4

Here are a couple of contributions related to your question: 1- Very recently, Chris Ferrie created an open-source card game based on a toy version of quantum mechanics, called $<B|racket|S>$. 2- The company Phase Space Computing markets electronic kits that simulate quantum gates and simple quantum algorithms.


3

I am glad you enjoyed my experiments! :) I'd be happy to talk more about how I ran that project --- dm me at twitter.com/crazy4pi314. To your question, I don't know of any good papers or articles on the setup, but you can get a pretty reasonable demo of polarization-encoded BB84 with a few pretty common components: polarized laser pointer some half wave ...


3

Start in $$ a_0 | 01 \rangle + a_1 | 10 \rangle $$ Then apply $P \otimes I$ to get $$ a_0 * 1 | 01 \rangle + a_1*e^{i \Delta} | 10 \rangle $$ But that is the same up to phase as $$ e^{-i \Delta /2} (a_0 * 1 | 01 \rangle + a_1*e^{i \Delta} | 10 \rangle) $$ which simplifies to $$ a_0 e^{-i \Delta /2} | 01 \rangle + a_1 e^{i \Delta /2} | 10 \rangle $$


3

Yes. The kets themselves can have arbitrary labels, and it's just for you to establish the connection between them and the physical scenario. There's no reason why you can't have the physical scenario you've specified and, indeed, people frequently do.


2

There is a number of groups using time-bin encoding to realise computation/communication protocols. One example is Furusawa's group in Japan, which among other things works on measurement-based QC with time-bin encoding (e.g. 1706.06312). Another example that comes to mind is Silberhorn's group in Paderborn. They use time-bin encoding for various things, a ...


2

Yes! The first application of time bin photonic qudits that comes to mind is for quantum key distribution. Here's an example: https://arxiv.org/abs/1611.01139. I am sure there are more references out there though!


2

It looks like the only relation they say is $\text{IdentityMatrix}[3^2]=\sum P_{k,l}$. You get a linear combination of $P_{k,l}$. Those are vertices of a $d^2-1$ simplex so the coefficents $c_{k,l}$ are baryocentric coordinates. You can then match with the previous more general definition of $\rho_d$ term by term on each of the $c_{k,l}$. The inequalities ...


2

You seem to be thinking about "quantum memory" like it is one specific thing and there is only one specific way it can happen. In reality, what you describe is a valid notion of quantum memory. Another popular one, involving the element Yb, is this one: https://arxiv.org/abs/1701.04195.


2

Your understanding is correct. In the theory of photon polarization, the parametrization of the Bloch sphere (or its surfave) has traditionally another name. On the wikipedia page for the Jones calculus (the parametrization of the Bloch sphere surface), you'll find a table for the correspondence between kets and polarizations. To summarize, eigenstates ...


1

I see the heart of your question. I'd like to clarify a bit, before answering your question though. Matrices (aka operators) do not measure quantum states--they operate on them. Specifically, they project the state into the matrix's eigenvectors. We can then measure that projected state in a particular basis that may be the same or different than what the ...


1

A photon can be thought of as a tiny piece of a circularly polarized wave. In this sense, all polarization states of EM waves are a superposition of photons, each with a circular (left or right) polarization. Linearly polarized light could then be constructed as a pair of photons with left and right polarization (or spin). Maybe your question is whether ...


1

For the former part: Even a simple slab of glass can act as a phase shift quantum gate. The difference in path covered is $(n-n_0)L \equiv \delta L$ and the time difference is $\delta L/c_0$ and then the phase shift is proportional to this time shift. Or just divide this time phase difference by some time $T$ taken by the light in a vacuum to travel the same ...


1

This is very much possible. And is a very general technique of how product systems in composite states are coupled. Here of the form $|n_1\rangle |n_2\rangle$. This kind of general ket is a solution of the Hamiltonian interaction/coupling terms like $V\sim (a_1^\dagger a_2 +h.c)$ which describe the exchange of one quanta (between the two optical cavities ...


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