Quantum Superposition Emanuel Di Nardo
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Quantum SuperpositionEmanuel Di Nardo
Overview
In the quantum world all is uncertainEach element exists in all its possible states...at same time
Positive is also Negative, Up is also Down On is also Off
But when we bring it in the "classic" world all became certain
Overview
● States
● Entanglement
● Wave function
● Superposition
● Computing
Briefly
Each quantum “element” is a wave and exists a relationship between its pure states.
It permits the existence of these states at the same time (superposition).
Briefly
Two or more wave functions describe the same quantum state.
If each state can be characterized by each wave function it is a linear combination of them.
It is a property of Schrödinger equation
States
A state can be represented by a vector in the Hilbert space
Exist two categories for a state:a. Pure;b. Mixed;
States
Values of states are described by the vector eigenvalues (also called eigenstates)
A system with a linear combination of eigenstates can have only a probabilistic measurement of each state
States
From this uncertainty we can derive the
Heisenberg uncertainty relation
...We are able to know only one state at a time
States
The uncertainty can be extended to a case of more particles such as two electron on an orbit
Due the relationship between them a knowledge of the former automatically give us the latterPhenomena well-known as entanglement
Entanglement
Quantum states in a system are linked each others. In a two particles system this linkage can’t be broken also they are infinitely far
Entanglement
Information is transferred immediately without waiting time
Opposite to the classical physics rules (Einstein Special Relativity)
Entanglement
EPR Paradox and the violation of locality principle.
Should we interpret it as the existence of unknown hidden variables?
Bell’s theorem
Entanglement
Bell demonstrates that local principle produces a violation of reality principle
Indeed there is a violation of Bell’s inequality and the result gives more reliability to
“Copenhagen interpretation”
Wave function
We described that a state can be characterized by a wave function in the space and time
It is a peculiar wave in the complex space that gives us a probabilistic amplitude, or better, the density distribution of a state.
Wave function
It contains all the information about the entire system
So it is possible to derive all properties of a particle from it
Wave function
From these properties it is possible to declare:
“It is the projection of a quantum state on the eigenstates base space”
that is described in the Schrödinger equation
Wave function
The Schrödinger equation:
It is the time evolution of a state in a systemWe can compare it to Newton’ second lawin mechanics, but with a linear partial differential equation as shown above.
Superposition
At the end how could we define “superposition”?
Informally...It is the overlap of the quantum laws already shown:
“Superposition of quantum laws”
Superposition
Formally…Quantum systems can be in two or more simultaneous different states.
“Schrödinger’s cat”
Superposition
“Schrödinger’s cat”
Superposition
More formally when a combination of solutions of its states is a solution of a linear equation it obeys to superposition law.
If three state vectors resolve then
Superposition
It is possible to measure the effect of a wave on a quantum object. At a specific wave frequency, the material progressively shifts from one state to another, and that is detected by Rabi oscillations.
Superposition
When a particle interacts with the environment, “after a time”, it collapses in the measured state
This principle is called decoherence
Superposition
The video shows how “imagine” a
superposition and its measurements
before decoherence
happens
Quantum Computing
Quantum physics is used also in computing
The powerful of quantum computing is on superposition
It uses qubit instead of bit
Quantum Computing
Qubit is a linear combination of 0 and 1:
Elaborations by qubits is performed simultaneously on 0 and 1. It is opposite to bit.
Quantum Computing
This capacity outperform the classical computing
Using more qubits we get a qubit register. More qubit means more calculus power.
Quantum Computing
In plain words we obtain a “natural parallel (super)computing“
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