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

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25%

Many paths

One path

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25%

Many paths

One path

**Past shutter changes possible futures**

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

"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

"But if the waves are there,

and all is the wave function,

isn't reality still partly there?"

-- Avi (negative variant)

"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"

"...I think I'll go work on a

different interpretation"

"The wave functions are all"

"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)

"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"

**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"

"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)

"No problem. If we place *probes in space* that *weakly interact* with passing waves, they will register a ** small trace** wherever the local

But the interaction must be

These

Local waves usually have an

-- Lev (version 2.0)

"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

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*

**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

A simple modification makes an entire bit transferrable *without local carriers*

**1**

This modified protocol with no carriers in the transmission channel has now been confirmed experimentally by our colleagues in Hefei

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)

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"

**Congratulations on 30 years of not interacting!**