How to communicate
a QR code without a trace
Theory Team:
Justin Dressel, Lev Vaidman
Institute for Quantum Studies, Chapman University
Experimental Team:
Wei-Wei Pan, Xiao Liu, Xiao-Ye Xu, Qin-Qin Wang, Ze-Di Cheng,
Jian Wang, Zhao-Di Liu, Geng Chen, Zong-Quan Zhou,
Chuan-Feng Li, Guang-Can Guo
CAS Key Laboratory of Quantum Information, Hefei, China
30th Anniversary of Interaction-free Measurements, 2023/04/28
Interaction-free Measurement
0%
25%
Many paths
One path
Interaction-free Measurement
0%
25%
Many paths
One path
Past shutter changes possible futures
Interaction-free? Measurement
25%
"Source emits forward green wave
Shutter disturbs the configuration
The wave encodes likelihoods
holistically and does not
describe local reality for each trial
(Don't even try to think about
how each random result occurs)"
--Bohr, probably
Interaction-free? Measurement
"Source emits forward green wave
Detector emits backward red wave
Reality is where they overlap
There is no particle
All is the wave function"
-- Lev (version 1.0, world D)
Shutter blocks both waves
Future click at D retrocausally affects past trajectory
Interaction-free? Measurement
"But if the waves are there,
and all is the wave function,
isn't reality still partly there?"
-- Avi (negative variant)
Interaction-free? Measurement
"No, reality is local like a particle,
but only exists where the two
retarded and advanced waves
overlap each other in an extended spacetime region
The other waves that don't
overlap do interact with
other bits of reality, but are not reality themselves despite being part of the wavefunction,
which is the only reality"
Interaction-free? Measurement
"...I think I'll go work on a
different interpretation"
Interaction-free? Measurement
"The wave functions are all"
Interaction-free? Measurement
Interaction-free? Measurement
"Only particles are detectable and have
localized mass and charge and spin
By conservation laws, there can't be
many worlds or wave function collapse,
so there must be a way to
tell a coherent story about how this one
reality evolves to get the results we see
To gain understanding, look at dynamics
of the measurable properties
The dynamics are nonlocal in space and are determined by both past and future boundary conditions, with uncertainty in the present that protects causality"
--Yakir (unique, following destiny)
Interaction-free? Measurement
"See? Nonlocal equations of motion for properties
The particle is aware of the shutter remotely
while still taking one path locally
There is no wave function in reality"
Interaction-free? Measurement
Heresy!
"See? Nonlocal equations of motion for properties
The particle is aware of the shutter remotely
while still taking one path locally
There is no wave function in reality"
Interaction-free? Measurement
"The relevant definition is much simpler:
Reality is what we can verify in experiment.
Everything else is just words and math."
-- Pragmatic experimentalists (lab frame, with funding)
Interaction-free? Measurement
"No problem. If we place probes in space that weakly interact with passing waves, they will register a small trace wherever the local wave actually went
But the interaction must be weak to not disturb the rest of the setup, like a test charge in freshman electromagnetism
These traces will be found exactly where forward and backward waves overlap
Local waves usually have an environment that they weakly interact with, so will leave small traces everywhere they go"
-- Lev (version 2.0)
Interaction-free! Measurement
"What is weakly measured in such a post-selected setup will exactly correspond to the weak values of the particle properties, which will indeed reveal where it has been"
A weak measurement experiment should give results consistent with both pictures:
retrocausal wave dynamics,
or nonlocal particle dynamics
A particle leaves no first-order trace along the shutter path when later found at D
\hat{U}_\epsilon = e^{-i\epsilon\hat{\Pi}}
\displaystyle \langle D | \hat{U}_\epsilon|\psi\rangle = \frac{\langle D | e^{-i\epsilon\hat{\Pi}}|\psi\rangle}{\langle D | \psi \rangle} \langle D | \psi \rangle = \left[\sum_{n=0}^\infty (-i\epsilon)^n \Pi_w^{(n)}\right] \langle D | \psi \rangle
|\psi\rangle
\langle D |
Prepare
Interaction
Post-select
\displaystyle \Pi_w^{(n)} \equiv \frac{\langle D | \hat{\Pi}^n | \psi \rangle}{\langle D | \psi \rangle}
"Modular Value"
Multiplicative amplitude correction from interaction
nth order "Weak Value"
Amplitude
Weak values as evolution traces
When \(\epsilon\) is sufficiently small, the 1st order weak value is the small trace of the interaction:
\displaystyle (1 - i\epsilon\,\Pi_w)\langle D | \psi \rangle
Interaction-free? Communication
Avi can send information to Lev
at detector D using the shutter
This information has no local carrier that leaves a first-order trace
If \(\epsilon^2\) is below the noise floor, then information is transferred without any apparent carriers in the transmission channel
Interaction-free? Communication
However, when Avi does not use the shutter, there is a trace in the interferometer arm, so only a half-bit is transferred without carriers
Interaction-free! Communication
A simple modification makes an entire bit transferrable without local carriers
1
Interaction-free! Communication
This modified protocol with no carriers in the transmission channel has now been confirmed experimentally by our colleagues in Hefei
Interaction-free! Communication
Interaction-free! Communication
Interaction-free! Communication
Interaction-free! Communication
QR Code of Heifei Lab: 21025 bits in raster scanned array
Sent by repeated attempts until first successful heralded click for each sequential bit
Error rates: 2.3% for 1, 10% for 0 (no redundant encoding used here)
Interaction-free! Communication
Bit 1
Bit 0
Calibration
"See? Just as I said, no first-order trace where the forward and backward waves overlap"
-- Lev (version 2.1)
"You mean negaparticles"
The End?
Congratulations on 30 years of not interacting!
How to communicate a QR code without a trace
By Justin Dressel
How to communicate a QR code without a trace
Invited talk for the 30th Anniversary Conference on Interaction Free Measurement, Chapman University, 2023/04/27
