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--- en:quantum_registers [2021/01/12 21:06]
jaddawyn
+++ en:quantum_registers [2021/01/16 10:29] (current)
@@ Line 1: / Line 1: @@
 ====== Quantum registers ======
-Playing with one qubit is fun, but not sufficient to run algorithms. You we'll see that later: we need a lot than 1 qubit for interesting purposes.\\
+Playing with one qubit is fun, but not sufficient to run algorithms. You we'll see that later: we need many more than 1 qubit for interesting purposes.\\
-When more than one qubit is in the game, we use quantum registers containing several.\\
+When more than one qubit are in the game, we use quantum registers containing several.\\
 \\
 Let's considers the following experiment:
 {{ :en:intrication.png |}}
-At the left we have a source of qubits XXX
+(1) At the left we have a source of qubits (or quantum particles) emitted by a single source in two separate direction. At the right we have two detectors facing the trajectory of qubits.\\
+(2) Each qubit is traveling from the source to the detector in a superposed state between |0> and |1> before being read |0> or |1>.
+\\
+\\
+We could imagine that the behavior with two qubits is the same than one qubit separated from the another. But we have two qubits emitted by the same source, and it changes everything because in this case they are **entangled**. \\
+That means that the result of the top qubit is linked to the result of the bottom qubit. Their probabilities are linked one to the other.\\
+\\
+If we would have two sources with two detectors, each qubit would be in the state seen in the previous chapter:\\
+;#;
+<m 13>delim{|}{psi}{}> = alpha delim{|}{0}{}> + beta delim{|}{1}{}></m>
+;#;
+But since we have a single source emitting two entangled qubits we have amplitudes on all possible result:
+;#;
+<m 13>delim{|}{psi}{}> = alpha delim{|}{00}{}> + beta delim{|}{01}{}> + gamma delim{|}{10}{}> + delta delim{|}{11}{}></m>
+;#;
+And because Greek letters does not help to know the corresponding state we use only alpha with the state in little for amplitudes:
+;#;
+<m 13>delim{|}{psi}{}> = alpha_00 delim{|}{00}{}> + alpha_01 delim{|}{01}{}> + alpha_10 delim{|}{10}{}> + alpha_11 delim{|}{11}{}></m>
+;#;
+And the associated matrix is:
+;#;
+<m 13>delim{[}{matrix{4}{1}{alpha_00 alpha_01 alpha_10 alpha_11}}{]}</m>
+;#;
+\\
+\\
+This is crazy isn't it? When they are detected, qubits are in different places in space, yet there is a link between the result read by detectors. However during their travel from source to detectors (at the speed of light) each of them are in a superposed states:all states at the time or |0> and |1> at the same time - you choose.\\
+\\
+This is one of the great mystery of quantum mechanics. John Stewart Bell proposed three possibilities:
+  * particles communicates during the travel,
+  * particles shares information when leaving the source,
+  * particles should not be considered as two separate objects but as one.
+In 80's, it has been demonstrated that the two particles does not share the information at their start. Therefore they must exchange the information when measured by detectors. But that would mean the information is transmitted faster than light. What is impossible according to Einstein's special relativity.\\
+\\
+This mystery has not been solved and we still don't know how particles share amplitudes of probabilities. We will come back on this mystery later because it is fascinating. It will also leads us to another big notion of quantum physics: **quantum teleportation**.
+\\
+\\
+XXX Donner un exemple d'amplitudes avec 2 qubits. XXX
 <columns 100% 50% ->
@@ Line 12: / Line 48: @@
 <newcolumn>
 ;;#
-Next: XXX
+Next: [[en:single_qubit_gates|Single qubit gates]]
 ;;#
 </columns>

Quantum leap

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