The bit is the most basic unit of information in classical computing and classical information in quantum computation and quantum information. A quantum bit, or qubit, plays a similar role. The qubit actually means and compare its properties to those of classical bits. We're going to describe qubits as mathematical objects with certain specific properties.
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| Qubits in Multiple State |
It is true that qubits, like bits, are realized as actual physical systems. The beauty of treating qubits as abstract entities allow scientists to construct a general theory of quantum computation and quantum information independent of any particular physical system.
What is then a qubit?
Just as a classical bit has a state, either zero or one, a qubit also has a state. Two possible states for a qubit are the states ket zero and ket one, which are similar to the states zero and one of a classical bit. This weird notation is called the Dirac notation and is a standard notation for representing a state in quantum mechanics.
Let's now explore the fundamental difference between a bit and a qubit. It is always possible to examine a bit to determine if it is in state zero or one. For example, computers do this all the time when they retrieve the contents of their memory. Rather remarkably, it is not possible to examine a qubit to determine its quantum state. For learning the quantum state of a qubit, we need to learn the values of alpha and beta. However, quantum mechanics tell us that we can only acquire much more restricted information about the quantum state. When we measure a qubit, we get either the result cat zero with probability alpha squared or the result cat one with probability beta squared.
So from a single measurement, we will not be able to learn the values of both alpha and beta. Thus, in general, a qubit state is a unit vector in a two dimensional complex vector space, and measurement collapses it into one of the bases. Qubit's ability to be in superposition states runs counter to our common sense. A classical bit is like a coin, either heads or tails up. By contrast, a qubit can exist in a continuum of states between cat zero and cat one until it is observed. Let us emphasize again that when a qubit is measured, it only ever gives zero or one as the measurement result. Probabilistically, for example, a qubit can be in the state which, when measured, gives the result 00:50 percent of the time and the result 150 percent of the time. This state, which is in an equal superposition of cat zero and cat one, is quite an important quantum state and is sometimes denoted by ket plus.
Although qubits seem strange, they are in fact real. Experiments extensively validate their existence and behavior, and they can be realized using a wide range of physical systems. In order to get a sense of how a qubit can be realized, let's see some of the ways it can occur as
the two different polarizations of a photon as the alignment of a nuclear spin in a uniform magnetic field, as two states of an electron orbiting a single atom. In the atom model, the electron can exist in either the so called ground or excited states, which we'll refer to as ket zero and cat one, respectively. By shining light on the atom with appropriate energy and for an appropriate length of time, it is possible to move the electron from the ket zero state to the ket one state and vice versa. But more interestingly, by reducing the time we shine the light, an electron initially in the state of ket zero, can be moved halfway between ket zero and ket one into the ket plus state.
Historically, a great deal of attention has been given to the meaning or interpretation that might be attached to superposition states and to the inherently probabilistic nature of observations on quantum systems. However, for almost all practical purposes related to quantum information processing, it is not necessary to concern with such discussions.
How much information is represented by a qubit.
Paradoxically, we can do infinite binary expansion of values alpha and beta, so in principle, it could store infinite information. However, this conclusion turns out to be misleading because of the behavior of a qubit when observed, recall that measurement of a qubit will give only either zero or one. Furthermore, measurement changes the state of a qubit, collapsing it from its superposition of cat zero and cat one to the specific state consistent with the measurement result.
For example, if the measurement of cat plus gives zero, then the state of the qubit after measurement will be cat zero.
Why does this type of collapse occur?
Nobody knows until now. We simply accept it as a law of nature and include it as one of the fundamental postulates of quantum mechanics. What is relevant for our purposes is that from a single measurement, one obtains only a single bit of information about the state of the qubit, thus resolving the apparent paradox. Nevertheless, there is something conceptually important going on here. When nature performs an operation on a closed quantum system of qubits without performing any measurement, she does keep track of all the infinite parameters of alpha and beta. Even though that information is hidden from us, nature conceals a great deal of hidden information, and even more interestingly, the potential amount of this extra information grows exponentially with the number of qubits.
Understanding this hidden quantum information lies at the heart of what makes quantum mechanics a powerful tool for information processing and the future of computation. In this article we focused on what a qubit means, what we can do with it, and what we can. Furthermore, much of the discussion was on a single qubit. In the coming videos, we will explain what happens if we have more than one qubit entanglement.
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