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===Bloch Sphere=== | ===Bloch Sphere=== | ||
In quantum mechanics, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit). The Bloch sphere is a unit 2-sphere, with antipodal points corresponding to a pair of mutually orthogonal state vectors. The north and south poles of the Bloch sphere are typically chosen to correspond to the standard basis vectors <math>|0\rangle</math>, <math>|1\rangle</math> respectively, which in turn might correspond e.g. to the spin-up and spin-down states of an electron. This choice is arbitrary, however. The points on the surface of the sphere correspond to the pure states of the system, whereas the interior points correspond to the mixed states. | In quantum mechanics, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit). The Bloch sphere is a unit 2-sphere, with antipodal points corresponding to a pair of mutually orthogonal state vectors. The north and south poles of the Bloch sphere are typically chosen to correspond to the standard basis vectors <math>|0\rangle</math>, <math>|1\rangle</math> respectively, which in turn might correspond e.g. to the spin-up and spin-down states of an electron. This choice is arbitrary, however. The points on the surface of the sphere correspond to the pure states of the system, whereas the interior points correspond to the mixed states. | ||
===Quantum One Way | ===Quantum One Way Function=== | ||
Based on the fundamental principles of quantum mechanics, QOWF was proposed by Gottesman and Chuang [https://arxiv.org/abs/quant-ph/0105032] and its definition is presented as follows.</br> | Based on the fundamental principles of quantum mechanics, QOWF was proposed by Gottesman and Chuang [https://arxiv.org/abs/quant-ph/0105032] and its definition is presented as follows.</br> | ||
'''Definition 1''' Let k, |f_k\rangle be classical bits string of length <math>L_1</math>, quantum state of <math>L_2</math> qubits, respectively. A function <math>f : k\rightarrow |f_k\rangle</math>, where <math>|f_k\rangle</math> satisfies <math>\langle f_k|f_{k'}\le\delta < 1</math> for k\ne k', is called a QOWF under physical mechanics if | '''Definition 1''' Let k, <math>|f_k\rangle</math> be classical bits string of length <math>L_1</math>, quantum state of <math>L_2</math> qubits, respectively. A function <math>f : k\rightarrow |f_k\rangle</math>, where <math>|f_k\rangle</math> satisfies <math>\langle f_k|f_{k'}\rangle\le\delta < 1</math> for k\ne k', is called a QOWF under physical mechanics if | ||
(1) Easy to compute: The mapping <math>f : k\rightarrow |f_k\rangle</math> is easy to compute by a quantum polynomial-time algorithm. | (1) Easy to compute: The mapping <math>f : k\rightarrow |f_k\rangle</math> is easy to compute by a quantum polynomial-time algorithm. | ||
(2) Hard to invert: Given <math>|f_k\rangle</math>, it is impossible to invert k by virtue of fundamental quantum information theory. | (2) Hard to invert: Given <math>|f_k\rangle</math>, it is impossible to invert k by virtue of fundamental quantum information theory. | ||
===Gate Teleportation=== | ===Gate Teleportation=== | ||
The idea comes from one-qubit teleporation. This means that one can transfer an unknown qubit |ψi without actually sending it via a quantum channel. The underlying equations explain the notion. See [[Supplementary Information#1|Figure 1]] for circuit.<br/> | The idea comes from one-qubit teleporation. This means that one can transfer an unknown qubit |ψi without actually sending it via a quantum channel. The underlying equations explain the notion. See [[Supplementary Information#1|Figure 1]] for circuit.<br/> | ||