Testing the effects
of gravity
and motion on
entanglement
Ivette Fuentes- University of Vienna
Relativistic quantum information and metrology
Current Postdocs
Luis Cortés Barbado
Richard Howl
Former Postdocs
Antony Lee
Andrzej Dragan
Carlos Sabín
Mehdi Ahmadi
Angela White
Jason Doukas
Current PhD students
Tupac Bravo Ibarra
Karishma Hathlia
Maximilian Lock
Dominik Šafránek
Jan Kohlrus
Ana Lucia Baez
Former Msc students
Richard Howl
Former PhD students
Nicolai Friis
Antony Lee
project student
Kevin Truong
Bartosz Regula
entanglement
entangled pair
The quantum era is
reaching relativistic regimes
• Practical aspects (necessary corrections)
• Innovation: new technologies
• Fundamental aspects
Real world experiments
Real world experiments
144 km
Space-QUEST project: distribute
entanglement from the International
Space Station.
X.-S. Ma, et. al Nature 2012
First quantum transmission sent through space
2600 km
Vallone et. al arXiv:1406.4051 2014
Future experiments
Space-QUEST project:
distribute entanglement from
the International Space Station.
Space Optical Clock project
QUANTUS: quantum gases in
microgravity
STE-QUEST: Space-Time
Explorer and Quantum
Equivalence Principle Space
Test
Relativistic regimes
GPS:
At these regimes relativity
kicks in!
What are the effects of gravity and motion on
quantum properties?
On earth: Dynamical Casimir effect
Delsing’s group at Chalmers University
Relativistic effects in
quantum fields
Currently:
Experiments on
implementing
gates through
relativistic motion
Testing QFT: particle creation by a moving
boundary
Precision
NIST Pair of Aluminum Atomic Clocks Reveal
Einstein's Relativity at a Personal Scale
One clock keeps time to within 1 second in
about 3.7 billion years
Quantum field theory in curved spacetime
• Classical spacetime+ quantum fields
• Incorporates Lorentz invariance
• Combines quantum mechanics with
relativity at scales reachable by
near-future experiments
Quantum communications go relativistic
Friis, Lee, Truong, Sabin, Solano, Johansson & Fuentes PRL 2013
Bruschi, Ralph, Fuentes, Jennewein & Razavi, PRD 2014
observable effects in
satellite-based quantum
communications
teleportation and cryptography are affected by motion
corrections: local rotations and trip planning
Earth-based demonstration: superconducting circuits
Future relativistic quantum technologies
Deepen our understanding of
the overlap of quantum theory
and relativity
Can relativistic effects help?
Gravimeters, sensors, clocks
Our understanding of nature
QUANTUM PHYSICS
RELATIVITY
Space-based experiments
Bruschi, Sabin, White, Baccetti, Oi, Fuentes
Highlight of New J. Phys. (2014)
Effects of gravity and
motion on
entanglement
Quantum field theory basics
determinant of the metric
field equation: Klein Gordon
solutions
creation and annihilation operators
metric
2. The transformation
Bogoliubov transformations
BEAM SPLITTER
Θ
Θ
(transmittivity)
(squeezing)
PARAMETRIC
AMPLIFIER
Examples: change of observer, space-time dynamics, moving cavity
EXAMPLE: UNRUH EFFECT
Minkowski spacetime in 1+1 dimensions
(flat spacetime = no gravity!)
Timelike killing observers
(a) inertial observer
(b) uniformly accelerated observers
trace
k’
k’
Bob
Rob
thermal state
Similar effect in black holes: Hawking radiation
acceleration r
Rob is causally disconnected from region II
acceleration r
Alice and Rob
Fuentes-Schuller, Mann PRL 2005
Adesso, Fuentes-S, Ericsson PRA 2007
k’
k
k’
Rob Alice Bob
more realistic states:
Entanglement • observer-dependent
• degrades with acceleration , vanishes for ∞ acceleration
quantifying entanglement
PURE STATES:
Schmidt basis
Measure of entanglement:
DEFS:
use density matrix
reduced density matrix (subsystem A)
von Neumann entropy
DEF:
entanglement between A and B
MIXED STATES
=
no analogue to Schmidt decomposition
(entropy no longer quantifies entanglement)
but necessary condition for separability (no negative eigenvalues) suggest to use
negativity
=
sum of negative eigenvalues of
covariance matrix formalism
covariance matrix: information about the state
symplectic matrix: evolution
computable measures of
bipartite and multipartite
entanglement, metrology
techniques
Alice falls into a black hole
Fuentes-S, Mann PRL 2005
Adesso & Fuentes-S 2007
horizon
BH
horizon
BH
1+1
“3+1”
Alice
Rob
Entanglement
Classical correlations
part of Rindler space
degraded for
escaping observers
Lost entanglement
multipartite entanglement
between modes
inside and outside the BH
Entanglement cosmology
Ball, Fuentes-S, Schuller PLA 2006
toy model
expansion rate
expansion factor
no particle
interpretation
• calculate entanglement
asymptotic past
unentangled
state
“History of the universe
encoded in entanglement”
asymptotic future
• excitingly, can solve for
•Entanglement between localized systems
•cavities
•detectors
•localized wave-packets
•gravity effects on quantum properties
•earth-based and space-based experiments
entanglement generated
Friis, Bruschi, Louko & Fuentes PRD 2012
Friis and Fuentes invited at JMO 2012
Bruschi, Louko, Faccio & Fuentes 2012
general trajectories
continuous motion
including circular acceleration
initial separable squeezed state
entanglement: negativity
Effects of motion on entanglement
Bruschi, Fuentes & Louko PRD (R) 2011
Bogoliubov transformations
acceleration
Entanglement gets degraded
length
BEC in spacetime
mean field
quantum fluctuations
effective metric
Fagnocchi et. al NJP 2010
Visser & Molina-Paris NJP 2010
real spacetime metric
analogue metric
Space-based experiments
Bruschi, Sabin, White, Baccetti, Oi, Fuentes
Highlight of New J. Phys. (2014)
Effects of gravity and
motion on
entanglement
Application: phononic accelerometer
Example
Ahmadi, Bruschi, Sabin, Adesso, Fuentes, Nature Sci. Rep. 2014
Bruschi, Louko, Faccio & Fuentes NJP 2013
Particle creation resonance
acceleration
inertial-uniformly accelerated
3. The output
Update on experimental results
Superconducting circuits
Bruschi, Sabin, Kok, Johansson, Delsing & Fuentes SR 2016
simulate field inside a cavity which travels in a
spaceship using superconducting circuits
Coming soon: First experimental results
with Rupert Ursin’s group in Vienna
entanglement under uniform acceleration in flat space
entanglement in the space-time of the earth
Future experiments: non-uniform acceleration
Satellite-based experiments
Conclusions
Acceleration and and gravity have
observable effects on entanglement
Experiments promise to help deepen our
understanding of the overlap of quantum
theory and
relativity