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                What is a qubit? Just as a classical bit has a state – either 0 or 1 – a qubit also has a state.
Two possible states for a qubit are the states |0> and |1>, which as you might guess correspond to the states 0 and 1 for a classical bit. Notation like ‘|>’ is called the Dirac notation, and it’s the standard notation for states in quantum mechanics.


The difference between bits and qubits is that a qubit can be in a state other than |0> or|1>.
It is also possible to form linear combinations of states, often called superpositions: |ψ> = α|0> + β|1> with the numbers α and β being  complex numbers.
Put another way, the state of a qubit is a vector in a two-dimensional complex vector space. The special states |0> and |1> are known as computational basis states, and form an orthonormal basis for this vector space.

Another difference is that the value of the bit can be determined at any time: computers do this all the time when they retrieve the contents of their memory, to check whether it is in state 0 or 1. On the contrary, we cannot examine a qubit to determine its quantum state, that is, the values of α and β. Instead, quantum mechanics tells us that we can only acquire much more restricted information about the quantum state. When we measure a qubit we get either the result 0, with probability|α|2, or the result 1, with probability|β|2, with |α|2 +|β|2 = 1, since the probabilities must sum to one.

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"The essence of my theory is precisely that no independent properties are attributed to space on its own. It can be put jokingly this way. If I allow all things to vanish from the world, then following Newton, the Galilean inertial space remains; following my interpretation, however, nothing remains.."
Letter from A.Einstein to Karl Schwarzschild - Berlin, 9 January 1916

"Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the 'old one'. I, at any rate, am convinced that He is not playing at dice."
Einstein to Max Born, letter 52, 4th december 1926

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