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Quantum mechanics, is, to the best of our knowledge, the way (almost everything in) the world works. It's not solely about describing "matter waves", although this was fundamental to its inception. It's not solely about describing microscopic phenomena. It's about a fundamental conception of "mechanics" (it's in the name!), an attempt to describe how ...


7

Taking a look at your questions, I would suggest you forget about the wave particle duality being this foundational principle of quantum mechanics. Rather, I would say there are two (at least, these two are the most obvious) important defining characteristics of QM, which are made clear in the Hilbert space formalism: States are represented by vectors, and ...


4

We don't know what quantum mechanics is about, the theory is formulated in an instrumental way. The postulates of quantum mechanics tell you how to compute the outcome of experiments. When you try to look beyond this, take into account that the experimental apparatus used, the observers etc. are also made out of the atoms and molecules, you are forced to ...


4

To add to ACuriousMind's answer by bringing my personal experience to the table, I too had the background mathematics for many years and understood perfectly all the algebraic machinations in many textbooks but was utterly baffled. My problem was that I was "out" of QM for a long time: I had an elementary exposure to it in undergraduate engineering which was ...


3

The basic idea upon which Quantum Mechanics is based is the wave-particle duality. The basic idea is that classically dynamics of configurations fails and needs to be modified. Particle wave duality is ultimately too vague to be a fundamental explanation. So it is seem that particles on these microscopic phenomena behave as waves. Those matter waves ...


3

Partial transposition flips the sign of $\sigma_y$ on the $B$ system. If you now conjugate the resulting matrix with $I\otimes\sigma_y$, you moreover flip the sign of $\sigma_x$ and $\sigma_z$, and thus of all Pauli matrix. On the other hand, this conjugation preserves the spectrum, as claimed. Note that it is only claimed that the corresponding matrices ...


2

Not with certainty. However, Alice can probabilistically tell them apart by performing a measurement that asks "is the state of the system $(|0\rangle + |1\rangle)/\sqrt{2}$?" For example, if the qubit were a spin $1/2$ particle and $|0\rangle$ and $|1\rangle$ were spin up and spin down, this would correspond to measuring spin along the $\hat{x}$ direction ...


2

It's important to remember that the quantum state is physical, and not merely a description of our knowledge or ignorance of a system. At every point during Alice's experiment, the pair has a single quantum state (insofar as the measurement apparatus can be treated as classical), but Alice, Bob and Charlie have different degrees of knowledge about what that ...


2

Entanglement is what cannot be created by local operations and classical communication (LOCC), so it can be used to do otherwise impossible tasks in a scenario where one is restricted to LOCC. Now what is the most general LOCC protocol? A measures, communicates the outcome, B measures (conditional on the first outcome), communicates the outcome, A ...


2

It might help to distinguish two possible understandings of the question "what is quantum mechanics about?": What kinds of physical systems, processes, etc., is quantum mechanics particularly useful for representing; how, that is, should we use or apply quantum mechanics? What is the theory saying about the nature of the world; how, that is, should we ...


2

A photon is an elementary particle with zero mass, moves always with the velocity of light c, and has energy given by E=h*nu . It has spin +1 or -1 and its wavefunction also has a polarization which will build up the polarization of the emergent from many photons classical electromagnetic wave. Its energy is a property that characterizes the emitting ...


2

One single photon is not enough for you to see objects. If there would be just one photon coming to your eye, you would first see only darkness (before the photon arrives), then you would notice a dim point for very short time (when the photon hit your retina), followed by darkness again. You can see objects because there is a constant flow of huge amount ...


1

I had the same conceptual problems you are having when I was studying QM. Let me spray a bit of philosophy which allowed me to finally move on and concentrate on the mathematical stuff which actually matters :) Quantum states are rays in the Hilbert space (or points in the projective Hilbert space, or etc.). All states have the same physical meaning: they ...


1

When the theory of relativity was developed, Minkowski created the mathematical tool of space-time to easily describe and solve for transformations using geometric methods. Even Einstein at the time viewed this as a mathematical tool but later realized that the actual geometry of space-time was the explanation for gravity and non-Euclidean geometry of ...


1

Lots of people have similar ideas and in fact I answered this very question in another post ("FTL" Communication with Quantum Entanglement?), which isn't actually a duplicate question (just the answer is duplicated). Basically the answer in a nutshell is that entanglement always destroys quantum coherence. What Bob (observer B) observes by ...


1

If you just sent a qubit in some state $|\psi\rangle$ from one place to another, it would be very difficult to protect the information it instantiates from decoherence. The decoherence is a result of the dependence of an outside system on the quantum information in the qubit. But by using entanglement it is possible for a system to instantiate quantum ...


1

A sum-frequency system with a "hot" mirror could act something like an optical switch: Unlike a switch, the output frequency will be different from either of the inputs. Edit: For an example of sum-frequency generation crystals see: Thorlabs Introduction To Periodically Poled Lithium Niobate (PPLN) (PDF) Thorlabs also sells hot mirrors.


1

Yes, such a kind of exact decomposition is always possible. This is shown in Barenco et al., Elementary gates for quantum computation (Sec. 8, pg. 27 in the arXiv preprint), based on work by Reck et al. (which gives a corresponding decomposition where each elementary operation is the identity except for a $2\times 2$ submatrix). The construction given ...



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