Download m NV Centers in Quantum Information Technology ! De-Coherence Protection &

m
NV Centers in Quantum
Information Technology !
De-Coherence Protection &
Teleportation!
Brennan MacDonald-de Neeve, Florian Ott, and Leo Spiegel!
The NV Center!
•  Point Defect in Diamond!
•  Interesting Physics in negatively
charged state NV-1!
NC
•  Total electron spin S=1!
• 
14N
Nuclear Spin I=1!
VC
Di Vincenzo Criteria!
1.  Well-defined qubits!
2.  Initialization!
3.  tcoherence > tgate operation!
4.  Universal set of quantum gates!
5.  Qubit specific read-out!
6.  Convert from stationary to mobile
qubit!
7.  Faithful transmission!
Relevant Ground State Energy
Structure!
B0 = 500 G!
|1⟩e!
2.9 MHz!
1.4 GHz!
5.1 MHz!
|0⟩e!
|é⟩N!
|ê⟩N!
Relevant Ground State Energy
Structure!
B0 = 500 G!
|1⟩e!
Electron Spin Modulation:!
MW Rabi Driving at 1.4 GHz
with driving strength 40 MHz!
2.9 MHz!
1.4 GHz!
5.1 MHz!
|0⟩e!
|é⟩N!
|ê⟩N!
Relevant Ground State Energy
Structure!
B0 = 500 G!
|1⟩e!
Electron Spin Modulation:!
MW Rabi Driving at 1.4 GHz
with Rabi frequency at 40 MHz!
2.9 MHz!
•  2 qubit register!
•  qubit modulation via
Rabi driving!
•  entanglement through
hyperfine interaction!
1.4 GHz!
5.1 MHz!
|0⟩e!
|é⟩N!
Electron Spin Modulation:!
RF Rabi Driving at 2.9 MHz
with Rabi frequency at 30 kHz!
|ê⟩N!
Spin Initialization from Excited State!
1)  Electron Spin using LASER
pumping!
532 nm!
S=0!
mS=0!
mS=+/–1!
N. B. Manson et al. Phys. Rev. B 47, 104303 (2006). !
Spin Initialization from Excited State!
1)  Electron Spin using
LASER pumping!
2)  Nuclear Spin using LASER
pumping at B = 500 G!
532 nm!
S=0!
mS=0!
mS=+/–1!
N. B. Manson et al. Phys. Rev. B 47, 104303 (2006). !
V. Jacques et al. Phys. Rev. Lett. 102, 057403 (2011). !
FIG.
2 (color online). Nuclear-spin
polarization mechanism.
deterministic quantum tele- the other spin state (Fig. 1d). This optical pumping mechanism allows
re attractive candidates for high-fidelity spin state initialization24,27: from the data in Fig. 1d, we
1 single-shot detecing, their
estimate a preparation error into the mS 5 0 ground state of
Hanson
3–6
d qubits . Here we demon- 0.3 6 0.1%, which is a drastic reduction of the 11 6 3% preparation
nt of a multi-spin quantum
b
te system by implementing a
150
ts states with mS 5 0. A typical
es originally developed in
10
s we study, is shown in Fig. 1c
y read-out of the electronic
N
Vvacancy
B). Under
resonant
excitation
PL
Spectrum
of opticallyV excited
1
centre
in diamond,
A1
decays
with
time
owing
to
a
NV Center:!
o three nearby
nuclear spin
NVA A
NV A
NV
0.1
ates
that we
induces
shelving into
Ex
versely,
can distinguish
!
al pumping
mechanism
allows
le
shot by mapping
it onto,
• 
m
=
0
is
bright
5,8 data
: from
1d,
we (Ex)!
S in Fig.
MW
onic
spinthe
. Finally,
we show
10 μm
he
mS 5
of (A )!
mS = ±1
•  0 mground
= -1state
is dark
demonstrate
initialization,
mS = 0
S
1
nread-out
of the 11
6
3%
preparation
in a single experic
d
chniques suitable for exten115
b
1,000
pave the way for a test of
100
NV A
Ex
NV A
and the implementation of
80 A1
110
800
Ex
60
ion protocols.
40
600
vacancy centre (NV) in dia-A
1
20
A system for investigating
Atate
15
0
Ex
400
ent spin coherence9–12 with a
0 1 2 3 4 5
10
e, the host nitrogen nuclear
200
A1
5
MW isotopic
I 5 1) and nearby
±1
mS =the
0
0
erfine interactions
with
mS = 0
0
10
20 30 40 50
0 2 4 6 8 10 12 14
g development of few-spin
Time (μs)
Laser detuning (GHz)
ested as building blocks for
,000
mputation18100
and distributed Figure 1 | Resonant excitation and electronic spin preparation of a
Ex
NV A
nitrogen–vacancy centre. a, Scanning electron microscope image of a solid
A1
ications
require
80 high-fidelity
800
immersion lens representative of those used in the experiments (for details, see
60 spins. There
ment of multiple
Supplementary Information). The overlaid sketch shows the substitutional
40 few-spin sysnt
control over
600
nitrogen and the adjacent vacancy that form the NV. Inset, scanning confocal
20
stsL.for
the simultaneous
pre- 477,
Robledo
et
al.
Nature
574–578
(2011).!
microscope
image
of NV A (logarithmic colour scale). kct, 1,000 counts.
0
f400
multi-spin registers,
0 1 2 3which
4 5 b, Energy levels used to prepare and read out the NV’s electronic spin (S 5 1 in
Read-Out!
Intensity (kct s–1)
Intensity
(kct s–1)
Intensity
Fraction of outco
deterministic quantum tele- the other spin state (Fig. 1d). This optical pumping mechanism allows
re attractive candidates for high-fidelity spin state initialization24,27: (ii)
p Fig.
= 1 1d, we
from the data in
0.2
1
ing, their single-shot detec- estimate a preparation error into the mS 5 0 ground state of
Hanson
d qubits3–6. Here we demon- 0.3 6 0.1%, which is a drastic reduction of the 11 6 3% preparation
nt of a multi-spin quantum
0.6
a
b
mI = {0, +1}
te system by implementing
150
ts states with mS 5 0. A typical
es originally developed in
preparation
0.4
10
s we study, is shown in Fig. 1c
y read-out of the electronic
N
Vvacancy
B). Under
resonant
excitation
p=1
PL
Spectrum
of opticallyV excited
1
centre
in diamond,
(iii)
A1
with Center:!
time
owing
to a
0.2
NV
o decays
three nearby
nuclear
spin
NVA A
NV A
NV
0.1
ates
that we
induces
shelving into
Ex
versely,
can distinguish
2.874
2.876 2.878 2.880 2.882
!
al
pumping
mechanism
allows
le shot by mapping it onto,
Microwave
frequency (GHz)
• 5,8. data
mS in
= Fig.
0weisshow
bright
: from
1d,
we (Ex)!
MW
onic
spinthe
Finally,
10 μm
he
mS 5
state
of (A )!
mS = ±1
•  0 mground
=
-1
is
dark
demonstrate
initialization,
mS = 0
S
1
c
Ø 
Can
also
be used to read out
nread-out
of the 11
6
3%
preparation
in a single experic
d
mI by using a CNOT gate:!NV B
chniques suitable for exten115
b
1,000
mI = –1
pave the way for a test of
NV A
0.8 Ex 100
NV A
and the implementation of
80 A1
110
800
Ex
N
60
ion protocols.
40
0.6
600
vacancy centre (NV) in dia-A
1
20
A system for investigating
Atate
15
0
Ex
400
ent spin coherence9–12 with a
0 |0〉
1 2 3 4 5
10
0.4
e, the host nitrogen nuclear
200
A1
5
MW isotopic
I 5 1) and nearby
±1
mS =the
0.20
0
erfine interactions
with
mS = 0
0
10
20 30 40 50
0 2 4 6 8 10 12 14
p=2
g development of few-spin
Time (μs)
Laser detuning (GHz)
ested as building blocks for
0.0
,000
mputation18100
and distributed Figure 1 | Resonant excitation and electronic spin
0 preparation
5 of a 10
15
Ex
NV
A
nitrogen–vacancy
centre.
a,
Scanning
electron
microscope
image
of
a
solid
A1
ications
require
high-fidelity
80
800
Counts
in N see
= 3 repetitions
immersion lens representative of those used in the experiments
(for details,
60 spins. There
ment of multiple
Supplementary Information). The overlaid sketch shows the substitutional
40 few-spin sysnt
control over
600
nitrogen
the adjacent
vacancy
that form the NV.
scanning confocal
20
Figure
3 and
Nuclear
spin
preparation
andInset,
read-out.
a, Measurement-based
stsL.for
the simultaneous
preRobledo
et
al.
Nature
477,
574–578
(2011).!
microscope
image
of
NV
A
(logarithmic
colour
scale).
kct,
1,000
counts.
0
400
14
f multi-spin registers,
0 1 2 3which
4 5
Read-Out!
Intensity (kct s–1)
Fraction of occurrences
Intensity
(kct s–1)
Intensity
|
spin.
Earth’s
ambient
magnetic field of
preparation
of used
a single
b, Energy levels
to prepareN
andnuclear
read out the
NV’s In
electronic
spin (S
5 1 in
Decoherence!
Decoherence is caused by all the undesired interactions of a quantum
state with its environment which shortens its lifetime.!
D
h spins!
1
free evolution
)
P
0
τ
0
100
(π/2)x
(π/2)x
114 B (G)
G. de Lange et al. Science 330, 60–63 (2010).!
0
0.2
0.4
τ (µs)
0.6
0.8
uantum control pulses and NV centers appear as
y level diagrams of the NV center electron spin
agnetic field splits the NV spin triplet electronic
d by the spin sublevels mS = 0 (labeled j0〉) and
NV1. For the pulsed experiments, the same Rabi
probed using Ramsey interference. Solid line is
Decoherence!
Decoherence is caused by all the undesired interactions of a quantum
state with its environment which shortens its lifetime.!
D
h spins!
1
free evolution
)
P
0
τ
0
100
(π/2)x
(π/2)x
114 B (G)
G. de Lange et al. Science 330, 60–63 (2010).!
0
0.2
0.4
τ (µs)
0.6
0.8
uantum control pulses and NV centers appear as
Ø  Dynamic
decoupling:
flipping of the qubit spin state to
y level diagrams
of the NV
center electronPeriodic
spin
agnetic fieldaverage
splits the NV
spinthe
triplet
electronic
out
interactions
with the environment.!
d by the spin sublevels mS = 0 (labeled j0〉) and
Viola
et al.experiments,
Phys. Rev Athe
58,same
2733Rabi
(1998). !
NV1. ForL.the
pulsed
probed using Ramsey interference. Solid line is
ownloaded from http://rsta.royalsocietypublishing.org/ on May 20, 2015
Dynamical Decoupling!
4751
Review. Robust dynamical decoupling
(a)
(b)
y
Sx
Sz
(c)
–x
Sz
Sy
t
t
y
y
t/2
(d)
Sz
y
Cn–1
t
y
x
Cn–1
Hahn Echo!
N
t/2
x
Cn–1 Cn–1
Carr–Purcell–Meiboom–Gill!
yN
XY-4!
mical decoupling pulse sequences. The empty and solid rectangles represent 90◦ and
A. and
M. Souza
et al. Phil.
R. of
Soc.
370, 4748–4769
(2012).
!
pectively,
N represents
theTrans.
number
iterations
of the cycle.
(a) Initial
state
Hahn spin-echo sequence. (c) CPMG sequence. (d) CDD sequence of order N ,
d C = t.
and decoupling. We experimentally demonstrate
g a two-qubit register in diamond operating at room
uantum tomography reveals that the qubits involved
ation are protected as accurately as idle qubits. We
rover’s quantum search algorithm1, and achieve
ticularly promising for the
tures12–22, in which differen
spins, superconducting res
form different functions. D
to be decoupled at its own
Decoherence in multi-qubit gates!
1)
couple to
a Qubits
Unprotected
each
other but
also
quantum
gate
to environment!
e–
n
b
c
Protected
storage:
Decoupling
e–
n
Protected
quantum gate
e–
d
NV cen
C
C
N
V
C
n
C
e
|1↑〉
Environment
Environment
|1
Environment
Nuclear drivin
Gate
Decoupling
Gate + decoupling
z
N. van der Sar et al. Nature 484, 82–86 (2012). !
x
y
R X( )
14
and
tion decoupling.
and decoupling.
We experimentally
We experimentally
demonstrate
demonstrate
ticularly
ticularly
promising
promising
for thef
12–22
gusing
a two-qubit
a two-qubit
register
register
in diamond
in diamond
operating
operating
at room
at room
, in
which
, in which
differen
d
tures12–22
tures
uantum
re. Quantum
tomography
tomography
reveals
reveals
that the
that
qubits
the qubits
involved
involved
spins,spins,
superconducting
superconducti
res
ation
operation
are protected
are protected
as accurately
as accurately
as idleasqubits.
idle qubits.
We We
form different
form different
functions.
functiD
1
, and1, achieve
and achieve
to be decoupled
to be decoupled
at its own
at its
rm
rover’s
Grover’s
quantum
quantum
searchsearch
algorithm
algorithm
Decoherence in multi-qubit gates!
2)b Qubits
decoupled
d
c
c
Protected
Protected
Protected
Protected
from
each
other and quantum
storage:
storage:
quantum
gate gate
Decoupling
Decoupling
environment!
1)
to b
a Qubits
a couple
Unprotected
Unprotected
each
otherquantum
but
alsogate
quantum
gate
to environment!
e–
e–
n
n
e–
e–
n
n
e–
e–
n
dNV cenN
C
C
N
C
n
e
V
C
e
|1↑〉
Environment
Environment
Environment
Environment
C
|1|1
Environment
Environment
Nuclear
Nuclea
drivin
Gate Gate
decoupling
+ decoupling
Decoupling
Decoupling Gate +Gate
z
N. van der Sar et al. Nature 484, 82–86 (2012). !
x
y
z
y
x R X( )
14
1
operation
and
tion decoupling.
and decoupling.
and decoupling.
We experimentally
We experimentally
We experimentally
demonstrate
demonstrate
demonstrate
ticularly
ticularly
promising
ticularly
promising
for
promi
thef
12–22 12–22 12–22
ggates
using
a two-qubit
using
a two-qubit
a register
two-qubit
register
in diamond
register
in diamond
inoperating
diamond
operating
at
operating
room
at room
at
room
, intures
which
, in which
differen
, in wh
d
tures
tures
uantum
erature.
re. Quantum
tomography
Quantum
tomography
tomography
reveals
reveals
thatreveals
the
that
qubits
the
that
qubits
involved
the qubits
involved
involved
spins,spins,
superconducting
spins,
superconducti
supercon
res
ation
operation
gate are
operation
protected
are protected
are as
protected
accurately
as accurately
as accurately
as idleasqubits.
idleasqubits.
idle
Wequbits.
We
formWe
different
form form
different
functions.
different
functiD
f
1
, and1, achieve
and1, achieve
and to
achieve
be decoupled
to be decoupled
to be at
decoupled
its own
at its
perform
rm
rover’s
Grover’s
quantum
Grover’s
quantum
search
quantum
search
algorithm
search
algorithm
algorithm
Decoherence in multi-qubit gates!
1)
to b Protected
2)b Qubits
only
d
dNV cen
dN
a Qubits
a couple
a Unprotected
b decoupled
c
c
c3) Qubits
Protected
Protected
Unprotected
Unprotected
Protected
Protected
Protected
each
otherquantum
but
also
from
each
other
and quantum
decoupled
storage:
storage:
storage:
quantum
gate
quantum
gate gate
quantum
gate
quantum
gate from
gate
C
C
C
Decoupling
Decoupling
Decoupling
to environment!
environment!
environment!
N
e–
e–
e–n
n
e–
n
e–
e–n
n
e–
n
e–
e–n
n
C
n
e
V
C
e
e
|1↑〉
|1|1
Environment
Environment
Environment
Environment
Environment
Environment
Environment
Environment
Environment
Nuclear
Nuclea
drivinN
Gate Gate Gate
Gate +Gate
decoupling
+Gate
decoupling
+ decoupling
Decoupling
Decoupling
Decoupling
z
N. van der Sar et al. Nature 484, 82–86 (2012). !
x
y
z
y
x RX( x)
14
1
Qubit Coupling
Qubit Coupling
Generally desirable
Fast coupling for fast qubit manipulation
Qubit Coupling
Generally desirable
Fast coupling for fast qubit manipulation
But we pay a price
We also get faster coupling to the environment
”Fast” and ”Slow” Qubits
Encode Physical Qubits in:
”Fast” and ”Slow” Qubits
Encode Physical Qubits in:
I
atomic states
”Fast” and ”Slow” Qubits
Encode Physical Qubits in:
I
atomic states
I
superconducting circuits
”Fast” and ”Slow” Qubits
Encode Physical Qubits in:
I
atomic states
I
superconducting circuits
I
quantum dots
”Fast” and ”Slow” Qubits
Encode Physical Qubits in:
I
atomic states
I
superconducting circuits
I
quantum dots
I
NV centers
Two Qubit Gates
Two Qubit Gates
Difficult Scenario
Using ”fast” qubit as the control bit
Two Qubit Gates
Difficult Scenario
Using ”fast” qubit as the control bit
Question
Can we use dynamical decoupling to make a gate using the ”fast”
qubit as our control bit?
”Fast” and ”Slow” Qubits; NV Centers
”Fast” qubit: electronic spin
”Fast” and ”Slow” Qubits; NV Centers
”Fast” qubit: electronic spin
I
GHz energy splitting
”Fast” and ”Slow” Qubits; NV Centers
”Fast” qubit: electronic spin
I
GHz energy splitting
I
T2 = 3.5µs ; Rabi 2π pulse: 20ns
”Fast” and ”Slow” Qubits; NV Centers
”Fast” qubit: electronic spin
I
GHz energy splitting
I
T2 = 3.5µs ; Rabi 2π pulse: 20ns
”Slow” qubit: nuclear spin
”Fast” and ”Slow” Qubits; NV Centers
”Fast” qubit: electronic spin
I
GHz energy splitting
I
T2 = 3.5µs ; Rabi 2π pulse: 20ns
”Slow” qubit: nuclear spin
I
MHz energy splitting
”Fast” and ”Slow” Qubits; NV Centers
”Fast” qubit: electronic spin
I
GHz energy splitting
I
T2 = 3.5µs ; Rabi 2π pulse: 20ns
”Slow” qubit: nuclear spin
I
MHz energy splitting
I
T2 = 5.3ms ; Rabi 2π pulse: 30µs
Two Qubit Gates
Imagine
Two Qubit Gates
Imagine
Two Qubit Gates
Imagine
Two Qubit Gates
Imagine
Two Qubit Gates
Imagine
Two Qubit Gates
Not obvious whether this can work
Two Qubit Gates
Not obvious whether this can work
Building a 2-Qubit Gate
Electronic Spin
Nuclear Spin
mS = 0 : |0i
mS = −1 : |1i
mI = +1 : |↑i
mI = 0 : |↓i
Building a 2-Qubit Gate
Electronic Spin
Nuclear Spin
mS = 0 : |0i
mS = −1 : |1i
mI = +1 : |↑i
mI = 0 : |↓i
Building a 2-Qubit Gate
Electronic Spin
Nuclear Spin
mS = 0 : |0i
mS = −1 : |1i
mI = +1 : |↑i
mI = 0 : |↓i
Timescales ( µs )
Building a 2-Qubit Gate
Electronic Spin
Nuclear Spin
mS = 0 : |0i
mS = −1 : |1i
mI = +1 : |↑i
mI = 0 : |↓i
Timescales ( µs )
Building a 2-Qubit Gate
Electronic Spin
Nuclear Spin
mS = 0 : |0i
mS = −1 : |1i
mI = +1 : |↑i
mI = 0 : |↓i
Timescales ( µs )
Building a 2-Qubit Gate
Decoupling Pulse Sequence
τ − X − 2τ − Y − τ
Building a 2-Qubit Gate
Decoupling Pulse Sequence
τ − X − 2τ − Y − τ
Electronic Qubit in State |0i
exp( −iσ~z θ0 )exp( −iσ~x 2θ1 )exp( −iσ~z θ0 )
Building a 2-Qubit Gate
Decoupling Pulse Sequence
τ − X − 2τ − Y − τ
Electronic Qubit in State |0i
exp( −iσ~z θ0 )exp( −iσ~x 2θ1 )exp( −iσ~z θ0 )
Electronic Qubit in State |1i
exp( −iσ~x θ1 )exp( −iσ~z 2θ0 )exp( −iσ~x θ1 )
Building a 2-Qubit Gate
Special case 1
τ = (2n + 1)π/A
Building a 2-Qubit Gate
Special case 1
τ = (2n + 1)π/A
Example
Building a 2-Qubit Gate
Special case 1
τ = (2n + 1)π/A
Example
Building a 2-Qubit Gate
Special case 1
τ = (2n + 1)π/A
Example
Building a 2-Qubit Gate
Special case 2
τ = 2nπ/A
Building a 2-Qubit Gate
Special case 2
τ = 2nπ/A
Example
Building a 2-Qubit Gate
Special case 2
τ = 2nπ/A
Example
Building a 2-Qubit Gate
Special case 2
τ = 2nπ/A
Example
Building a 2-Qubit Gate
Combine special cases 1 and 2
obtain a conditional rotation gate
Experimental Results
Experimental Results
CNOT Gate ( θ = π )
Process fidelity:
Fp = Tr (χideal χ) = 83%
Experimental Results
CNOT Gate ( θ = π )
Process fidelity:
Fp = Tr (χideal χ) = 83%
For a State
|ψi = α |0i + β |1i
ρ = |ψi hψ|
Experimental Results
CNOT Gate ( θ = π )
Process fidelity:
Fp = Tr (χideal χ) = 83%
For a State
|ψi = α |0i + β |1i
ρ = |ψi hψ|
For an Operator
A = αI + βσx +P
γσy + δσz
ε(ρ) = AρA† = i,j χij Ei ρEj †
Testing Gate Robustness
Inject noise into the diamond
Reduce T2,SE from 251µs to
50µs
Testing Gate Robustness
Inject noise into the diamond
Reduce T2,SE from 251µs to
50µs
Reduce RF drive power to
nuclear spin
Gate time increases to 120µs
Testing Gate Robustness
Single qubit decoupling
apply (τ − π − τ )N
Inject noise into the diamond
Reduce T2,SE from 251µs to
50µs
Reduce RF drive power to
nuclear spin
Gate time increases to 120µs
Testing Gate Robustness
Single qubit decoupling
apply (τ − π − τ )N
Inject noise into the diamond
Reduce T2,SE from 251µs to
50µs
Reduce RF drive power to
nuclear spin
Gate time increases to 120µs
T2,N=16 = 234µs
Testing Gate Robustness
Apply CNOT
Input state
(|0i + i |1i) ⊗ |↑i
Desired output state
√
|ψi = (|0 ↑i + |1 ↓i)/ 2
Testing Gate Robustness
Apply CNOT
Input state
(|0i + i |1i) ⊗ |↑i
Desired output state
√
|ψi = (|0 ↑i + |1 ↓i)/ 2
Testing Gate Robustness
Apply CNOT
Input state
(|0i + i |1i) ⊗ |↑i
Desired output state
√
|ψi = (|0 ↑i + |1 ↓i)/ 2
State Fidelity
N = 16 : F =
reaches 96%
p
hψ| ρ |ψi
Running Grover’s Algorithm
Recall: Search Algorithm
I
Find entry in list of N elements
I
Number of oracle calls scales as
√
N
Running Grover’s Algorithm
Recall: Search Algorithm
I
Find entry in list of N elements
I
Number of oracle calls scales as
√
N
Running Grover’s Algorithm
Running Grover’s Algorithm
Final State Fidelity > 90%
Summary
Summary
I
Can construct 2-qubit gate protected from decoherence
Summary
I
Can construct 2-qubit gate protected from decoherence
I
Especially useful when control bit is ”fast”
Summary
I
Can construct 2-qubit gate protected from decoherence
I
Especially useful when control bit is ”fast”
I
Achieved process fidelities above 80%, and state fidelities
above 90% using an NV center
Summary
I
Can construct 2-qubit gate protected from decoherence
I
Especially useful when control bit is ”fast”
I
Achieved process fidelities above 80%, and state fidelities
above 90% using an NV center
I
Ultimate goal: < 10−4
Quantum
Teleportation
NV - Centers
Framework
•
Unconditional teleportation
•
•
Any state can be transmitted
Remoteness
•
Sender and reciever are reasonably separated
(3m)
Entanglement
•
Remote entanglement between NV electrons
•
Local entanglement: Spin rotation / Spin-selective
excitation
Electron-Photon
•
Local entanglement: Quantum interference photon detection
Photon-Photon
Teleporter Setup
Configuration
•
Alice NV-Center:
Transmission Qubit (1) Nuclear spin
Messenger Qubit (2) Electron spin
•
Bob NV-Center:
Reciever Qubit (3) Electron spin
•
Qubits 2 & 3 entangled in |
i23
Teleporter Setup
Initialization
•
•
Transmission Qubit initialized in |1i1
•
Projective measurement of Messenger
•
Prior to entanglement
Source State | i1 = ↵|0i1 + |1i1
•
After entanglement to avoid Dephasing
Teleporter Setup
Final State
Final State in Bell basis: •
| i1 ⌦ |
i23
1
= [|
2
+|
+|
+|
+
+
i12 (↵|1i3
|0i3 )
i12 (↵|1i3 + |0i3 )
i12 ( ↵|0i3 + |1i3 )
i12 ( ↵|0i3
|1i3 )]
Teleportation
•
Interaction between Qubits 1 and 2
•
CNOT followed by ⇡/2 Y-rotation of Transmitter
•
Projective measurements
•
Conditional Pauli-rotations
Teleportation
Interaction
•
Nuclear rotations controlled by Electron excitation
level:
Controlled ⇡/2 Y-rotation (on 1 controlled by 2)
⇡ Y-rotation (unconditional on 2)
Controlled ⇡/2 Y-rotation (on 1 controlled by 2)
•
Effectively: ⇡/2 Y-rotation (unconditional on 1)
Teleportation
Interaction
Overall state after interaction:
•
Ry1 (⇡ /2 )UCN OT (| i1 ⌦ |
1
[|11i12 (↵|1i3
|0i3 )
2
+ |01i12 (↵|1i3 + |0i3 )
+ |10i12 (↵|0i3
|1i3 )
+ |00i12 (↵|0i3 + |1i3 )]
i23 ) =
Teleportation
Interaction
Overall state after interaction:
•
Ry1 (⇡ /2 )UCN OT (| i1 ⌦ |
1
[|11i12 ( xz | i3 )
2
+ |01i12 ( x | i3 )
+ |10i12 ( z | i3 )
+ |00i12 ( | i3 )]
i23 ) =
Teleportation
Measurement
•
Direct measurement on messenger
•
Projective measurement on transmitter
•
CNOT on |0i2 electron (on reinitialized
messenger, controlled by transmitter)
Direct measurement on messenger
Teleportation
Pauli rotations
Depending on measurement:
•
|00i12
|10i12
|01i12
|11i12
7!
7
!
7
!
7
!
z
x
xz
Results
Tomography for Y on Bob’s side to confirm
alignment of reference frames
•
6 unbiased states transmitted. Fidelity 0.77
•
Outlook
Remote Entanglement
Mutliple Qubits per node:
•
•
NV Centers are a good candidate for Quantum
networks
Entanglement fidelity high enough to close
detection loophole of Bell Inequality
•