Can We Use Quantum Entanglement To Communicate Faster Than The Speed Of Light?
The quest for superluminal communication
You can read this post on Medium.
Nothing travels faster than the speed of light. We all know that. OK, it is what we believe today. It is a theory — Einstein's theory of relativity. A pretty good one, to be fair.
If something is faster than the speed of light, we say it is superluminal. Einstein tells us that time stops if you travel at the speed of light. And, time would go backward if you traveled faster than the speed of light.
Time travels lead to contradictions. You could go back in time and prevent some history-changing events from happening. And, in math and physics, if something leads to contradictions, we conclude it is false.
But, our beliefs and even the best theories must be subject to scrutiny. I mean, have you ever seen how fast light is?
My everyday experiences suggest that light is not that fast at all. When I turn on the TV, I first hear the sound, then somewhat later, I see the pictures.
When I watch TV, I eventually end up with Star Trek or Star Wars. But, guess what, the Enterprise has a warp drive, and the Millennium Falcon has a hyperdrive. So the speed of light doesn't seem to be a big issue.
Enough with the anecdotes and the science fiction. What about quantum entanglement?
Entanglement describes an extremely strong correlation between particles. Entangled particles remain perfectly correlated even if separated by great distances.
For instance, we have two quantum bits (qubits). We put one into an equal state of superposition using the Hadamard gate. If we measured it, we'd see it as either 0 or 1, each with a probability of 50%. But we don't measure it — because measuring a qubit collapses its state of superposition. Instead, we entangle it with another qubit using the controlled NOT-gate (CX).
from qiskit import QuantumCircuit, Aer, execute
from qiskit.visualization import plot_histogram
qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0,1)
qc.measure_all()
results = execute(qc,Aer.get_backend('qasm_simulator'), shots=10000).result().get_counts()
plot_histogram(results)
No matter how often we run this quantum circuit, we always see that the values of both qubits match. For example, the following figure depicts the results of running the circuit 10,000 times.
OK, they are perfectly correlated, so what?
If we measure one of two entangled qubits, the other instantly changes its state to account for the value we measured. The emphasis is on instantly.
When we say the state of the particle changes instantly, we mean instantly. Not after a few seconds. Not after a tiny fraction of a second. But instantly.
The state change does not rely on any signal being sent from one particle to the other—the change of state results from the fact that both particles share a state.
So, maybe we can exploit this phenomenon for superluminal communication — that is communication faster than the speed of light.
Let's meet Alice and Bob. They are the superstars of physical thought experiments. Alice and Bob are on opposite sides of the universe. Yet, each of the two has one of a pair of entangled qubits. Moreover, they both know that their qubits are perfectly correlated.
So, when Alice looks at her qubit, she gets a random result. Either 0 or 1. Moreover, Bob's qubit instantaneously jumps into a state that corresponds to whatever Alice saw. When he looks at his qubit, he gets the same random outcome.
Suppose instead that Bob measures his qubit before Alice does. Now, Alice's qubit changes its state to correspond to Bob's. But, when Alice measures her qubit, what does she now get? Again, it is a random outcome.
While Alice and Bob acquire correlated random numbers, there's no information transmission from one party to another. It appears as if they looked at their shared past. They can conclude that the respective other knows the same. But shared knowledge is no communication.
They're not giving up so quickly, though. They try something different. Alice manipulates her qubit before measuring it. She applies another Hadamard gate on it.
The following code creates such a situation.
from qiskit import QuantumCircuit, Aer, execute, QuantumRegister, ClassicalRegister
from qiskit.visualization import plot_histogram
qr = QuantumRegister(2)
cr = ClassicalRegister(1)
qc = QuantumCircuit(qr,cr)
qc.h(0)
qc.cx(0,1)
qc.h(0)
qc.measure(qr[0], cr[0])
results = execute(qc,Aer.get_backend('qasm_simulator'), shots=10000).result().get_counts()
plot_histogram(results)
The results — from Alice's perspective — haven't changed at all.
She still sees a random outcome.
So, let's look at what Bob sees.
Bob's outcome didn't change either.
We only can see what changed if we look at the overall quantum system. When Alice and Bob look at the outcomes together — that means they communicate their results — they see that Alice's action changed how the two qubits correlate to each other.
Of course, Alice can do many other things with her qubit than applying another Hadamard gate. But nothing she does changes what Bob sees. Only when they look at their qubits together can they see an effect.
So, even though two qubits can be entangled over vast distances, we can't use them for instantaneous communication!
No matter what Alice and Bob do with their qubits, they can't send information to each other. Only if they re-entangle or unentangle their qubits can they exchange information.
So, for instance, Alice wants to send Bob a 1. If she applies a NOT-gate (X) on her qubit and they apply another entangling gate (CX) on both of their qubits, then we can see that Bob's outcome changed.
from qiskit import QuantumCircuit, Aer, execute, QuantumRegister, ClassicalRegister
from qiskit.visualization import plot_histogram
qr = QuantumRegister(2)
cr = ClassicalRegister(1)
qc = QuantumCircuit(qr,cr)
qc.h(0)
qc.cx(0,1)
qc.x(0)
qc.cx(0,1)
qc.measure(qr[1], cr[0])
results = execute(qc,Aer.get_backend('qasm_simulator'), shots=10000).result().get_counts()
plot_histogram(results)
The following figure depicts what Bob sees.
So, to communicate with each other, we need to entangle qubits — or particles. But, the entangling action is a kind of communication itself. So, Einstein's theory of relativity holds — so far.
We can't use entanglement for superluminal communication. And, this is a good thing because we wouldn't need to travel physically to change the course of history. If we could tell our earlier selves the outcomes of certain actions, I'd bet it had dramatic changes.