability should carry over to plasmonic metamaterials, whose properties are the result of many individual plasmonic systems acting collectively, and can be used to engineer optical states of light. Here, we report an experimental demonstration of quantum state filtering, also known as entanglement distillation, using a metamaterial. We show that the metamaterial can be used to distill highly entangled states from less entangled states. As the metamaterial can be integrated with other optical components this work opens up the intriguing possibility of incorporating plasmonic metamaterials in on-chip quantum state engineering tasks.

## Introduction

Entanglement plays a key role in a wide variety of quantum information processing
tasks^{1}, enabling quantum communication protocols such as quantum key
distribution^{2} and quantum computing algorithms providing massive
computational speedup compared to conventional computers^{3,4,5,6}. From
a fundamental perspective, entanglement is also at the heart of many foundational
quantum phenomena^{7}. The task of carrying out filtering operations to
improve the amount of entanglement in non-ideal generated states is therefore of great
importance in quantum information processing and in studies of fundamental quantum
physical effects. Photonic systems in particular represent a flexible test-bed for
developing quantum technologies and probing deeper into the foundations of quantum
theory^{8}. Previous work on photonic entanglement filtering, also
called entanglement distillation^{9}, used standard bulk optical
components^{10}. Here, we explore the possibility of using metamaterials
for this vital task. Metamaterials have recently emerged as highly versatile systems for
controlling the behavior of light^{11,12,13,14}. They are made up of
regularly spaced subwavelength components that react collectively to a given optical
field in order to elicit a bulk optical response. The use of plasmonic nanostructures
for photonic metamaterials is a natural choice due to their electric and magnetic
resonances falling within the optical domain^{11}. A wide range of
applications of plasmonic metamaterials for the optical sciences have been demonstrated
so far in the classical regime, including the use of negative refractive index
materials^{15,16,17,18} for superlensing and nano-imaging^{19,20}, transformation optics^{21} and sensing^{22}. In the quantum regime, less is known about plasmonic metamaterials^{23}
and theoretical studies have so far looked at achieving a negative refractive index by
manipulating quantum emitters^{24}, as well as the incorporation of
metamaterials with waveguides for reducing the impact of loss in quantum state
transfer^{25} and entanglement generation^{26}. Experimental
studies, on the other hand, have focused on basic quantum state transfer effects^{27,28}, absorption of single photons^{29} and quantum
interference effects^{30}. Despite some intriguing results, so far there
have been no studies investigating the use of metamaterials for quantum state
engineering tasks. Given the wide range of tasks made possible by using metamaterials in
the classical regime, exploring metamaterials in the quantum regime is an important
endeavour. Most recently the use of 2-dimensional metamaterials, known as
metasurfaces^{31,32,33,34,35}, has gained considerable attention
from the metamaterial community due to their ease of fabrication and overall
compactness. In this work we explore the use of 2-dimensional plasmonic metamaterials
for their potential in quantum state engineering and more specifically for the task of
entanglement distillation. These 2-dimensional metamaterials can be expected to be more
readily accessible than their 3-dimensional counterparts or standard bulk optical
components for realizing advanced quantum applications in the near future, as they have
the potential to be integrated into on-chip photonic structures^{36,37,38}. Our study builds upon previous work on the classical characterization of the
collective response of nanostructured arrays^{39,40}, and in the quantum
regime on the assisted-transmission of entanglement in periodic plasmonic nano-hole
arrays^{41} and the remote control of transmission of single
photons^{42}. However, different to these works, here we go beyond a
simple transmission scenario in the quantum regime and show that plasmonic
nanostructured arrays can be used not only for basic transfer of quantum information,
but also for the manipulation of quantum information in the form of quantum state
engineering. The results of our work open up a new horizon beyond previous studies of
basic passive systems. The quantum information in our experiment is encoded within the
polarisation degree of freedom of photons, which is one of the most widely used degrees
of freedom in bulk quantum photonic systems^{8}. However, its use in on-chip
photonic systems is challenging^{43}. Our demonstration of a metamaterial
component that can manipulate photonic polarisation at the quantum level and has the
potential for on-chip integration with a small lateral footprint is therefore highly
appealing. Moreover, in our work we have fully characterized the metamaterial using the
rigorous technique of quantum process tomography, showing how to characterize the
optical response of metamaterials in the quantum regime.

## Results

The task of entanglement distillation refers to the process of extracting a smaller
number of highly entangled states from an ensemble of less-entangled states^{9}. Entanglement shared between two parties (bi-partite entanglement) is
the simplest form of entanglement. A two-qubit state encoded in the polarization
degrees of freedom of two photons (each in a spatially separate path) of the
form

where and represent the horizontal and vertical polarization state of a photon, is a non-maximally entangled pure state for . It can be transformed into a maximally entangled state (a Bell state) of the form by using a local operator, acting on only one of the photons, that induces a polarization dependent modification of the amplitudes. In order to realize this operation we utilize polarization dependent extinction introduced by the collective action of many plasmonic resonators in a metamaterial.

The metamaterial used in our experiments consists of an assembly of gold nanoantennas
grown on an ITO-coated suprasil substrate, as described in the Supplementary Material. The final structure
represents an array of straight nanoantennas occupying a footprint of up to
10^{−4} cm^{2}, as shown in
Fig. 1a. The dimensions of the rod-like nanoantennas are
95–110 nm in length, 39 nm in width and
30 nm in height, with a spacing of 200 nm center-to-center
between them, thus achieving a nanorod density of
~10^{9} cm^{−2}. The
dimensions and the spacing of the antennas are much smaller than the wavelength of
the photons used in our experiments (790 nm), so only average values of
nanorod assembly parameters are important, and individual nanorod size deviations
have no influence on the optical properties that are well described by an effective
medium model^{31,32,33,34,35}. When V-polarized light impinges onto
vertical metallic nanoantennas of a certain length a plasmonic resonance is excited
in the form of light coupled to a collective oscillation of free electrons in the
conduction band – a localized surface plasmon (LSP). The generation of
the LSP leads to a dip in the transmission spectra of the light at the resonant
frequency. This dip reflects the fact that some of the light is reflected back into
the far field and some is absorbed by the LSP. Due to the Ohmic resistance faced by
the oscillating electrons, the energy used to excite them is partly dissipated, the
amount by which depends on the dimensions of the nanoantenna. The dimensions of the
nanoantenna also determine the resonant frequency of the LSP and therefore the
position of the dip in the overall transmission spectrum. On the other hand, light
polarized perpendicular (H-polarized) to the antennas does not excite the plasmonic
resonance and passes the sample almost unchanged. Fig. 1b
depicts the transmission spectra of two typical nanoantenna array metamaterials used
in our experiments. A clear polarization dependence of the transmission spectra is
seen.

In our setup (Fig. 1c), we prepared polarization entangled
photon pairs at a wavelength of
λ = 790 nm via spontaneous
parametric down conversion (SPDC) in Type-I phase matched nonlinear crystals
(β-barium borate, BBO) stacked together such that their optical axes are
orthogonal to each other^{44}. The SPDC pump laser with a wavelength of
λ = 395 nm is obtained by frequency
doubling the light from a mode locked Ti: Sapphire laser at
λ=790 nm. We arbitrarily set
of the entangled state by varying the polarization of the pump laser^{44}, *i.e.* when the polarization of the pump was set to diagonal polarization
the prepared photon pair was maximally entangled (),
whereas when it was set to horizontal polarization the prepared photons were in the
product state (). The
difference in the group velocity of photons with different polarization was
compensated by birefringent crystals (BC) and the phase between horizontal and
vertical polarization was adjusted by a set of quartz crystals represented as
PS.

We performed a series of experiments by inserting different metamaterial samples
(with different lithography parameters – hence different nanoantenna
resonance positions) into the optical path of one of the photons of the entangled
photon pair. One photon was transmitted through the metamaterial after which it and
the other photon of the pair were sent to independent single-mode-fiber-coupled
silicon avalanche photo diodes (APDs). Before being coupled into fibers the photons
passed through interference filters of bandwidth 2.7 nm, and a series of
a half-wave plate (HWP), a quarter-wave plate (QWP) and a polarizing beamsplitter
(PBS) placed on their respective paths. The interference filter and single mode
fiber performed the selection of the spectral and spatial mode of the photons
respectively. The HWP, QWP and PBS were used to choose the measurement basis states
, , and required for the
characterization of the final states using quantum state tomography^{45}
(QST). The spot size of the beam on the nanoantenna array of the metamaterial was
adjusted to be ~90 μm in diameter to ensure the
collective electromagnetic response of the nanoantennas
(~10^{6} nanoantennas in the beam path). We positioned
the different metamaterial samples such that the vertical polarization of the
photons was parallel to the long-axis of the nanoantennas.

In the first set of experiments, we performed quantum process tomography^{46,47} (QPT) to characterize the nanoantenna arrays used in our
experiments. QPT allows us to reconstruct the action of the metamaterial on the
polarization state of a single photon as an effective quantum channel. To
reconstruct the channel we probe the metamaterial with different photonic probe
states. For this purpose, we set the pump laser to H polarization so that two
photons with V-polarization are prepared by SPDC in one of the BBO crystals. We then
insert a HWP and a QWP in front of the metamaterial sample to prepare the first
photon in one of the four probe states , , and required for QPT. The HWP and QWP on the path of the
second photon were set such that V polarized photons are always detected by the APD.
The detection of a photon in the second path heralds the presence of a single probe
photon in the first path. The photons in the probe states in the first path were
sent to the metamaterial and QST was performed on the ones that were transmitted
through the metamaterial by recording the coincidence events, *i.e.* when APDs
in the first and second paths detect a photon at the same time. From the collected
experimental data, we reconstructed the single-photon process matrices, known as
χ matrices, for seven different metamaterial nanoantenna arrays. The
χ matrices obtained for two of the nanoantenna arrays are shown in Fig. 2 (see the Supplementary Material for all χ matrices). We found that the
χ matrices of the nanoantenna arrays

are well described by the χ matrix of a partial polarizer represented by
a single Kraus operator corresponding to a non-trace
preserving channel^{48}, *i.e.*
, where is the input
single-photon state in the polarization basis. This photonic channel is equivalent
to the general form , where the single-qubit Pauli
operators, , X, Y and Z, provide a complete basis for
the Hilbert space and the elements of the χ matrix are chosen to match
the action of (see Supplementary Material). In order to quantify how
close the metamaterial samples are to an ideal partial polarizer model we calculated
the process fidelity of the two χ
matrices shown in Fig. 2 to an ideal partial polarizer
. In general, the fidelity ranges from 0 to 1,
with 1 corresponding to a complete match for the channels. We find process
fidelities of and by
maximization over , which yielded and , respectively. The
values obtained from QPT agree well with the
measured values using classical FTIR (see Fig. 1b). These results confirm that the plasmonic metamaterial
fabricated with different nanoantenna array parameters has a polarization dependent
transmission in the low-light intensity quantum regime and can therefore be used to
induce a collective polarization dependent loss at the single-photon level.

Next, we performed experiments to demonstrate that our plasmonic metamaterial can be
used to distill highly entangled pure states from an ensemble of less-entangled pure
states. First, we generated the initial less-entangled pure state given in Eq. (1) by varying the polarization of the pump in order to set the
value of , and checked the entanglement distillation
performance of each of the nanoantenna arrays. As a control experiment, we sent one
of the photons of the prepared entangled state to a portion of the metamaterial
sample where there were no nanoantennas, *i.e.* the photon passes through the
glass substrate only, and performed QST of the two photons arriving at the APDs. The
reconstructed density matrix of this initial state is given in Fig.
3a. We estimate the purity of this state as
0.97 ± 0.01 using , with a value of 1 corresponding to a completely pure state^{47},
and subsequently calculate the value of as
using where is the density operator of
the state obtained from QST. The fidelity of this initial state with respect to the
non-maximally entangled state with is using and the fidelity
with respect to the maximally entangled state (with
) is . We also
calculated the entanglement of formation^{1} (EOF) that quantifies the
amount of entanglement in the generated bipartite state as
0.66 ± 0.01, verifying its non-maximal value of
entanglement.

After confirming the purity and the amount of entanglement of this initial non-maximally entangled state, we performed experiments with the state using the seven different metamaterial nanoantenna arrays. Figure 3b presents the reconstructed density matrix of the distilled state that had the highest EOF observed in our experiments. This distilled state has a fidelity of 0.95 ± 0.01 with respect to a maximally entangled state and an EOF of 0.93 ± 0.02. The density matrices of the distilled states obtained with the seven different nanoantenna arrays are given in the Supplementary Material. In Fig. 3c, we show the EOF, fidelity and purity of the distilled states for the seven nanoantenna arrays used in the experiments, confirming the applicability of these metamaterial arrays for distilling highly entangled states from less-entangled starting states. The purity of the output states keeps a constant high value (close to 0.95), which reflects the preservation of the coherence of the photons during the filtering process.

We also tested the performance of a fixed metamaterial nanoantenna array for entanglement distillation of different initial states of the form and . The results are shown in Fig. 3d which shows that when a fixed nanoantenna array is used, the fidelity and the EOF of the distilled state depend on the value of for the initial state, and that there is an value for which the specific array is optimal for entanglement distillation.

Next, we tested the ability of the local filtering process of the metamaterial nanoantenna arrays to distill entangled states with a higher amount of entanglement from partially mixed states containing lower amounts of entanglement. In order to prepare an entangled state of a partially mixed state, we placed a quartz crystal (12.8 mm thick) inserted between two HWPs in front of the metamaterial sample, as shown in Fig. 1c. Due to the group velocity difference between H and V polarizations, the quartz crystal partially destroys the coherence, resulting in the partially mixed state. We control the degree of decoherence by rotating the first HWP to prepare arbitrary superposition of H- and V-polarizations. The HWP after the quartz crystal is used to rotate the polarization back to the initial polarization basis. By using this technique, we prepared three different non-maximally entangled partially mixed states of the form and three of the form as starting states (see Supplementary Material) and performed the distillation process using a fixed metamaterial nanoantenna array. In Fig. 4, we present the density matrices of two of the initial mixed states and the final distilled states obtained from the metamaterial (see Supplementary Material for density matrices of the other four mixed states). From the tomographically reconstructed density matrix of each of the initial and distilled states, we estimated the fidelity and EOF (see Table 1). These values clearly show that the distilled states have a higher entanglement and a higher fidelity than the starting states. Table 1 also includes the estimated values of ε and λ before and after the distillation.

We should emphasize here that the filtering process and coincidence detection select a particular subensemble from the ensemble of the starting initial states, with coincidence detection rates before and after filtering corresponding to 4490 and 1823 counts per second, respectively. The amount of entanglement in the states in the selected subensemble is higher than the amount of entanglement of the larger ensemble containing the initial states. The unselected states have much lower entanglement. This does not contradict with the fact that entanglement of an ensemble of states cannot be increased by LOCC. That is, if we consider all the selected and unselected states the average entanglement does not increase. The metamaterial thus enables a quantum selection process to take place so that all of the partially entangled states can be distilled into a smaller number of higher entangled states that may then be used for further quantum information processing tasks.

## Discussion

Our experiment demonstrates that plasmonic metamaterials can be used for a quantum
information processing task in the form of the distillation of quantum entanglement.
This clearly shows that an array of nanostructures in a metamaterial can be used to
perform quantum state engineering. Our work goes beyond previous works in plasmonics
and metamaterials where the initial interest was to show that quantum features of
plasmons are similar to those of photons and that they are preserved during the
photon-plasmon-photon interconversion process^{23}. Another key
difference of our work is that it relies on the collective response of many
subwavelength plasmonic structures within the plasmonic metamaterial, which is in
stark contrast to most other studies where the quantum response of only single
plasmonic structures has been studied. Due to the 2-dimensional nature of the
metamaterial investigated, the nanoantenna structures can be fabricated with
well-controlled dimensions, providing a high quality design with a small-lateral
footprint. This makes it ideal for integration with wavelength-scale plasmonic^{36} and dielectric components^{37,38}, such as on-chip
optical waveguides, where it could be used for multiphoton entanglement
distillation^{49} and, if used in combination with additional
polarisation components^{50}, for a variety of other quantum information
processing tasks^{47}. Future work on developing tunable nanoantenna
structures^{51} could lead to 2-dimensional metamaterials that
provide enhanced functionality for entanglement distillation and more complex
quantum state engineering tasks by enabling one to tune the metamaterial response
for optimum performance. Here, challenges include the incorporation of support
mechanisms for delivering the stimulus for change, such as electronic wiring or heat
transfer. Despite such challenges, it is clear there are some fascinating
opportunities for metamaterials in the quantum regime.

## Additional Information

**How to cite this article**: Asano, M. *et al.* Distillation of photon
entanglement using a plasmonic metamaterial. *Sci. Rep.*
**5**, 18313; doi: 10.1038/srep18313 (2015).

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## Acknowledgements

This work was supported by JSPS Grant-in-Aid for Scientific Research (A) 25247068, (B) 15H03704 and (B) 26286068; The Karlsruhe School of Optics & Photonics (KSOP); The South African National Research Foundation; The South African National Institute for Theoretical Physics.

## Author information

## Affiliations

### Department of Material Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan

- Motoki Asano
- , Rikizo Ikuta
- , Takashi Yamamoto
- & Nobuyuki Imoto

### Institute of Applied Physics, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe, Germany

- Muriel Bechu
- & Martin Wegener

### Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe, Germany

- Muriel Bechu
- & Martin Wegener

### School of Chemistry and Physics, University of KwaZulu-Natal, Durban 4001, South Africa

- Mark Tame

### National Institute for Theoretical Physics, University of KwaZulu-Natal, Durban 4001, South Africa

- Mark Tame

### Department of Electrical and Systems Engineering, Washington University, St. Louis, MO 63130, USA

- Şahin Kaya Özdemir
- & Lan Yang

### Department of Electrical and Computer Engineering, Michigan Technological University, Houghton, MI 49931, USA

- Durdu Ö. Güney

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### Contributions

S.K.O., M.T. and D.Ö.G. conceived the idea, M.A., T.Y. and S.K.O. designed the experiments; M.B. fabricated and characterized the metamaterial samples, MA performed the experiments with help from R.I., M.T., T.Y. and S.K.O. All authors analyzed the experimental results, contributed to the discussions and interpretations. S.K.O., T.Y., L.Y. and M.T. wrote the manuscript with inputs from all authors. N.I. and M.W. supervised the project.

### Competing interests

The authors declare no competing financial interests.

## Corresponding authors

Correspondence to Şahin Kaya Özdemir or Martin Wegener or Nobuyuki Imoto.

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