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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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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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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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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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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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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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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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How do we know that photon entanglement isn't the result of the photons's states being predetermined? Photons are elementary particles, and elementary particles cannot be explained without quantum mechanics. Quantum mechanics describes the state of the photon and the system it resides in, all in one probability distribution. It is analogous to throwing ...


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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 ...


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Prohibition of information destruction due to unitarity is a hypocrisy (sorry, I go to reiterate some stuff from the Where does deleted information go? posting), and the concept of entropy is foggy, especially in the quantum context: in spite of definitions mentioned in previous answers, there is no possibility to ever know the quantum state of a ...


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Quantum entanglement can not be described as a predetermined correlation between particle's states because of the observed violations of Bell's inequalities. All of this is best explained in the language of science and math. If you want to avoid such explanations, you might try an explanation like this: quantum casino - less than zero chance. In short: would ...


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“Always a polytope” – definitely not. Moreover, in certain situation $Ω$, if a closed set, may not change at all; I mean product with the 0-dimensional set of states $Ω_{\rm id} = \{1\}$ (one point), considered as a subset of 1-dimensional vector space $V_{\rm id} = {\mathbb R}$. It has the only effect, the unit effect, and corresponds to 1-state quantum ...


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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 ...


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Mantras like “the Bloch sphere contains all of the observable information about the system” are junk. This implicitly refers to the concept of a (pure) quantum state, and confuses it with an important concept of observable, but quantum states are a tricky stuff and the word “information” may become especially treacherous. Let us start from mathematics. ...


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Conservation of information in quantum mechanics is a hypocrisy as much as it is so in classical mechanics. It is not conserved in the same sense as energy, charge, or momentum. When sages like Hawking and Penrose discuss whether does “information” survive destruction in a spacetime singularity, they mean something utterly different from the concept familiar ...


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No, the reasoning is wrong. When you need a N-qubit state, no difference entangled or not, you just initialize N qubits and then apply a unitary transformation (reversible). So, entropy produced during the initialization is proportional to the amount of information, without exponents.


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Observer, if you assume as someone watching the experiment or activity, is plainly wrong. Anything that can be detected and measured and thus, in principle, from infinitely hard calculation can tell us about the past or previous states, can be said to be information, and thus, entropy increased while the process was being carried out. Take for example, a box ...


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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 ...


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Looking at other similar questions... My understanding is that we can't use change events as a measure without knowing "when" measurements are made on one end we can't differentiate those changes from random changes (noise) on the other end. Why can't quantum teleportation be used to transport information? Improvements to my understanding are ...


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You use the letter S ambiguously to refer to both a system and the result of a measurement made on that system. It's important to distinguish them. So the situation is that two observers O1 and O2 independently make a measurement M of a system S and agree that the result of that measurement is X. It is tempting to conclude that the reason they agree is ...


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If I understand correctly, Alice and Bob generate an entangled pair of photons and each take one. Alice does something with hers (you specified a quantum eraser experiment at a particular time, but I won't make that assumption) while Bob does a standard double-slit experiment with his. A minor point here is that with one photon you'll never get interference ...


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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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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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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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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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A qubit is a (complex) vector, with $2$ complex coordinates, you may write it : $$\vec q = \alpha \vec 0 + \beta \vec 1 \tag{1}$$ Here $\alpha$ and $\beta$ are complex quantities and $\vec 0, \vec 1$ is a basis, so you have $\vec 0.\vec 0= \vec 1.\vec 1=1$, and $\vec 1.\vec 0 = \vec 0.\vec 1=0$. The qbit is generally normed to $1$, so you have ...


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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 ...


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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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Yes, it is true. The Planck length is defined as $$ L = \sqrt{\frac{G\hbar}{c^3}} $$ which, in the real world, happens to be equal to $1.616\times 10^{-35}\,{\rm m}$ (meters). In everyday life, we use units like the SI units – based on kilograms, meters, second, kelvins etc. But adult theoretical physicists often use smarter, more natural units chosen so ...


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It is not necessarily that you need to send a photon, or the more used term qubit at a time, the idea is to send wavepackets of qubits with the same polarization, carrying with it as little qubits as possible. It is a security measure and a technical one at the same time. The names I'll be using: Communication between Alice-Bob, with Alice the sender, Bob ...


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It's true quite generally (for seperable Hilbert spaces at least). The original proof is in "Proof of the Strong Subadditivity of Quantum Mechanichal Entropy", by Lieb and Ruskai (J. Math. Phys. 14, 1938–1941 (1973)). The main idea is to prove the finite-dimensional case, and then extend it by taking a limit of the inequality on finite-dimensional subspaces ...



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