Quantum Information Science
Using Photons

SHIGEKI TAKEUCHI

RESEARCH INSTITUTE FOR ELECTRONIC SCIENCE, HOKKAIDO UNIVERSITY

THE INSTITUTE OF INDUSTRIAL AND SCIENTIFIC RESEARCH, OSAKA UNIVERSITY

1. INTRODUCTION

Quantum information science has been attracting significant
attention recently. It harnesses the intrinsic nature
of quantum mechanics such as quantum superposition,
the uncertainty principle, and quantum entanglement
to realize novel functions. Its applications include quantum
cryptography, whose security is guaranteed by the
laws of physics, and quantum computing, which provides
computational power fundamentally superior to current
computers based on classical physics. Recently, quantum
metrology is emerging as another appealing application
of quantum information science.

Quantum information is based on so-called "qubits"
(quantum bits). There are many possible ways to physically
express a qubit, including electron spin, nuclear
spin and superconducting coherent devices. However,
photons offer some noteworthy advantages. Photons are
robust against decoherence and can be transmitted over
long distances(~tens of km), making them an indispensable
information carrier for communication and an important
tool for metrology. In addition, the operations
for single photons (single-qubit gates) are easily realized
by linear optical elements such as beam splitters (half
mirrors) and wave plates (polarization manipulators).

In this article, we present our recent results concerning
functional photonic quantum circuits and quantum metrology
that exceeds the standard quantum limit (SQL).
In section 2, as background, the concept of two-photon
interference is explained. In section 3, two photonic
quantum circuits, 'an entanglement filter'^{1,2)} and 'a heralding
controlled-NOT gate'^{3)} are introduced. In section
4 and 5, 'a four-photon interference experiment'^{4)} and
'an entanglement- enhanced microscope,'^{5)} both of which
surpass the SQL, are explained. In section 6, we summarize
this article and discuss future prospects.

**Fig. 1:** Hong-Ou-Mandel two-photon interference. When two
indistinguishable photons enter a half mirror, the two cases shown on
the right side do not occur due to quantum interference.

2. TWO-PHOTON INTERFERENCE AND PHOTONIC QUANTUM GATES

In quantum mechanics, when physical processes share the same initial and final states, 'interference' occurs. To
calculate the probability of observing such a phenomenon,
it is necessary to evaluate the probability amplitude
of each process, and then calculate the square of the absolute
when we consider the case where two photons
are incident to a beam splitter (Fig. 1).

Suppose two 'indistinguishable' photons are incident to
a beam splitter with a reflectivity of 50% (50:50 BS). If
the photons behaved like classical particles, there would
be four cases: (1) the left photon is reflected and the
right one is transmitted. (2) The opposite case (the right
photon is transmitted and the left photon is reflected.)
(3) Both photons are reflected. (4) Both photons are
transmitted. Since a 50:50 BS reflects a photon with a
probability of 50%, it is logical to assume a probability of
50% that a photon is emitted from both output ports simultaneously.
However, this probability is actually 0 due
to quantum interference; the respective probability amplitudes
of case (3) and case (4) have the same amplitude
but opposite signs, and thus completely and destructively
interfere. Hong, Ou and Mandel experimentally demonstrated
this phenomenon using pairs of photons generated
via a spontaneous parametric down-conversion
(SPDC) process.^{6)} This phenomenon is also called Hong-
Ou-Mandel (HOM) interference.

Two-photon interference has become a general tool
for quantum information processing. A photonic quan
tum circuit known as an 'entanglement filter'^{2)} utilizes
such two-photon interference at a 50:50 BS to monitor
the number of photons passing through specific optical
paths. This process can be used to realize quantum logic
gates that handle pairs of photonic qubits.^{7)} By adjusting
the reflectivity of the beam splitter, the two-photon
interference phenomena can be adapted to the required
function. A controlled-NOT (CNOT) gate that handles
two photonic qubits was realized using a beam splitter
with a reflectivity of 1/3 by both us and Ralph et. al.,
independently.^{8,9)} A CNOT gate requires two qubits, the
control qubit and the target qubit, as the input and output,
respectively. Only when the control qubit is is the
target qubit flipped.

Following that, we succeeded in demonstrating a CNOT
gate^{10)} using a partially polarizing beam splitter (PPBS),
which had a reflectivity 1/3 for horizontal polarization
and 1 for vertical polarization (Fig.2). Similar schemes
were reported independently by other groups.^{11,12)} The
operation of this compact CNOT gate is successful only
when the input photons are output from each of the output
modes. This CNOT gate can be considered a singlephoton
level all optical switch; only when the control
photon is vertically polarized is the polarization of the
target photon changed.

**Fig. 2:** Experimental demonstration of a photonic quantum gate using a partially polarizing
beam splitter (PPBS). (Upper panel) The experimental setup. Red lines (pink lines) represent
input (output) photons, whose polarization states are used as qubits. (Lower panel) The
measured and ideal truth tables for the controlled-NOT gate operation. 01 in input and
output denotes the state where the control qubit is 0 and the target qubit is 1. P is the
probability.

3. PHOTONIC QUANTUM CIRCUITS

We tried to combine several of the developed photonic
qubit quantum switches to make a quantum circuit with a
specific function. Figuratively speaking, our efforts may
be compared to making a radio (a functional circuit) by
combining transistors (an elementary device). Here we
discuss an entanglement filter as an example.

Figure 3 is a schematic illustrating the function of the entanglement
filter.^{1,2)} The filter transmits the input photon
pair only when the photon pair shares the same vertical
or horizontal polarization, keeping the coherence
between these two states. If one of the input photons is vertically polarized and the other is horizontally polarized,
the pair is rejected by the filter.

**Fig. 4:** A photonic quantum circuit for the entanglement filter. S1 and S2 are the input
ports, and S1_{OUT} and S2_{OUT} are the output ports. A1 and A2 are ancillary photon inputs. D1
and D2 are the photon detectors. BS is the beam splitter and PBS is the polarization beam
splitter.

**Fig. 5:** Physical implementation and experimental results of the entanglement filter. (Upper
panel) Photons are input at S1 and S2 and the results are output from S1_{OUT} and S2_{OUT}. The
ancillary photons are input at A1 and A2 and detected by photon detectors D1 and D2. The
detailed characteristics of PPBS A and PPBS B can be found elsewhere.^{2)} (Bottom panel) The
ideal and measured truth tables for the entanglement filter.

We consider the case when the two input photons have
diagonal polarization. Since a photon with diagonal polarization
is in a superposition of the horizontal and
vertical polarization state , the input state is a superposition
of the four states as follows.

The entanglement filter only transmits the components so the output state is

which is a polarization entangled state.

Figure 4 shows a photonic quantum circuit for such an
entanglement filter, as proposed in 2002.^{1)} In this circuit,
four 50:50 beam splitters (BS1~BS4) are used as quantum
gates (where two-photon interference occurs).

For example, the two-photon interference at BS3 is used
to monitor the number of photons routed to BS3; only
when a single photon state is routed to BS3 is the single
photon detection event at detector D2 possible (Fig. 4
inset).

It was diffcult to realize this circuit, because it contains
not only four two-photon interferences, but also concatenated
multi-path (classical) interferences where optical
path length differences must be controlled and maintained
to an accuracy of a few nanometers.

We realized this entanglement filter^{2)} (Fig. 5) by adapting
the displaced Sagnac architecture with PPBSs, where
the concatenated multi-path interferences were passively
stabilized. Even when one of the devices (a mirror or
beam splitter) was tilted or displaced due to vibration or
thermal drift, both optical paths experienced the same
change since they pass through the same optical devices.
As a result, the path length difference was robust against
such disturbances.

The bottom panel of Fig. 5 shows the ideal and measured
truth tables of the entanglement filter. In the ideal
case, the HH and VV inputs are output with a probability
equal to unity but the HV and VH inputs are terminated,
i.e., the output probability is zero for all four outputs in
these cases. In the measured table, the output for HV
and VH inputs are well suppressed while those for HH
and VH inputs are maintained. We also checked that our
filter works with input photons in a superposition of the
H and V polarized states and confirmed that such operation
cannot be realized by a classical device.

Recently, we successfully developed a quantum circuit
for the 'heralded' CNOT gate operation,^{3)} whose successful
operation can be heralded by the success signal.
Therefore, photon number monitoring at the output
required for the previous CNOT gate (Fig. 2) is not necessary.
This heralded CNOT gate was proposed by Knill,
Laflam me and Milburn^{7)} as a basic element for scalable
linear optics quantum computation, but was not realized
for 10 years.

4. MULTI-PHOTON INTERFERENCE BEATING
THE STANDARD QUANTUM LIMIT

In the previous section, we saw that the manipulation
of the quantum states of multiple photons is possible
through the use of linear optical circuits and multiphoton
interference. In this section, we will discuss the applications
of such multi-photon entangled states for quantum
metrology.

**Fig. 6:** Single-photon and entangled-photon interference.

**Fig. 7:** Experimental setup for the four-photon NOON state interferometer. The displaced
Sagnac interferometer in the main panel is, in principle, the same as the Mach-Zender
interferometer in the inset. One or two pairs of photons are generated via SPDC in the beta
barium borate (BBO) crystal and are then injected into the interferometer. Photons are
counted by single photon counting modules (SPCM) at modes e and f. The phase is
modi"ed by a rotating phase plate (PP).

**Fig. 8:** Experimental results. (a) Single photon count rate in mode e as a function of the
phase plate (PP) angle with single-photon input _{ab}.(b) Two-photon count rate in modes
e and f for input state _{ab}. (c) Four-photon count rate with three photons in mode e and
one photon in mode f for the input state _{ab}. Accumulation times for one data point were
(a) 1 s, (b) 300 s, and (c) 300 s.

Phase measurements using optical interferometery
are applicable to many fields, for example, astronomy
(gravitational wave detection), engineering (optical fiber
gyroscopes) and life sciences (differential contrast
microscopy). There are two important concepts for such
measurements: precision and sensitivity. In principle,
precision can be improved by increasing the probe light
intensity or the number of measurements made. However,
the sensitivity is fundamentally limited by the precision
per unit power or the number of photons provided
by the probe light. The left panel of Fig. 6 shows a typical interference fringe observable using classical light (laser
etc.) or single photons. Suppose we are trying to detect a
small phase shift from a bias phase. When we set the bias
phase to that where the slope of the interference fringe
is maximum, the change in the output due to the phase
shift is maximized and the highest sensitivity achieved.
For single photons (a classical light source), the sensitivity
limit (the standard quantum limit is given by
where *N* is the number of photons in a given state.
The right panel of Fig. 6 shows an interference fringe
when the input is a superposition of two photon states:
(1) a two-photon state is in the upper path and no photons
are in the lower path and (2) no photons are in the
upper path and a two-photon state is in the lower path:

A generalized state for *N* photons, is
usually called a 'NOON' state.

Interestingly, the fringe period becomes half of that for
the single photon case. As a result, the slope of the interference
fringe becomes twice as steep, yielding sensitivity
beyond the . The fringe period of an* N* photon
NOON state is 1/N of that of the single photon case.
For the multiple photon case, the sensitivity limit (the
Heisenberg limit) is given by 1/N.^{13)}

Recently, we demonstrated four-photon interference
exceeding the .^{4)} Using parametric fluorescence
and a stably displaced Sagnac interferometer (Fig. 7),
we observed one-photon, two-photon and four-photon
interference fringes with high visibilities (Fig. 8).^{14)} The
visibility is a parameter describing the quality of the
interference as follows:

where _{max} and _{min} are the maximum and minimum
photon counts. The sensitivity degrades when the visibility
is lower. The sensitivity also depends on the method
used to observe the correlation of the photons at the output.
For the scheme we adopted, the threshold visibility
required to surpass the was 82%. The visibility of
the four-photon interference fringe shown in Fig. 8(c)
was 916%, clearly exceeding the threshold.

5. AN ENTANGLEMENT-ENHANCED
MICROSCOPE

Optical phase measurement is playing an important
role in microscopy. Differential interference microscopes
(DIM), which detect the optical path-length difference
between two adjacent optical paths at the sample, are
widely used for the evaluation of opaque materials or
the label-free sensing of biological tissues. A laser confocal
microscope (LCM) combined with a DIM (LCMDIM,
Fig. 9, left panel) has recently been used to observe
the growth of ice crystals with a single molecular step
resolution. The depth resolution of such measurements
is determined by the signal-to-noise ratio (SNR) of the
measurement, and the SNR is in principle restricted by
the .

Recently, we proposed and demonstrated an entanglement-
enhanced microscope^{5)} which is based on an
LCM-DIM (Fig. 9, right panel). Instead of laser light
and an intensity measurement, entangled photons (in
the NOON state) and a coincidence measurement were
used. The SNR of the entanglement microscope is times better than the conventional LCM-DIM restricted
to the .

**Fig. 9:** (Left panel) Illustration of LCM-DIM. (Right panel) illustration of the entanglementenhanced
microscope. The red and blue lines indicate horizontally and vertically polarized
light.

**Fig. 10:** Experimental results obtained with the entanglement microscope. (a) Atomic force
microscope (AFM) image of a glass plate sample (BK7) with a Q shape on its surface carved
in relief with an ultra-thin step using optical lithography. (b) Section of the sample outlined
in red in (a). The height of the step is estimated to be 17.3 nm from this data. (c) Image of the
sample using an entanglement-enhanced microscope where a two-photon entangled
state is used to illuminate the sample. (d) Image of the sample using single photons (a
classical light source).

In the experiment, we used a two-photon NOON state
(N=2) source as the probe. (Fig. 10). The sample was a
glass plate with a Q shape on its surface carved in relief
with an ultra-thin step of ~ 17 nm using optical lithography
(Figs. 10 a and b). Figures 10 c and d show the twodimensional
scan images of the sample using entangled
photons and single photons, respectively. The step of the
Q-shaped relief is clearly seen in Fig. 10 c, whereas it is
obscure in Fig. 10 d. The average total number of photons
contributing to these data is set to 920 per position
assuming unity detection effciency. In a detailed analysis,
the SNR of Fig. 10 c is 1.350.12 times better than 10 d,
which, taking the visibility of the single and two-photon
interferences into account, agrees well with the theoretical
prediction of 1.35

6. SUMMARY

In this article, we introduced our recent developments
of quantum circuits and quantum metrology using photons.
We showed that two-photon interference can be
used as a 'photon-photon' switch, and experimentally
demonstrated an entanglement filter. We also showed
that the sensitivity and the SNR can be improved to
times higher than that achieved using a classical light
source, and demonstrated an entanglement-enhanced
microscope surpassing the .

Increasing the number of photons is of the utmost importance.
When we are able to use a ten-photon NOON
state (N=10) the SNR will be more than 3 times higher
than the SQL. In other words, the same SNR can be
achieved with just 10 % of the photon flux. Recently it
has been predicted that multi-photon interference calculations
for a given photonic network will be problematic
for conventional computers, and the task may be beyond
the power of state-of-the-art super computers when N ~
10 to 30.^{16)} Photonic quantum simulators^{17)} that evaluate
exact solutions of molecular energy levels have been
proposed and their application to hydrogen molecules
demonstrated (H2).^{18)} Effcient single photon sources,^{19)}
effcient photon number detectors, and integrated photonic
quantum circuits are important research areas for the
continual advancement of this field.

The works reported here were supported in part by
Core Research for Evolutionary Science and Technology
(CREST) of the Japan Science and Technology Corporation
(JST), Grant-in-Aids from the Japan Society for the
Promotion of Science (JSPS), the Quantum Cybernetics
Project of JSPS, the FIRST Program by JSPS, the Project
for Developing Innovation Systems run by the Ministry
of Education, Culture, Sports, Science and Technology
(MEXT), the Global Center of Excellence program
run by MEXT, and the Research Foundation for Opto-
Science and Technology.

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**Shigeki Takeuchi** is a Professor of the Research Institute for Electronic Science (RIES) at Hokkaido
University. He received Ph. D degrees from Kyoto University in 2000. He became an associate
professor, and a professor of RIES, Hokkaido University in 2000 and 2007. His interest lies in
understanding and controlling the nature of light quanta (photons).