# Bit software; qubit hardware

Quantum information is the information of the state of a quantum system.

— Wikipedia on Quantum information

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\displaystyle{\begin{aligned} |a|^2 + |b|^2 &= 1 \\ \end{aligned}}

For a system with the superposition state

\displaystyle{\begin{aligned} | \psi \rangle &= a~| \psi_L \rangle + b~| \psi_R \rangle \\ \end{aligned}},

quantum information is the information of the superposition coefficients $\displaystyle{a}$ and $\displaystyle{b}$.

— Me@2022-03-03 07:11:10 PM

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A quantum state is not a state. Instead, it is a property of a physical system. It is a statistical property of a variable of an experimental setup.

— Me@2022-02-20 06:44:32 AM

— Me@2022-03-03 07:53:09 PM

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Quantum information does not exist in physical spacetime. Instead, it exists in the experiment-setup designer’s time. In this sense, it exists in meta-physical time.

It is not information that exists in a physical system. Instead, it is the information about the physical system.

— Me@2022-02-20 11:27:31 PM

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Quantum computers are implemented by using qubits, encoding information in the system property (aka quantum state) itself. A qubit is stored in the property of the system, not just arrangements of particles of the system as in a classical media.

Classical information is stored in microscopic setups, such as the arrangements of microscopic particles, of a system.

Quantum information is stored in macroscopic setups, such as the magnetic field direction for maintaining an electron spin’s superposition state, of a system.

— Me@2022-02-20 11:30:37 PM

— Me@2022-03-03 10:29:53 PM

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quantum information ~ a system property

conservation of quantum information ~ a property of those system properties

— Me@2022-02-20 8:13 AM

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You can locate a piece of classical information in a physical system/information media.

You cannot locate a piece of quantum information in a physical system, because quantum information is stored in the statistical properties of that physical system, which includes objects and experimental processes.

You have to do a large number of identical experiments in order to extract those statistical patterns.

For example, for a fair dice, the numbers on its faces, its weight, etc. are classical information. However, the probability value of getting (such as) 2, which is $\displaystyle{\frac{1}{6}}$, is quantum information; it does not exist in physical spacetime.

— Me@2022-02-20 11:46:40 PM

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“State” and “property” have identical meanings except that:

State is physical. It exists in physical time. In other words, a system's state changes with time.

 

Property is mathematical. It is timeless. In other words, a system's property does not change. (If you insist on changing a system's property, that system will become, actually, another system.)

For example, “having two wheels” is a bicycle’s property; but the speed is a state, not a property of that bicycle.

— Me@2022-02-20 06:44:32 AM

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state ~ the easiest-to-change property of a system

— Me@2022-02-21 08:52:34 PM

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Classical information is stored in the states of a system (information media).

Quantum information is stored in the properties of a system.

— Me@2022-02-21 08:52:34 PM

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A qubit might for instance physically be a photon in a linear optical quantum computer, an ion in a trapped ion quantum computer, or it might be a large collection of atoms as in a superconducting quantum computer. Regardless of the physical implementation, the limits and features of qubits implied by quantum information theory hold as all these systems are mathematically described by the same apparatus of density matrices over the complex numbers.

— Wikipedia on Quantum information

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Note that while a bit is a software object, a qubit is a physical object.

— Me@2022-02-23 05:19:02 PM

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