# Tag Info

12

You are totally right in your assumption about transporting qubits from Alice to Bob implies something physical. Usually problems/situations that have this setup of a transmission between two parties are called quantum communications. These problems/situations sometimes disambiguate by calling their qubits "flying qubits" which are almost always photons. ...

7

Your analysis of Eve's cheating doesn't seem quite right (although the final answer is correct). What you need to say is: Assume Alice prepares a particular state in one of the bases. You could assume that's $|0\rangle$, but you can make the argument more generally. With 50% probability, Eve measures in the same basis that Alice prepared in (the 0/1 basis ...

7

As this is one of the first examples in Nielsen & Chuang, I'll go ahead and type out their explanation here for anyone else that is interested in entanglement for faster than light communication. The following is an abridged version of Nielsen & Chuang section 1.3.7 entitled 'Example: quantum teleportation' Quantum teleportation is a technique ...

6

Your initial calculations are correct. When Alice performs her first measurement and gets a 0 outcome then, as you say, Alice and Bob are left sharing a two-qubit state $$|\Psi\rangle=\alpha|00\rangle+\beta|11\rangle$$ (you can safely ignore the measured qubit). The problem is the statement She can tell Bob: "Your half of the EPR is now the qubit I ...

6

A necessary and sufficient condition on the unitary $B$ is that its columns all correspond to maximally entangled states. There also does not need to be any relationship between the two unitaries labeled $B$ and $B^{-1}$ in your figure: as long as you start with a maximally entangled state of systems 2 and 3, and then measure systems 1 and 2 with respect ...

5

No, you need to send only one photon (from the pair). The other party could generate entangled pair and send the entangled photon to you. Or it could be the third party that send both of you your photons $-$ prior to actual communication. Even if it's you who generate the entangled pair and share the entangled photon $-$ you could do it way before the time ...

5

No, you can't send more than 2 bits per transmitted qubit. Ultradense Coding would allow FTL Signalling. The basic problem is that, if either teleportation or superdense coding was slightly more efficient, iteratively nesting them inside of each other would allow you to send more encoded qubits than the number of physical qubits you sent. Suppose you could ...

5

No. As far as we know, entangled states do not permit faster than light communication. You might be able to use them for things like doubling bandwidth (see superdense coding) or sending quantum states, but that will all happen at the speed of light (or slower). It is true that entangled states do seem to know something about the constituent elements faster ...

5

For two parties to share an EPR pair means that each party has one qubit, and these two qubits together are in state $\frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$ (or one of the other Bell pairs). The entanglement swapping protocol is described, for example, in Wikipedia. It is the same as traditional (I almost wrote "classical" but caught myself in time) ...

4

That’s the public discussion stage: Alice and Bob can both announce which basis they chose for each round. If they happened to pick the same basis on a given round, they know that (in a perfect world) their answers were the same, so they can translate them into a 0/1 value that nobody else knows. That translation is arbitrary, and they’ve probably agreed it ...

4

Let's recap a bit: In classical information theory, the analogous formula is the Shannon noisy channel coding theorem. It's charming, because it is basically just a very simple optimization of the mutual information. The quantum channel capacity is that it is given by $$\lim\limits_{n\to\infty} \frac{1}{n}Q(T^{\otimes n})$$ where $T$ is the quantum ...

4

Collective measurements are normal measurements. You just need to be clear on the setting under which they are operating. I haven't delved deeply into the specific paper you mention (so it's always possible they make marginally different assumptions), but I expect it goes like this: You are looking at using many copies of the same channel. Encoding will, ...

4

An entangled quantum state, where one subsystem is held by each party, and there is no other communication, cannot be used to achieve communication. The two classes of operation that one party could perform on their quantum system are unitaries and measurements. A unitary performed on one quantum subsystem (Alice) does not change the other one (Bob), so ...

4

measurements in every circuit can be postponed or never performed in a circuit while achieving the same functionality of the circuit That's correct. But if the circuit involves two parties, this process will introduce quantum operations between the two parties. It will require a quantum communication channel, so that the qubits can be shuttled back and ...

3

You cannot directly send information using only entanglement like DaftWullie excellently explained. But here's what you can do Superdense coding: a) pre-share 2 entangled qubits between you and a friend b) then by sending a single qubit you can send 2 classical bits Teleportation: a) pre-share 2 entangled qubits between you and a friend b) when you want to ...

3

To answer this, contrast quantum teleportation with the swap gate. Ignoring everything in the middle, the effect of quantum teleportation is to get from state $|\phi00\rangle$ to $|00\phi\rangle$. This can obviously be accomplished with a simple application of the swap gate. So, why do we care about quantum teleportation? You'd never run the quantum ...

3

Mathematically, this has nothing to do with the positivity of $E$. It doesn't really have anything to do with $E$ at all - it's a property of the Bell states themselves (you've probably not got there yet, but they have the same reduced density matrices). I presume the reason for specifying the positivity of $E$ in the question is to help you make the ...

3

Here is an idea of how could this be solved. It is based on teleportation. First, Alice teleports her qubit by means of one of the EPR pairs that she shares with Bob. In order to do that, she sends the classical information she obtains by measuring her EPR halve and her qubit. Bob uses the clasical information received in order to reconstruct the qubit in ...

3

There is a set of two packages in Mathematica called "Quantum Notation" and "Quantum Computing" for Wolfram Mathematica Environment, and here you can very well mimic all three considerations you are concerned with and much more in the usual Dirac Notation and Quantum Circuit Formalism. The link to the packages are as follows: http://homepage.cem.itesm.mx/...

3

Reutter and Vicary Features of teleportation, dense coding and secure key distribution are mimicked even without having an honest quantum internet. The main idea is the groudit. That is a special type of groupoid where there certain bijections as sets given as extra data. That is for a given natural number $d$, think about $d$ finite groups all of ...

3

Enabling network sockets to handle 10k clients at the same time with over 1 gigabit per second Ethernet (the C10k problem), is different from making a quantum computer that can handle 10k qubits concurrently. Remember 10k bits is only 1.25kB which is not even enough to store a typical operating system. If you want to consider each qubit as a "client" in ...

3

It’s worth stating from the start that “Alice and Bob” scenarios are very different from quantum computation scenarios. The Alice and Bob scenarios are very much that there are two distantly separated locations between which it is impossible to directly perform quantum gates. Meanwhile in the quantum computing architectures you’re talking about, two-qubit ...

2

Since this is a homework-type question, I'll just outline the method: You begin in the state $(\alpha_0|0\rangle + \alpha_1|1\rangle) \otimes \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$. It can be written as $(\alpha_0|0\rangle_{A1}) \otimes \frac{1}{\sqrt{2}}(|0\rangle_{A2} |0\rangle_B + |1\rangle_{A2} |1\rangle_{B}) + (\alpha_1|1\rangle_{A1}) \otimes \... 2 Absolutely! BB84 can be implemented over LiFi. There are however certain constraints and inefficiencies involved, which will have to be taken into account for implementation - possibly leading to the usage of BB84 variants like Decoy State, with higher efficiencies than pure BB84. A four non-orthogonal polarization basis encoded single photon would be very ... 2 This happens for any maximally entangled state$|\Psi\rangle$and operator$E$. Indeed, a maximally entangled state is, by definition, one whose partial trace is the maximally mixed one. Writing$|\Psi\rangle\equiv\sum_{ij}\psi_{ij}|ij\rangle$, this means that$\sum_i \psi_{ij}\bar\psi_{kj}=\delta_{ik}/D$, with$D$the dimension of each space ($D=2$in your ... 2 In my understanding, the key part for entanglement to increase capacity is to have a suboptimal channel. Suppose the input of you channel can take value in the set$X$, and note$G(X)$the graph where nodes are possible inputs and there is an edge between to inputs if the range of their corresponding output is overlapping, i.e. When going through the channel ... 2 I will try to succinctly answer your first question given that I possess little knowledge regarding entanglement assistance. Shannon's capacity theorem (the noisy channel coding theorem) states that for any code$\mathbf{C}$of code rate$R \leq C$, where$C$represents the channel capacity, an encoding and decoding scheme of rate$R$with a probability of ... 1 It is important to note that Step 5 is a classical step. Different protocols exist to correct keys, for instance the Cascade- and Winnow-protocols. With this you reveal bits of information in specific ways, due to which you learn if there are errors and where these are located. 1 I wanted to expand on DaftWullie's accepted answer in case it is helpful to others. DaftWullie's is correct; mine is only a continuation of the same idea. Consider the one-qubit state$\psi = \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$. We know that applying the Hadamard matrix$H = \frac{1}{\sqrt{2}}\begin{bmatrix}1& 1 \\ 1 & -1\end{bmatrix}\$ will ...

1

What are the biggest bottlenecks in the realization of a global quantum network (ie quantum internet)? It would seem only complexity, getting everything working together, with high reliability, for a long enough period of time. The OSI description of network layers describes 7 layers, quantum networks will likely end up with more but we can already ...

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