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Decoherence has been used to understand the collapse of the wave function in quantum mechanics. Decoherence does not generate actual wave-function collapse.  It only provides an explanation for apparent wave-function collapse, as the quantum nature of the system "leaks" into the environment.  That is, components of the wave function are decoupled from a coherent system and acquire phases from their immediate surroundings.  A total superposition of the global or universal wavefunction still exists (and remains coherent at the global level), but its ultimate fate remains an interpretational issue.  Specifically, decoherence does not attempt to explain the measurement problem.  Rather, decoherence provides an explanation for the transition of the system to a mixture of states that seem to correspond to those states observers perceive.  Moreover, our observation tells us that this mixture looks like a proper quantum ensemble in a measurement situation, as we observe that measurements lead to the "realization" of precisely one state in the "ensemble".

Decoherence has been used to understand the collapse of the wave function in quantum mechanics. Decoherence does not generate actual wave-function collapse.  It only provides an explanation for apparent wave-function collapse, as the quantum nature of the system "leaks" into the environment.  That is, components of the wave function are decoupled from a coherent system and acquire phases from their immediate surroundings.  A total superposition of the global or universal wavefunction still exists (and remains coherent at the global level), but its ultimate fate remains an interpretational issue.  Specifically, decoherence does not attempt to explain the measurement problem.  Rather, decoherence provides an explanation for the transition of the system to a mixture of states that seem to correspond to those states observers perceive.  Moreover, our observation tells us that this mixture looks like a proper quantum ensemble in a measurement situation, as we observe that measurements lead to the "realization" of precisely one state in the "ensemble".

消相干已经被用来理解量子力学中波函数的崩塌。退相干并不产生实际的波函数崩溃。它只是提供了一个明显的波函数崩溃的解释，因为系统的量子本质“泄漏”到环境中。也就是说，波函数的组成部分与相干系统解耦，并从其周围环境中获取相位。全局波函数或普适波函数的完全叠加仍然存在(并且在全局水平上仍然是相干的) ，但它的最终命运仍然是一个解释问题。具体来说，退相干并不试图解释测量问题。相反，退相干解释了系统向混合状态的转变，这些状态似乎与观察者感知到的状态相对应。此外，我们的观察告诉我们，这种混合物在测量情况下看起来像一个正常的量子系综，因为我们观察到测量导致精确的“系综”中的一个状态的“实现”。

退相干被用来理解量子力学中波函数的崩塌。退相干并不产生实际的波函数崩溃，它只是提供了一个明显的波函数崩溃的解释，因为系统的量子本质“泄漏”到环境中。也就是说，波函数的组成部分与相干系统解耦，并从其周围环境中获取相位。全局波函数或普适波函数的完全叠加仍然存在(并且在全局水平上仍然是相干的) ，但它的最终命运仍然是一个解释问题。具体来说，退相干并不试图解释测量问题。相反，退相干解释了系统向混合状态的转变，这些状态似乎与观察者感知到的状态相对应。此外，我们的观察告诉我们，这种混合物在测量情况下看起来像一个正常的量子系统，因为我们观察到测量导致精确的“系统”中的一个状态的“实现”。

Decoherence has been used to understand the [[collapse of the wave function]] in quantum mechanics. Decoherence does not generate ''actual'' wave-function collapse.  It only provides an explanation for ''apparent'' wave-function collapse, as the quantum nature of the system "leaks" into the environment.  That is, components of the wave function are decoupled from a [[Coherence (physics)#Quantum coherence|coherent system]] and acquire phases from their immediate surroundings.  A total superposition of the global or [[universal wavefunction]] still exists (and remains coherent at the global level), but its ultimate fate remains an [[Interpretations of quantum mechanics|interpretational issue]].  Specifically, decoherence does not attempt to explain the [[measurement problem]].  Rather, decoherence provides an explanation for the transition of the system to a [[Mixed state (physics)|mixture of states]] that seem to correspond to those states observers perceive.  Moreover, our observation tells us that this mixture looks like a proper [[quantum ensemble]] in a measurement situation, as we observe that measurements lead to the "realization" of precisely one state in the "ensemble".

Decoherence has been used to understand the [[collapse of the wave function]] in quantum mechanics. Decoherence does not generate ''actual'' wave-function collapse.  It only provides an explanation for ''apparent'' wave-function collapse, as the quantum nature of the system "leaks" into the environment.  That is, components of the wave function are decoupled from a [[Coherence (physics)#Quantum coherence|coherent system]] and acquire phases from their immediate surroundings.  A total superposition of the global or [[universal wavefunction]] still exists (and remains coherent at the global level), but its ultimate fate remains an [[Interpretations of quantum mechanics|interpretational issue]].  Specifically, decoherence does not attempt to explain the [[measurement problem]].  Rather, decoherence provides an explanation for the transition of the system to a [[Mixed state (physics)|mixture of states]] that seem to correspond to those states observers perceive.  Moreover, our observation tells us that this mixture looks like a proper [[quantum ensemble]] in a measurement situation, as we observe that measurements lead to the "realization" of precisely one state in the "ensemble".

Decoherence represents a challenge for the practical realization of [[quantum computer]]s, since such machines are expected to rely heavily on the undisturbed evolution of quantum coherences.  Simply put, they require that the coherence of states be preserved and that decoherence is managed, in order to actually perform quantum computation.  The preservation of coherence, and mitigation of decoherence effects, are thus related to the concept of [[quantum error correction]].

Decoherence represents a challenge for the practical realization of [[quantum computer]]s, since such machines are expected to rely heavily on the undisturbed evolution of quantum coherences.  Simply put, they require that the coherence of states be preserved and that decoherence is managed, in order to actually perform quantum computation.  The preservation of coherence, and mitigation of decoherence effects, are thus related to the concept of [[quantum error correction]].

 

==Mechanisms机制==

==Mechanisms机制==

To examine how decoherence operates, an "intuitive" model is presented.  The model requires some familiarity with quantum theory basics.  Analogies are made between visualisable classical [[phase space]]s and [[Hilbert space]]s.  A more rigorous derivation in [[Dirac notation]] shows how decoherence destroys interference effects and the "quantum nature" of systems.  Next, the [[density matrix]] approach is presented for perspective.

To examine how decoherence operates, an "intuitive" model is presented.  The model requires some familiarity with quantum theory basics.  Analogies are made between visualisable classical [[phase space]]s and [[Hilbert space]]s.  A more rigorous derivation in [[Dirac notation]] shows how decoherence destroys interference effects and the "quantum nature" of systems.  Next, the [[density matrix]] approach is presented for perspective.

 

Rabi oscillations]]

Rabi oscillations]]

An N-particle system can be represented in non-relativistic quantum mechanics by a wave function <math>\psi(x_1, x_2, \dots, x_N)</math>, where each x_i is a point in 3-dimensional space.  This has analogies with the classical phase space.  A classical phase space contains a real-valued function in 6N dimensions (each particle contributes 3 spatial coordinates and 3 momenta).  Our "quantum" phase space, on the other hand, involves a complex-valued function on a 3N-dimensional space.  The position and momenta are represented by operators that do not commute, and <math>\psi</math> lives in the mathematical structure of a Hilbert space.  Aside from these differences, however, the rough analogy holds.

An N-particle system can be represented in non-relativistic quantum mechanics by a wave function <math>\psi(x_1, x_2, \dots, x_N)</math>, where each x_i is a point in 3-dimensional space.  This has analogies with the classical phase space.  A classical phase space contains a real-valued function in 6N dimensions (each particle contributes 3 spatial coordinates and 3 momenta).  Our "quantum" phase space, on the other hand, involves a complex-valued function on a 3N-dimensional space.  The position and momenta are represented by operators that do not commute, and <math>\psi</math> lives in the mathematical structure of a Hilbert space.  Aside from these differences, however, the rough analogy holds.

一个 n 粒子系统可以用一个波函数 < math > psi (x _ 1，x _ 2，dots，x _ n) </math > 来表示，其中每个 x < sub > i </sub > 是三维空间中的一个点。这与经典的相空间有相似之处。一个经典的相空间包含一个6 n 维的实值函数(每个粒子分配3个空间坐标和3个动量)。另一方面，我们的“量子”相空间涉及到一个3n 维空间上的复值函数。位置和动量由不交换的操作符表示，并且存在于希尔伯特空间的数学结构中。然而，撇开这些差异不谈，这个粗略的类比还是成立的。

一个 N 粒子系统可以用一个波函数 <math>\psi(x_1, x_2, \dots, x_N)</math> 来表示，其中每个 x_i 是三维空间中的一个点。这与经典的相空间有相似之处。一个经典的相空间包含一个6N 维的实值函数(每个粒子分配3个空间坐标和3个动量)。另一方面，我们的“量子”相空间涉及到一个3N 维空间上的复值函数。位置和动量由不交换的操作符表示，并且存在于希尔伯特空间的数学结构中。然而，撇开这些差异不谈，这个粗略的类比还是成立的。

An ''N''-particle system can be represented in non-relativistic quantum mechanics by a [[wave function]] <math>\psi(x_1, x_2, \dots, x_N)</math>, where each ''x_i'' is a point in 3-dimensional space.  This has analogies with the classical [[phase space]].  A classical phase space contains a real-valued function in 6''N'' dimensions (each particle contributes 3 spatial coordinates and 3 momenta).  Our "quantum" phase space, on the other hand, involves a complex-valued function on a 3''N''-dimensional space.  The position and momenta are represented by operators that do not [[Commutativity|commute]], and <math>\psi</math> lives in the mathematical structure of a [[Hilbert space]].  Aside from these differences, however, the rough analogy holds.

An ''N''-particle system can be represented in non-relativistic quantum mechanics by a [[wave function]] <math>\psi(x_1, x_2, \dots, x_N)</math>, where each ''x_i'' is a point in 3-dimensional space.  This has analogies with the classical [[phase space]].  A classical phase space contains a real-valued function in 6''N'' dimensions (each particle contributes 3 spatial coordinates and 3 momenta).  Our "quantum" phase space, on the other hand, involves a complex-valued function on a 3''N''-dimensional space.  The position and momenta are represented by operators that do not [[Commutativity|commute]], and <math>\psi</math> lives in the mathematical structure of a [[Hilbert space]].  Aside from these differences, however, the rough analogy holds.

 

Different previously isolated, non-interacting systems occupy different phase spaces. Alternatively we can say that they occupy different lower-dimensional subspaces in the phase space of the joint system.  The effective dimensionality of a system's phase space is the number of degrees of freedom present, which—in non-relativistic models—is 6 times the number of a system's free particles.  For a macroscopic system this will be a very large dimensionality.  When two systems (and the environment would be a system) start to interact, though, their associated state vectors are no longer constrained to the subspaces.  Instead the combined state vector time-evolves a path through the "larger volume", whose dimensionality is the sum of the dimensions of the two subspaces.  The extent to which two vectors interfere with each other is a measure of how "close" they are to each other (formally, their overlap or Hilbert space multiplies together) in the phase space.  When a system couples to an external environment, the dimensionality of, and hence "volume" available to, the joint state vector increases enormously. Each environmental degree of freedom contributes an extra dimension.

Different previously isolated, non-interacting systems occupy different phase spaces. Alternatively we can say that they occupy different lower-dimensional subspaces in the phase space of the joint system.  The effective dimensionality of a system's phase space is the number of degrees of freedom present, which—in non-relativistic models—is 6 times the number of a system's free particles.  For a macroscopic system this will be a very large dimensionality.  When two systems (and the environment would be a system) start to interact, though, their associated state vectors are no longer constrained to the subspaces.  Instead the combined state vector time-evolves a path through the "larger volume", whose dimensionality is the sum of the dimensions of the two subspaces.  The extent to which two vectors interfere with each other is a measure of how "close" they are to each other (formally, their overlap or Hilbert space multiplies together) in the phase space.  When a system couples to an external environment, the dimensionality of, and hence "volume" available to, the joint state vector increases enormously. Each environmental degree of freedom contributes an extra dimension.