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8

I actually don't think that this view of light being in a quantum superposition is anything new: what Discover magazine is describing (I believe) is the stock standard picture of how one would describe a system of cells, molecules, chloroplasts, fluorophores, whatever interacting with the quantised electomagnetic field. My simplified account here (answer to ...


5

The "Kronecker product", better known as the tensor product, is the natural notion of a product for spaces of states, when these are considered properly: A space of states is not a Hilbert space $\mathcal{H}$, but the projective Hilbert space $\mathbb{P}\mathcal{H}$ associated to it. This is the statement that quantum states are rays in a Hilbert space. ...


4

The role of coherence in biological electron transport, e.g. within chromophores, is an open and actively researched problem in quantum optics/quantum chemistry. The two classic theoretical treatments which kick-started the field are by Plenio & Huelga and Mohseni et al.. Since then an enormous literature has emerged on the topic. A basic, generic model ...


4

This is not an answer for the obvious reason that this question cannot be answered easily, hence why it is an open area of research. What I will provide though is links to how something like this is done. The idea resides in the dynamics of open quantum systems, which are systems that are constantly interacting with the environment and hence tend to become ...


4

I.The cause of the quantum entanglement is that the wave-function (w.f.) of the involved particles doesn't have the form of the w.f. of independent particles. So, let's begin by defining what is the w.f. of independent particles. The w.f. of a single particle, let's call it A, can look like $$|A> = \frac {\lvert x_A \rangle + \lvert y_A \rangle.} ...


4

Quantum computing research already has improved our understanding of the basic laws of nature in what I think are several important ways. "Quantum" does not mean "microscopic" One of the types of system used to implement quantum bits (qubits) is a superconducting resonant circuit. These circuits are large enough to see with your naked eye, yet they exhibit ...


2

Given that the $\mathcal E_i$ are linear operators, i.e., $\mathcal E_i(\alpha A + B)=\alpha \mathcal E_i(A) + \mathcal E_i(B)$ for all $A$ and $B$, it is true that $\mathcal E_1(\rho)=\mathcal E_2(\rho)$ for all $\rho\ge0$ implies that $\mathcal E_1=\mathcal E_2$. The argument goes as follows: Every operator $A$ can be written as $A=X+iY$, with ...


2

$x$ is compatible with $p_y$ that means they have the same eigenvectors. That is perhaps not the best way to say it. The fact that $x$ and $p_y$ are compatible tells you that there exists at least one set of basis vectors which are simultaneously eigenvectors of both $x$ and $p_y$. Let's call this set $\{v\}$. Similarly, the fact that $x$ and $y$ are ...


2

A quantum state does not have any classical memories or classical output, period: a classical memory refers eventually in every application to the process of data stored by copying. As it has been proven quantum states cannot be copied. However they can be entangled. A quantum memory may store a quantum state, but not for the purpose of copying in any ...


2

In the context of physics, there are "natural" equivalence relations motivated by the following notion: mathematical objects that determine the same physics should be considered equivalent. These equivalence relations lead to partitions of the sets on which they are defined. Equipped with this idea, let's examine the two points you mention: Let $\mathcal ...


2

This is quite simple. Consider the operator $H$ on the Hilbert space $\mathscr{H}$, in your simple example it has a spectral resolution: $$H=\sum_{n}E_n \lvert n\rangle\langle n \rvert\; .$$ Each eigenvalue has multiplicity 1. Now the operators $H_1$ and $H_2$ on $\mathscr{H}\otimes\mathscr{H}$ have the same spectrum of $H$, but each eigenvalue has ...


2

Here is the erroneous step: "Now, if Alice between the steps 3 and 4 (the ideal time would be as the photons get very close to 4, right before the double slit as expected from their synchronized clocks and known distance),measures the polarisation of her photons, the entanglement is broken before Bob's photons arrive at the double slit at step 4. Thus the ...


2

ACuriousMind's Answer pretty much summed up the reasons, which are essentially mathematical. If you want to grasp the "physical significance", then I suggest you should work through an example: think of two quantum systems, each with three base states: $\left.\left|1\right.\right>$, $\left.\left|2\right.\right>$ and $\left.\left|3\right.\right>$. ...


2

What makes you think that information can be transferred in this way in the first place? I cannot tell you why your method won't work if I don't know what method you have in mind. In any case, I can take a guess as to what you're referring to. Suppose we have a pair of electrons in the state (up to normalization) $\left| +\right> \left| -\right> ...


2

The density matrix formalism follows naturally from a state vector formalism when we average over a part of variables. It is not a "more general", but a more common approach in practical applications. Sometimes it is the only possible formulation due to experimental restrictions.


2

Density matrix is NECESSARY when the quantum system is not in a PURE state, i.e. it cannot be described by a wave-function. Such a case is when a beam of freely moving electrons is not spin-polarized, i.e. there is no direction in space along which all the electrons have the same spin-projection. (For finding whether the electrons are polarized, and on ...


2

State vectors define pure quantum states of a system, and, for an isolated system, evolve with time following the Schrödinger equation (in the Schrödinger picture; in the Heisenberg picture they are constant. Density matrices define classical statistical mixtures of pure quantum states. These can arise in two ways: When we have incomplete information ...


2

Yes, as it turns out there are distinct types of multipartite entanglement not witnessed by the spectra of reduced states. The simplest example is probably the one from Bennett et al., "Exact and asymptotic measures of multipartite pure-state entanglement", Phys. Rev. A 63, 012307 (2000). For the case of three 4-dimensional systems, consider the states ...


1

The density operator combines pure quantum states into a mixed quantum state. The basic idea is to take a system composed of many pure states and to represent them as a single object, which evolves in time, as a complete system. In this example, the mixed state is represented as a Block sphere, and the $\vec{\sigma}$ is a pauli matrix. The Bloch sphere is ...


1

Can this scenario be considered as erasure of information as referred to in Landauer's principle? No. The reason is that the whole process is reversible and Landauer's principle specifically needs an irreversible step - otherwise no "erasure" can have taken place. Where's the problem? It's here: The state $$\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)$$ ...


1

A density matrix is a matrix that describes a quantum system in a mixed state, a statistical ensemble of several quantum states. This should be contrasted with a single state vector that describes a quantum system in a pure state. The density matrix is the quantum-mechanical analogue to a phase-space probability measure (probability distribution of position ...


1

Since this seems a homework exercise, here's a sketch: I'm not sure about the $\mathcal{N}$-part in the formular, but in general: Note that $\sigma_i$ form an orthonormal basis of the Hermitian matrices according to the Hilbert-Schmidt inner-product ($\langle A,B\rangle:=\operatorname{tr} (A^{\dagger}B)\rangle$). This means that you can write $$ ...


1

Let's say that "decoherence" is that transition from a pure quantum state to a mixed state due to interactions with the environment. (A reasonable definition?) Mixed states are NOT decohered states, they are states where the phases of the wavefunctions are well defined, just not in an eigenstate that will give a unique eigen value at measurement. ...


1

There is no precise answer to the cause of entanglement is known (I did not come across any such answer). The superposition principle and the tensor product structure of Hilbert space of combined system leads to the possibility of entangled state. It is well understood in the case of pure state, but for the mixed state case it is quite involved.


1

To answer your question shortly: No, they are not the same phenomenon. First of all, it is much easier to think of quantum states as vectors (in something called the Hilbert space, but simply put they obey linearity), and not as particles or waves. Superposition Let's start with a single particle qubit (since you're talking about quantum information) ...



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