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INTRASYSTEM ENTANGLEMENT GENERATOR AND UNAMBIGUOS BELL STATES DISCRIMINATOR ON CHIP

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Bell measurements, jointly projecting two qubits onto the so-called Bell basis, constitute a crucial step in many quantum computation and communication protocols, including dense coding, quantum repeaters, and teleportation-based quantum computation. A problem is the impossibility of deterministic unambiguous Bell measurements using passive linear optics, even when arbitrarily many auxiliary photons, photon-number-resolving detectors, and dynamical (condi-tionally changing) networks are available. Current proposals for going over the 50% upper bound without using experimentally challenging nonlinearities rely on using entangled photon ancilla states and a sufficiently large interferometer to combine the signal and ancilla modes. We demonstrate that the novel Multiple Rail architecture, based on the propagation of a single photon in a complex multipath optical circuit (or multiwaveguide optical circuit), provides the possibility to perform deterministic Bell measurements so to unambigu-ously discrimate all four Bell States.
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INTRASYSTEM ENTANGLEMENT GENERATOR AND UNAMBIGUOS BELL STATES
DISCRIMINATOR ON CHIP
Fabio Antonio Bovino
Department SBAI, SAPIENZA University of Rome
via Antonio Scarpa 14/16, 00161, Rome
ABSTRACT
Bell measurements, jointly projecting two qubits onto the
so-called Bell basis, constitute a crucial step in many quan-
tum computation and communication protocols, including
dense coding, quantum repeaters, and teleportation-based
quantum computation. A problem is the impossibility of
deterministic unambiguous Bell measurements using passive
linear optics, even when arbitrarily many auxiliary photons,
photon-number-resolving detectors, and dynamical (condi-
tionally changing) networks are available. Current proposals
for going over the 50% upper bound without using experi-
mentally challenging nonlinearities rely on using entangled
photon ancilla states and a sufficiently large interferometer to
combine the signal and ancilla modes. We demonstrate that
the novel Multiple Rail architecture, based on the propagation
of a single photon in a complex multipath optical circuit (or
multiwaveguide optical circuit), provides the possibility to
perform deterministic Bell measurements so to unambigu-
ously discrimate all four Bell States.
Index TermsQuantum communication, Quantum
computing, Entanglement, Quantum gates.
1. INTRODUCTION
Quantum technology is a fundamentally new way of harness-
ing Nature, it has potential for a truly revolutionary innovation
and promise the next generation of products with exciting and
astounding properties that will affect our lives profoundly.
They will have a great influence in defence, aerospace, energy
and telecommunication sectors. If this process is to continue
in the future, new, quantum technology will replace or sup-
plement what we have now. In particular, Quantum Informa-
tion Technology can support entirely new modes of informa-
tion processing based on so called quantum bits or qubits. Its
eventual impact may be as great as or greater than that of its
classical predecessor. There is almost daily progress in devel-
oping promising technologies for realizing quantum informa-
tion processing with various advantages over their classical
counterparts [1–31].
Thanks to Italian Ministry of Defence, PNRM "Contratto N.168 di Rep.
del 18-03-2016 - Repubblica Italiana "Copernico", for funding.
Photons are unsurpassed as qubits in terms of decoherence
times, mobility and achievability of high-fidelity single-qubit
operations. Thus far, entanglement experiments in optics have
been very clean, and an optical quantum processor would
obviously have an advantage in connecting to a quantum
"network" (no need to convert between stationary and fly-
ing qubits). All-optical quantum processing became feasible
when, in 2001, a breakthrough known as the KLM (Knill-
Laflamme-Milburn) scheme showed that scalable quantum
computing is possible using only single-photon sources and
detectors, linear optical circuits and quantum teleportation:
recent approaches based on cluster states or error encod-
ing made an all-optical architecture are serious contenders
for the ultimate goal of a large-scale quantum computer. This
scheme relies on quantum interference with auxiliary photons
at a beam splitter and single-photon detection to induce not-
deterministic interactions. In the past ten years, the KLM
scheme has moved from a mathematical proof of concept,
towards practical realization, with demonstrations of sim-
ple quantum algorithms and theoretical developments that
dramatically reduce the resource overhead [32].
Optical integrated circuits offer great potential for realiz-
ing previously unfeasible large-scale quantum circuits. This
flexible architecture can be used to implement key quantum-
computation elements, including universal Control N OT
(CN OT )gates based on integrated directional couplers and
reconfigurable single-qubit operations using phase controllers
based on the thermo-optical effect of silica. However, this
architecture suffers not only of the overhead of multiple
sources, detectors and ancillary qubits, but it needs to main-
tain the complete coherence between single photons in which
qubits are encoded [33–41]. Existing schemes typically
require thousands of single photon sources (photon guns),
temporal (and spectral) coherence between photon sources,
extensive adaptive switching which is experimentally chal-
lenging, noisy large quantum memories for repeat-until-
success strategies. To overcome the KLM limitation, we
introduced a novel architecture and physical representation
of a quantum machine. The idea is based on the exploita-
tion of the so called "Classical Entanglement". “Classical
Entanglement” or “Intra-System Entanglement” should not
be confused with “entanglement simulations in classical op-
7993978-1-5386-4658-8/18/$31.00 ©2019 IEEE ICASSP 2019
Fig. 1. Scheme of a Bell States generator in terms of quantum
gates.
tics”, but it denotes the occurrence of some mathematical
and physical aspects of quantum entanglement in classical
beams of light. We show the possibility to encode the whole
state space in a complex optical circuit based on Multiple
Rail (MR) architecture: any quantum state is encoded and
processed trough different single-mode waveguide [42, 43].
Therefore, it is possible to realize quantum devices that show
deterministic and not probabilistic behavior, as quantum en-
tanglers, Bell measurements and teleportation schemes. Bell
measurements, jointly projecting two qubits onto the so-
called Bell basis, constitute a crucial step in many quantum
computation and communication protocols, including dense
coding, quantum repeaters, and teleportation-based quantum
computation. A Multiple Rail (MR) architecture, based on
the propagation of a coherent pulse in a complex multipath
optical circuit, provides unambiguous discrimination of all
four Bell States and deterministic teleportation.
2. BELL STATE SYNTHESIZER
The deep ways that quantum information differs from clas-
sical information involve the properties, implications and
uses of quantum entanglement. Entanglement has always
been a key issue in the ongoing debate about foundation
and interpretation of Quantum Mechanics, since Einstein
and Schroedinger expressed their deep disatisfaction about
this astoneshing part of quantum theory. Untill 1965, when
Bell published the famous inequality by which he demon-
strated that EPR’s (Einnstein, Podolsky and Rosen) local and
realistic vision of world was wrong, all discussions about
entanglement were theoretical, sometimes metatheoretical or
metaphysical. Nowadays entanglement is a physical resource
and a fondamental key for quantum information and in par-
ticular for quantum computing, then it is fundamental task
the engineering of entanglement syntetizer. The logic opera-
tion sequence that provides entanglement syntesis by starting
from two independent qubits is obtained by the circuit shown
in Fig.(1). The circuit represents the product of Hadamard
gate (H) applied to the first qubit followed by CN OT , with
the first bit as the source and the second bit as the target. It is
straightforward to see that this circuit transforms the standard
basis to the entangled basis
j00i=) j00i=1
p2(j00i+j11i) =
+;
j01i=) j01i=1
p2(j01i+j10i) =
+;
j10i=) j10i=1
p2(j00ij11i) =
;
j11i=) j11 i=1
p2(j01ij10i) =
:(1)
Similarly, we can invert the transformation by running the cir-
cuit backwards (since both CN OT and Hsquare to the iden-
tity); if we apply the inverted circuit to an entangled state,
and then measure both bits, we can learn the value of both
the phase bit and the parity bit. Of course, Hacts on only
one of the qubits; the “nonlocal” part of our circuit is the
CN OT gate – this is the operation that establishes or re-
moves entanglement. We can rewrite the product CN OT
(HI)in CN OT S W AP (IH)S W AP so that we
can implement the Bell Synthesizer by the physical circuit
described in Fig.(2). The Mach-Zehnder (MZ) interferome-
ter is the building block for the engeneering of the quantum
gates. Consider two orthogonal optical modes represented by
the annihilation operators ^aand ^
band the vacuum modes j0ia
and j0ib. We define our logical qubits as j0i= ^ayj00iand
j1i=^
byj00i.
Fig. 2. Physical implementation of a Bell State Synthesizer.
7994
Fig. 3. Optical, Electronics and mechanics integration of InP
Entangler. Note the gold contacts for MZ voltage setting and
control, and thermistor to thermalize the integrated structure.
That is, single photon occupation of one mode represents
a logical zero, whilst single photon occupation of the other
represents a logical one. Let us consider a Mach-Zehnder in-
terferometer. The first beam splitter prepares a superposition
of possible paths, the phase shifters inside modify quantum
phases in different paths and the second beam-splitter com-
bines all the paths together. By setting the first phase-shifter
we are able to control the amplitude probability to obtain the
single photon in the first or in the second path. A second phase
shifter can control the phase factor between the two amplitude
probabilities, so that the M Z interferometer is a universal
single qubit gate. The extension of the "dual rail" configu-
ration to a "multiple rail" one provides two- qubit gates, as
Hadamard,SW AP and C N OT gate.
3. PHYSICAL IMPLEMENTATION OF THE BELL
STATE SYNTHESIZER
We used the InP technology to engineering the Bell States
generator. In Fig.(3) the scheme of the physical chip is
showed. In particular, it is possible to appreciate the smart
input-output system so that a single bundle of eight fiber pro-
vides the injection and the extraction of light pulses. The gold
metalized contacts on the top of waveguides provide to set the
voltage for the fine control of each Mach Zehnder interfer-
ometer. To implement the XPauli gates we used symmetric
MZ (i.e without differential path length between upper and
lower arms) which are in cross state by default. To implement
HADAM ARD gate, in order to change the M Z initial state
from cross operation to 50=50 operation, a differential path
length equivalent to a =2phase shift has been introduced.
The length increment is 118nm assuming an effective refrac-
tive index neff = 3:28@1:55m wavelength. This length
increment is in the order of the process resolution (about
200nm) making the initial state uncertain. The InP Chip
is integrated in a custom packaging which provides the ex-
ternal electrical connectorization for each quantum gate and
thermalization thanks to a thermistor. The electrical control
of each Mach Zender is performed by a Custom Polarizing
Board. A mechanical structure provides the assembly of all
single components. The metallic holed base also gives a
strong support to protect the bundle of Polarizing Maintain-
ing fibers. After the packaging and the integration the Mach
Zehnders of each quantum gate were characterized in terms
of Voltage-Current curve and in terms of optical response.
4. EXPERIMENTAL BELL STATE GENERATION
AND UNAMBIGUOS DISCRIMINATION WITHOUT
ANCILLA
In the experiment, an attenuated coherent state with an
avarage number of photon = 0:1was injected in the first
waveguide of the Bell State generator. The first waveguide
corresponds to the state j00i, so that at the output of the
chip we have the excitation of the Bell state j+i, that is
the quantum superposition of the state j00iand j11iwith the
same probability amplitude. Now we introduce the operation
represented in Fig.(4): the Bell state generator creates an
entangled state, which is subjected to a total swap gate with
a supplementary phase shifting. After the operation a Bell
measurement is applied on the new state. In the physical
implementation the Polarization Maintaining output fibers
are short-cutted and an external phase modulator is inserted
to control the relative phase of the states j00iand j11i. The
phase shifter provides the state j00i+ei' j11i=p2that is
re-injected in the chip and measured by four single photon
detectors (ID Quantique), one detector for each input (output)
fiber. In particular, only the first and the third waveguides,
corresponding to the states j00iand j10i;will be excited, and
the following phase dependent response will be obtained:
out = cos2'
2j00i+isin2'
2j10i:
Fig. 4. The Bell state generator create an entangled state,
which experiments a total swap gate and a supplemetary
phase shifting. Then a Bell measurement provides the dis-
crimination of the new state..
7995
Fig. 5. Discrimination of entangled states by a Bell measure-
ment. By changing the voltage applied to the external phase-
shifter the state +is transformed in the state . The chip
provides unambiguos Bell measurements with a visibility bet-
ter than 99%. The error bar is smaller of the dot dimension.
The experimental results are shown in Fig.(5). The visi-
bility of the curves, defined as (Max Min)=(M ax +M in),
is better than 99%, and provides a clear discrimination of the
states. The outputs corresponding to the state j01iand j11i
are negligeble and not reported in Fig.(5). A Conventional
Bell measurement, based on a 50=50 Beam Splitter and two
Polarizing Beam Splitters, can not discrimante between +
and state [20]:
5. CONCLUSIONS
We demonstrated the operation of Bell state synthesizer on
chip based on InP technology. With the same chip an un-
ambiguos Bell measurement was performed with very high
visibility. The high level experiment and the results show that
more complex circuits can be built with the same architec-
ture and technology to perform more complicated logic opera-
tions. Finally, the introduction of the multiple rail architecture
could make a practical quantum computer a reality. The in-
vestigation has started from the designing of building blocks,
and it follows up with their engeneering and final integration
in a first pototype of reconfigurable quantum processor able
to perform complex operations.
The architecture is efficient and can be extended to high
number of qubits. The important difference with other
schemes of quantum computing is that we do not need to
repeat the calculation a lot of times with “single photon
states”, but we just perform the operation in a single shot by
using a pulse with a lot of photons. In fact, with this archi-
tecture each photon of the pulse will interact only with itself,
and it will contribute to the total result of the computation in a
single shot. This feature will provide the use of off-the-shelf
integrated laser systems and classical detectors (not single
photon detectors): then the engineering, and the realization
of large circuits able to perform very complex calculations is
possible with the current technology. As an example, to com-
plete an elaboration with a “conventional” optical quantum
computer we need to repeat calculation for 1 sec with a clock
of 1GHz; with this new architecture we can perform one cal-
culation per clock’s cycle: we can perform 1 Giga operation
per second. An other amazing property of this architecture is
the possibility of reconfiguration of the gate: it realizes a sort
of quantum FPGA. This demonstrates that, in principle, the
same device can solve different kind of computations.
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Lasers and LEDs have a statistical distribution in the number of photons emitted within a given time interval. Applications exploiting the quantum properties of light require sources for which either individual photons, or pairs, are generated in a regulated stream. Here we review recent research on single-photon sources based on the emission of a single semiconductor quantum dot. In just a few years remarkable progress has been made in generating indistinguishable single photons and entangled-photon pairs using such structures. This suggests that it may be possible to realize compact, robust, LED-like semiconductor devices for quantum light generation © 2010 Nature Publishing Group, a division of Macmillan Publishers Limited and published by World Scientific Publishing Co. under licence. All Rights Reserved.
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Quantum computers promise to exceed the computational efficiency of ordinary classical machines because quantum algorithms allow the execution of certain tasks in fewer steps. But practical implementation of these machines poses a formidable challenge. Here I present a scheme for implementing a quantum-mechanical computer. Information is encoded onto the nuclear spins of donor atoms in doped silicon electronic devices. Logical operations on individual spins are performed using externally applied electric fields, and spin measurements are made using currents of spin-polarized electrons. The realization of such a computer is dependent on future refinements of conventional silicon electronics.
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We study the use of entanglement purification for quantum communication over long distances. For distances much longer than the coherence length of a corresponding noisy quantum channel, the fidelity of transmission is usually so low that standard purification methods are not applicable. It is possible, however, to divide the channel into shorter segments that are purified separately and then connected by the method of entanglement swapping. This method can be much more efficient than schemes based on quantum error correction, as it makes explicit use of two-way classical communication. An important question is how the noise, introduced by imperfect local operations (that constitute the protocols of purification and the entanglement swapping), accumulates in such a compound channel, and how it can be kept below a certain noise level. To treat this problem, we first study the applicability and the efficiency of entanglement purification protocols in the situation of imperfect local operations. We then present a scheme that allows entanglement purification over arbitrary long channels and tolerates errors on the percent level. It requires a polynomial overhead in time, and an overhead in local resources that grows only logarithmically with the length of the channel.
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Matter waves inside periodic potentials are well known from solid-state physics, where electrons interacting with a crystal lattice are considered. Atomic Bose-Einstein condensates inside light-induced periodic potentials (optical lattices) share many features with electrons in solids, but also with light waves in nonlinear materials and other nonlinear systems. Generally, atom-atom interactions in Bose-Einstein condensates lead to rich and interesting nonlinear effects. Furthermore, the experimental control over the parameters of the periodic potential and the condensate make it possible to enter regimes inaccessible in other systems. In this review, an introduction to the physics of ultracold bosonic atoms in optical lattices is given and an overview of the theoretical and experimental advances to date.
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Quantum teleportation enables one to transfer any arbitrary quantum state from one particle to another. In the experiments presented here we use parametric down-conversion to produce entangled photon pairs and two-photon interferometry to perform the necessary projection onto entangled states, the so-called Bell state analysis. This allows us to teleport the polarization state from one photon to the other and to entangle photons that have never interacted with one another in the past.