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

• Practical aspects (necessary corrections) • Innovation: new technologies • Fundamental aspects

The quantum era is reaching relativistic regimes

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

GPS:

At these regimes relativity kicks in!

Relativistic regimes

What are the effects of gravity and motion on quantum properties?

On earth: Dynamical Casimir effect

Testing QFT: particle creation by a moving boundary

Relativistic effects in quantum fields Currently: Experiments on implementing gates through relativistic motion

Delsing’s group at Chalmers University

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

teleportation and cryptography are affected by motion corrections: local rotations and trip planning Earth-based demonstration: superconducting circuits

Friis, Lee, Truong, Sabin, Solano, Johansson & Fuentes PRL 2013 Bruschi, Ralph, Fuentes, Jennewein & Razavi, PRD 2014

observable effects in satellite-based quantum communications

Future relativistic quantum technologies

Gravimeters, sensors, clocks Can relativistic effects help?

Deepen our understanding of the overlap of quantum theory and relativity

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

field equation: Klein Gordon

solutions

creation and annihilation operators

metric

determinant of the metric

2. T

he tr

ansf

orm

atio

n Bogoliubov transformations

Θ BEAM SPLITTER

(transmittivity) Θ

PARAMETRIC AMPLIFIER

(squeezing)

Examples: change of observer, space-time dynamics, moving cavity

EXAMPLE: UNRUH EFFECT

trace thermal state

Timelike killing observers

(a) inertial observer

(b) uniformly accelerated observers

k’

Minkowski spacetime in 1+1 dimensions (flat spacetime = no gravity!)

k’

acce

lera

tion

r

Bob Rob

Rob is causally disconnected from region II

Similar effect in black holes: Hawking radiation

Alice Bob

k k’

Rob

k’

acce

lera

tion

r

Entanglement • observer-dependent • degrades with acceleration , vanishes for ∞ acceleration

Fuentes-Schuller, Mann PRL 2005 Adesso, Fuentes-S, Ericsson PRA 2007

Alice and Rob

more realistic states:

quantifying entanglement

Measure of entanglement:

Schmidt basis PURE STATES:

no analogue to Schmidt decomposition (entropy no longer quantifies entanglement)

MIXED STATES

negativity = sum of negative eigenvalues of

use density matrix

reduced density matrix (subsystem A)

von Neumann entropy

DEFS:

DEF: entanglement between A and B =

but necessary condition for separability (no negative eigenvalues) suggest to use

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

BH

horizon

BH

horizon

“3+1” 1+1 part of Rindler space

Rob Alice

Entanglement Classical correlations

degraded for escaping observers

Lost entanglement multipartite entanglement between modes inside and outside the BH

Fuentes-S, Mann PRL 2005 Adesso & Fuentes-S 2007

Entanglement cosmology

no particle interpretation

unentangled state

“History of the universe encoded in entanglement”

toy model expansion rate

expansion factor

• calculate entanglement

asymptotic past

asymptotic future

• excitingly, can solve for

Ball, Fuentes-S, Schuller PLA 2006

•Entanglement between localized systems

•cavities

•detectors

•localized wave-packets

•gravity effects on quantum properties

•earth-based and space-based experiments

entanglement: negativity

Friis, Bruschi, Louko & Fuentes PRD 2012 Friis and Fuentes invited at JMO 2012 Bruschi, Louko, Faccio & Fuentes 2012

entanglement generated

initial separable squeezed state

general trajectories continuous motion including circular acceleration

Effects of motion on entanglement Bruschi, Fuentes & Louko PRD (R) 2011

Bogoliubov transformations

acceleration length

Entanglement gets degraded

BEC in spacetime mean field

quantum fluctuations

effective metric

real spacetime metric analogue metric

Fagnocchi et. al NJP 2010 Visser & Molina-Paris NJP 2010

Space-based experiments Bruschi, Sabin, White, Baccetti, Oi, Fuentes Highlight of New J. Phys. (2014)

Effects of gravity and motion on entanglement

Exam

ple

Application: phononic accelerometer

inertial-uniformly accelerated

acceleration

Ahmadi, Bruschi, Sabin, Adesso, Fuentes, Nature Sci. Rep. 2014

Bruschi, Louko, Faccio & Fuentes NJP 2013 Particle creation resonance

3. T

he o

utpu

t Update on experimental results

simulate field inside a cavity which travels in a spaceship using superconducting circuits

Bruschi, Sabin, Kok, Johansson, Delsing & Fuentes SR 2016

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

Acceleration and and gravity have observable effects on entanglement Experiments promise to help deepen our understanding of the overlap of quantum theory and relativity

Conclusions