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No, decoherence is not a new fundamental feature of quantum physics. It is a phenomenon which occurs when you couple a system with a few degrees of freedom to one with a lot of degrees of freedom and which you can derive from the postulates of quantum physics. There really is no measurement problem. Once you get a classical probability distribution (up to ...


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This might not be what Nakahara has in mind, but one can make sense of this using the idea of projective Hilbert spaces. Let $\mathcal{P}(\mathcal{H})$ denote the projective space associated to the "normal" space $\mathcal{H}$. The subset of separable states is not a subvectorspace in the proper sense, as Holographer notes. Yet it can be understood as a ...


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Actually there is a theorem in quantum mechanics called the no cloning theorem which says that you can't clone a quantum state. However teleportation is possible and has been done experimentally, the teleportation here is the sense that you destroy the quantum state in one place and recreate in another place.


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Basically it means that in the case of OAM=0 the wave fronts make a structure similar to a stack of plates, and in the case of OAM=1 they make a helix-like structure, and 1 refers to the helix multiplicity (for a double helix it would be 2 and so on). One cannot be changed to the other continuously, so this is a topological feature. There are other ...


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There is a hybrid "quantum computer game" http://www.scienceathome.org/ which pursues two different objectives: On the one hand, it is an attempt to popularization of quantum physics, but it is at the same time a research programme for which a numerically hard and expensive optimization problem occurring in quantum control was translated into a ...


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The collapse of the wavefunction is not a real physical process. It's a feature of a particular interpretation of quantum mechanics, the Copenhagen interpretation (CI). Other interpretations, such as the many-worlds interpretation (MWI), don't have such a collapse. The different interpretations make the same predictions about all observables, and therefore ...


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Note that the space of separable states is not a vector space, and in particular not a subspace of the total Hilbert space: the sum of two separable states is unlikely to be separable. So dimension here means something more general than vector space dimension. Having said that, I would disagree with the author on his dimension! I would say that the space of ...


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If $A^\prime$ and $B^\prime$ commute then there exists a set of mutual eigenvectors of $A^\prime$ and $B^\prime$. For any eigenbasis of $A^\prime$ there exists a unitary transformation $W$ which takes that basis to the mutual eigenbasis of $A^\prime$ and $B^\prime$. Consequently if there is a unitary operation such that $ |\langle \psi | b \rangle |^2 = ...


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Correct me if I'm wrong, but your line of thinking goes like this... Since quantum fields do not commute in general one can have finite variances for, e.g., particle number. Since the vacuum states defines a probability distribution we can find the corresponding entropy. However, here we are dealing with quantum physics. The entropy is in general $S ...


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There is Qcraft, which is a mod of the game minecraft. According to its developers, It lets players experiment with quantum behaviors inside Minecraft’s world, with new blocks that exhibit quantum entanglement, superposition, and observer dependency.


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The Bekenstein bound, $$ S \le \frac{2\pi rE}{\hbar c},$$ is a limit on the natural log of the number of possible states (i.e., the information content) of a spherical region of space of radius $r$, containing mass-energy $E$. The mass of the hydrogen atoms in the observable universe is $\sim 10^{54}$ kg, and nonbaryonic dark matter is probably about 5 ...


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An absorption grating is a grating, where the parallel bars are absorbing. This is in contrast to a reflection grating, where the bars would be reflecting, and a phase grating, where the bars are transmissive, but will change the phase of the incident waves. In general, physical gratings can (and usually will) introduce combinations of these three effects.


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The charge of an atom is defined by its constituent number of protons/electrons and local fluctuations in their density distribution which cause instantaneous dipoles, unless we are talking about ions which have a permanent charge. Charge is a classical concept that has real meaning in classical physics and can be described in various fields ...


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The identity is true in any dimension. To see this, notice that both the left and right hand sides of the equation you wrote down are linear operators on the tensor product of vector spaces, so to show that they are equal, it suffices to show that they agree on a basis. Since the basis for a tensor product is the set of all tensor products of basis ...


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Hint: Start by representing $\psi$ and $\rho$ in the basis $\{ \vert x\rangle,\vert y\rangle\}$. Shouldn't be too difficult to calculate the action of $U$ once you've done that. If you don't know how to take the partial trace, post the intermediate result and ask back. These steps will produce an equation like $$ A_{xy}(\psi,\rho)\vert x\rangle\langle ...


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I will give you an easier assignment to start with: explain the origin of Newton's laws, using nothing but statistical mechanics of Newtonian systems. Can you do it? No. Statistical mechanics follows from Newton's laws PLUS a few assumptions about phase space averaging. In the same way decoherence does not lead you beyond the framework of quantum ...


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Two types of cloning going on here. Biological cloning is possible now. Take a cell, make it behave like a freshly fertilized egg and grow a copy. Your clone will look the same but be somewhat younger. Random features (like some animal hair patterns) are not clonable. As biological clones grow from a single cell it will not be atomically identical if the ...


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The density matrix for a pure state $|\psi\rangle$ is $\rho=|\psi\rangle\langle\psi|$. Note that this is a matrix in the sense that it takes some vector $|\phi\rangle$ to the vector $\rho|\phi\rangle=|\psi\rangle\langle\psi|\phi\rangle$. It has components $$\rho_{ij}=\langle e_i|\rho|e_j\rangle=\langle e_i|\psi\rangle\langle\psi|e_j\rangle=\psi_i ...


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It is certainly possible to clone mammals. Scientists have done that. One can replicate many things well enough for them to be functionally indistinguishable for all practical purposes. Industrial mass production processes do just that. Some of the chips in your computer are fabricated with such a precision, that some of their structures (e.g. gate ...


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What about positivity? The product of bounded positive operators is positive if they commute (see proof below), otherwise there is no guarantee. If your initial POVMs are not compatible, in general, the operators of the final candidate POVM is not made of positive operators and thus they do not define a POVM. Proposition. If $A,B \geq 0$ where $A,B :\cal ...


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First, note that a unitary transformation can not modify the commutation relations.. $$AB-BA=C$$ Use the fact that $U^\dagger U=U U^\dagger=1$ to get, $$AU U^\dagger B-BU U^\dagger A=C$$ and then multiply by the conjugate transpose from the left and $U$ from the right, $$ U^\dagger AU U^\dagger B U^\dagger- U^\dagger BU U^\dagger AU^\dagger= U^\dagger C ...



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