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As noted by hwlau, quantum circuits always correspond to unitary operators. For the question to be meaningful, you have to start with some set of gates that you consider building blocks. The rules of combination in linear algebra terms are essentially matrix multiplication and Kronecker product, the first corresponding to sequentially applying two circuits, ...

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The matrix you quote has the following determinant $$\det\left( \begin{array}{c c c} -1+2/8& 2/8& 2/8\\ 2/8 & -1+(2/8) & 2/8\\ 2/8 & 2/8 & -1+(2/8) \end{array} \right) = -1/4$$ which is not unitary required by quantum mechanics. It implies that your matrix is not possible to be constructed using any standard quantum gates which ...

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A short addendum to Emilio Pisanty's last paragraph. The information storable in one continuous variable (i.e. one real number, which in principle encodes $\aleph_0$ bits) is precisely quantified by Shannon's noisy channel coding theorem. Let's suppose we have a normalized real variable $x \in [0,1]$: the interval represents the fact that we have a finite ...

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As a remark, you have not enough information to recover the original state, but you have not enough information even to recover the structure of the original state, think for instance about the following quantum states : $\rho_{CLASSIC} = \begin{pmatrix} ... 7 This is a frequently-encountered 'boobytrap' in information theory, but it turns out that having a continuous degree of freedom does not entail free access to an infinite amount of information. First of all, while the wavefunction is continuous, you can discretize it quite easily. We know every nucleus and electron in your brain is confined to within a box, ... 1 I will assume the author means that each party has one qubit of the entangled state $$\rho=\frac {|00\rangle \langle 00|+|11\rangle\langle11|}{2}$$ Which is interesting because$\rho$isn't a pure state. Anyway this state is a "key"; in the sense that without it parties should not make any sense of the data being transmitted. I am not going any ... 1 Coherent states, although strictly quantum, are "isomorphic" to classical states. They are also isomorphic in the same way to one-photon states. There are bijective maps between any pair of the following three sets: (i) the set of all quantum coherent states (ii) the set of all one-photon states and (iii) and the set of all solutions of Maxwell's equations. ... 4 Coherent states are quantum states, but they have properties that mirror classical states in a sense that can be made precise. To be concrete, let's consider coherent states in the context of the simple harmonic quantum oscillator which have precisely the expression you wrote in the question. One can demonstrate the following two facts (which I highly ... 3 You have pinpointed an important nuance of quantum information theory. A perfectly entangled state is, in some sense, like a single bit in a one time pad: just two copies of a shared random bit. In fact, the teleportation protocol is perfectly analogous — not the same, but certainly analogous — to transmitting a message securely using a one-time ... 2 It is all about what meaning you put into the words "quantum" and "classical". Fock space and elements of this space are notions that belong to quantum theory of radiation and have no direct relation to states of radiation in classical electromagnetic theory, so the coherent state may be called "quantum" with good reason. However, coherent states have ... 3 If coherent state are indeed the most classical states (which means that the mean value of the EM fields obeys the classical Maxwell equations), the state used in the paper you mentioned are not coherent state (at least in the arXiv paper), but cat states ! The state$|\alpha\rangle+|-\alpha\rangle\$ is not a coherent state ! It is the superposition of two ...

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This was shown by Konstantin Iakoubovskii and Guy J Adriaenssens 2001 J. Phys.: Condens. Matter 13 6015 doi:10.1088/0953-8984/13/26/316. Their optical absorption experiments show that single substitutional nitrogen centers trap vacancies about eight times more efficiently than the substitutional nitrogen pairs. In my own reasoning, I would say that have to ...

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Generally the way you prove something is minimal is by 1) enumerating all possible smaller configurations, or 2) looking at it in terms of a finite set of states, and showing that nothing smaller could hold the necessary number of states.

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I have confirmed with Zurek, he told me that it was wrong (at least the period-wise) and it has been pointed out many times by other people including Animesh Dutta.

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Which of these explanations is more correct or do they supplement each other? All of them and none of them? Those explanations all look like they're biased towards particular interpretations of quantum mechanics. I think each arose out of people's favorite interpretation for quantum phenomena. For example, Quantum computers perform operations in ...

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