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Quantum cryptography ("QC") isn't a method of encryption; it's a method of generating a random shared secret (random bits known to Alice and Bob but not to the eavesdropper). Actually, if Alice and Bob don't already have a shared secret, or at least some way of authenticating each other, then they are vulnerable to a man-in-the-middle attack even if they use ...

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It is a perfectly well-defined expression because the tensor product is a linear space. The vectors $|v\rangle\otimes |w\rangle$ form a basis of the whole tensor-product vector space, so any vector (including Bell's state) in this space may be written as linear combinations of such basis vectors. $$|\psi \rangle = \sum_{ij} c_{ij} |v_j\rangle\otimes ... 3 Unitarity of quantum mechanics prohibits information destruction. On the other hand, the second law of thermodynamics claims entropy to be increasing. If entropy is to be thought of as a measure of information content, how can these two principles be compatible? I don't think there's anything inherently quantum-mechanical about this paradox. The same ... 3 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 ... 3 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 ... 3 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 ... 3 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 ... 2 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. 2 In qutip we use use the scipy ode solvers and in particular the 12th order Adams-Bashforth method via zvode. Solving for the evolution of the density matrix is just a standard ode equation provided that you pick a basis representation to express the Liouvillian in matrix form, and the density matrix as a column vector by stacking the matrix columns, for ... 2 The Second Law of Thermodynamics states that the entropy of the universe always increases or stays constant. This means that we can reduce the entropy of the gas in the box (gas compressed from the whole box to half the box at constant temperature), only if we increase the entropy somewhere else. For example, we can compress the gas, doing work on it, and ... 2 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. 2 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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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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Yes, this is exactly the principle used in an etalon. A notable example of this is the LIGO experiment to detect gravitational waves. LIGO uses arms that are 4 km long, but the mirrors at each end bounce the light 150 times (75 round trips) so the optical length of the arms is 600 km. It's this large optical path length that enables the tiny effects of ...

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For every reflection in the mirror you will loose some light. In my knowledge the best polished mirror has ~ 99% reflecting ability. But lets stick to 90%. A common mirror has less than 10% reflectivity. After 10000 reflections the intensity of the out going light is $(0.9)^{10000}$ of the incoming light. On the other hand, optical fiber uses total internal ...

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All different QKD protocols are well covered in most Quantum Information textbooks, e.g. Quantum Information by Jaeger. Trying to give a complete, understandable coverage of the matter is impossible in a post like this, so I'll just give you an overview: In the E91 scheme, entangled photon pairs are used between Alice & Bob, and unlike the single-photon ...

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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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You need to be a bit (pardon the pun) more strict about the size of the (Hilbert) space you're playing with. A qu_bit can be in a superposition of two (pure) states, but not more. For this reason, "real values 2, 3 and 4 in superposition" doesn't make sense. To draw an analogy to the binary system you mentioned, it's as if you're trying to stuff large ...

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