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第73行： − + + + − 在量子力学中，一个量子比特的一般量子态可以用它的两个标准正交基(或基向量)的线性叠加来表示。这些向量通常表示为+ + + 第96行：
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第141行： − + − [/math > .它们是用传统的 dirac ー或“ bra-ket”ー符号写成的; < math > | 0 rangle </math > 和 < math > | 1 rangle </math > 分别读作 ket 0和 ket 1。这两个标准正交基状态，< math > { | 0 rangle，| 1 rangle } </math > ，一起称为计算基础，被称为跨越量子位元的二维线性向量(Hilbert)空间。+ + + + + 第187行：
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→Bit versus qubit
对于一个由 n 个分量组成的系统，在经典物理学中对其状态的完整描述只需要 n 位，而在量子物理学中，它需要2<sup>n</sup> 复数。
对于一个由 n 个分量组成的系统，在经典物理学中对其状态的完整描述只需要 n 位，而在量子物理学中，它需要2<sup>n</sup> 复数。
==Bit versus qubit==
==Bit versus qubit比特与量子比特==
A [[binary digit]], characterized as 0 and 1, is used to represent information in classical computers.
A [[binary digit]], characterized as 0 and 1, is used to represent information in classical computers.
一个[[二进制数字]]，以0和1为特征，在经典计算机中用来表示信息。
When averaged over both of its states (0,1), a binary digit can represent up to one bit of [[Shannon information]], where a [[bit]] is the basic unit of [[information theory|information]].
When averaged over both of its states (0,1), a binary digit can represent up to one bit of [[Shannon information]], where a [[bit]] is the basic unit of [[information theory|information]].
当在两个状态（0,1）上取平均值时，一个二进制数字最多可以表示[[香农信息]]的一位，其中[[位]]是[[信息论|信息]]的基本单位。
In quantum mechanics, the general quantum state of a qubit can be represented by a linear superposition of its two orthonormal basis states (or basis vectors). These vectors are usually denoted as
In quantum mechanics, the general quantum state of a qubit can be represented by a linear superposition of its two orthonormal basis states (or basis vectors). These vectors are usually denoted as
在量子力学中，一个量子位的一般量子态可以用它的两个正交基态（或基向量）的线性叠加来表示。这些向量通常表示为
However, in this article, the word bit is synonymous with a binary digit.
However, in this article, the word bit is synonymous with a binary digit.
然而，在本文中，单词bit是二进制数字的同义词。
<math>| 0 \rangle = \bigl[\begin{smallmatrix}
<math>| 0 \rangle = \bigl[\begin{smallmatrix}
In classical computer technologies, a ''processed'' bit is implemented by one of two levels of low [[Direct Current|DC]] [[voltage]], and whilst switching from one of these two levels to the other, a so-called [[forbidden zone]] must be passed as fast as possible, as electrical voltage cannot change from one level to another ''instantaneously''.
In classical computer technologies, a ''processed'' bit is implemented by one of two levels of low [[Direct Current|DC]] [[voltage]], and whilst switching from one of these two levels to the other, a so-called [[forbidden zone]] must be passed as fast as possible, as electrical voltage cannot change from one level to another ''instantaneously''.
在经典的计算机技术中，一个“已处理”位是由两个低电平[[直流电|直流]][[电压]]中的一个实现的，当从这两个电平中的一个切换到另一个时，一个所谓的[[禁区]]必须尽可能快地通过，因为电压不能“瞬间”从一个电平切换到另一个电平。
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There are two possible outcomes for the measurement of a qubit—usually taken to have the value "0" and "1", like a bit or binary digit. However, whereas the state of a bit can only be either 0 or 1, the general state of a qubit according to quantum mechanics can be a [[Quantum superposition|coherent superposition]] of both.<ref name="nielsen2010">{{cite book |last1=Nielsen |first1=Michael A. | last2=Chuang | first2=Isaac L. |date=2010 |title=Quantum Computation and Quantum Information |publisher=[[Cambridge University Press]] |page=[https://archive.org/details/quantumcomputati00niel_993/page/n46 13] |isbn=978-1-107-00217-3 |title-link=Quantum Computation and Quantum Information (book) }}</ref> Moreover, whereas a measurement of a classical bit would not disturb its state, a measurement of a qubit would destroy its coherence and irrevocably disturb the superposition state. It is possible to fully encode one bit in one qubit. However, a qubit can hold more information, e.g. up to two bits using [[superdense coding]].
There are two possible outcomes for the measurement of a qubit—usually taken to have the value "0" and "1", like a bit or binary digit. However, whereas the state of a bit can only be either 0 or 1, the general state of a qubit according to quantum mechanics can be a [[Quantum superposition|coherent superposition]] of both.<ref name="nielsen2010">{{cite book |last1=Nielsen |first1=Michael A. | last2=Chuang | first2=Isaac L. |date=2010 |title=Quantum Computation and Quantum Information |publisher=[[Cambridge University Press]] |page=[https://archive.org/details/quantumcomputati00niel_993/page/n46 13] |isbn=978-1-107-00217-3 |title-link=Quantum Computation and Quantum Information (book) }}</ref> Moreover, whereas a measurement of a classical bit would not disturb its state, a measurement of a qubit would destroy its coherence and irrevocably disturb the superposition state. It is possible to fully encode one bit in one qubit. However, a qubit can hold more information, e.g. up to two bits using [[superdense coding]].
量子位的测量有两种可能的结果，通常取值“0”和“1”，如位或二进制数字。然而，尽管比特的状态只能是0或1，但根据量子力学，量子比特的一般状态可以是[[量子叠加|相干叠加]]；两者兼有。<ref name="nielsen2010">{{cite book |last1=Nielsen |first1=Michael A. | last2=Chuang | first2=Isaac L. |date=2010 |title=Quantum Computation and Quantum Information |publisher=[[Cambridge University Press]] |page=[https://archive.org/details/quantumcomputati00niel_993/page/n46 13] |isbn=978-1-107-00217-3 |title-link=Quantum Computation and Quantum Information (book) }}</ref> 此外，虽然对经典比特的测量不会干扰其状态，但对量子比特的测量会破坏其相干性并不可撤销地干扰叠加状态。在一个量子位中完全编码一位是可能的。然而，一个量子位可以容纳更多的信息，例如，使用[[超密集编码]]最多两位。
and
and
For a system of ''n'' components, a complete description of its state in classical physics requires only ''n'' bits, whereas in quantum physics it requires 2<sup>''n''</sup> complex numbers.<ref name="shor1996">{{cite journal|last1=Shor|first1=Peter|title=Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer∗|journal=SIAM Journal on Computing|volume=26|issue=5|pages=1484–1509|year=1997|arxiv=quant-ph/9508027|bibcode=1995quant.ph..8027S|doi=10.1137/S0097539795293172|s2cid=2337707}}</ref>
For a system of ''n'' components, a complete description of its state in classical physics requires only ''n'' bits, whereas in quantum physics it requires 2<sup>''n''</sup> complex numbers.<ref name="shor1996">{{cite journal|last1=Shor|first1=Peter|title=Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer∗|journal=SIAM Journal on Computing|volume=26|issue=5|pages=1484–1509|year=1997|arxiv=quant-ph/9508027|bibcode=1995quant.ph..8027S|doi=10.1137/S0097539795293172|s2cid=2337707}}</ref>
对于一个由“n”个分量组成的系统，在经典物理中对其状态的完整描述只需要“n”个位，而在量子物理中则需要2个复数。<ref name="shor1996">{{cite journal|last1=Shor|first1=Peter|title=Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer∗|journal=SIAM Journal on Computing|volume=26|issue=5|pages=1484–1509|year=1997|arxiv=quant-ph/9508027|bibcode=1995quant.ph..8027S|doi=10.1137/S0097539795293172|s2cid=2337707}}</ref>
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==Standard representation==
==Standard representation标准表示法==
\end{smallmatrix}\bigr]</math>. They are written in the conventional Dirac—or "bra–ket"—notation; the <math>| 0 \rangle </math> and <math>| 1 \rangle </math> are pronounced "ket 0" and "ket 1", respectively. These two orthonormal basis states, <math>\{|0\rangle,|1\rangle\}</math>, together called the computational basis, are said to span the two-dimensional linear vector (Hilbert) space of the qubit.
\end{smallmatrix}\bigr]</math>. They are written in the conventional Dirac—or "bra–ket"—notation; the <math>| 0 \rangle </math> and <math>| 1 \rangle </math> are pronounced "ket 0" and "ket 1", respectively. These two orthonormal basis states, <math>\{|0\rangle,|1\rangle\}</math>, together called the computational basis, are said to span the two-dimensional linear vector (Hilbert) space of the qubit.
它们是用传统的狄拉克或“bra–ket”符号写成的；<math>| 0\rangle</math>和<math>| 1\rangle</math>分别发音为“ket 0”和“ket 1”。这两个正交基态，<math>\{| 0\rangle，| 1\rangle\}</math>，统称为计算基，被称为跨越量子位的二维线性向量（Hilbert）空间。
In quantum mechanics, the general [[quantum state]] of a qubit can be represented by a linear superposition of its two [[Orthonormality|orthonormal]] [[Basis (linear algebra)|basis]] states (or basis [[vector space|vector]]s). These vectors are usually denoted as
In quantum mechanics, the general [[quantum state]] of a qubit can be represented by a linear superposition of its two [[Orthonormality|orthonormal]] [[Basis (linear algebra)|basis]] states (or basis [[vector space|vector]]s). These vectors are usually denoted as
在量子力学中，一个量子位的一般[[量子态]]可以用它的两个[[正交|正交]][[基（线性代数）|基]]态（或基[[向量空间|向量]]态）的线性叠加来表示。这些向量通常表示为
<math>| 0 \rangle = \bigl[\begin{smallmatrix}
<math>| 0 \rangle = \bigl[\begin{smallmatrix}
01 rangle = biggl [ begin { smallmatrix }
01 rangle = biggl [ begin { smallmatrix }
\end{smallmatrix}\bigr]</math>. They are written in the conventional [[List of things named after Paul Dirac|Dirac]]—or [[bra–ket notation|"bra–ket"]]—notation; the <math>| 0 \rangle </math> and <math>| 1 \rangle </math> are pronounced "ket 0" and "ket 1", respectively. These two orthonormal basis states, <math>\{|0\rangle,|1\rangle\}</math>, together called the computational basis, are said to span the two-dimensional [[Hilbert space|linear vector (Hilbert) space]] of the qubit.
\end{smallmatrix}\bigr]</math>. They are written in the conventional [[List of things named after Paul Dirac|Dirac]]—or [[bra–ket notation|"bra–ket"]]—notation; the <math>| 0 \rangle </math> and <math>| 1 \rangle </math> are pronounced "ket 0" and "ket 1", respectively. These two orthonormal basis states, <math>\{|0\rangle,|1\rangle\}</math>, together called the computational basis, are said to span the two-dimensional [[Hilbert space|linear vector (Hilbert) space]] of the quit.
它们写在传统的[[List of things named after Paul Dirac | Dirac]]-或[[bra–ket notation |“bra–ket”]]-符号中；<math>| 0\rangle</math>和<math>| 1\rangle</math>分别发音为“ket 0”和“ket 1”。这两个正交基态，<math>\{| 0\rangle，| 1\rangle\}</math>，统称为计算基态，被称为跨越量子位的二维[[Hilbert空间|线性向量（Hilbert）空间]]。
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Qubit basis states can also be combined to form product basis states. For example, two qubits could be represented in a four-dimensional linear vector space spanned by the following product basis states:
Qubit basis states can also be combined to form product basis states. For example, two qubits could be represented in a four-dimensional linear vector space spanned by the following product basis states:
量子位元基态也可以组合成乘积基态。例如，两个量子位可以在由以下积基态所跨越的四维线性向量空间中表示：
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