5

This is a purely hypothetical answer - I don't know if anybody has ever studied it, and have not attempted to find out - but think about public key cryptography. Current public key systems are based on the idea that some problems in the complexity class NP are probably hard to solve directly, but there exists a "proof" that lets you verify the solution ...


4

This is an interesting question that reflects a conflation of some concepts in quantum information sciences. TL/DR - there is no task in BB84 that corresponds to what we when we speak of quantum computation, so BB84 is not evidence of what researchers mean when they speak of "quantum supremacy". But historians will likely still consider the initial ...


3

To add on the answer of Martin Vesely: RSA is not save against a general quantum computer, because of Shor's algorithm (see link in other answer), which translates the problem at hand (in RSA) of factorizing large coprime numbers to a problem of period finding within a function (namely, the discrete logarithm). Quantum computers are, among other things, ...


3

First of all, it depends on the level of detail of your simulation. SimulaQron does not take into account noise, so I presume your simulation is only functional. Many BB84 functional simulations have been developed so far, and no one was so interesting to deserve publication in a research paper. Notice also that BB84 is the reference example in the ...


3

Application of Hadamard gates changes states $|0\rangle$ and $|1\rangle$ followingly: $\mathrm{H}|0\rangle = \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ $\mathrm{H}|1\rangle = \frac{1}{\sqrt{2}}(|0\rangle - |1\rangle)$ Identity operator does not change the state in any way, i.e. $\mathrm{I}|0\rangle = |0\rangle$ and $\mathrm{I}|1\rangle = |1\rangle$. Hence ...


3

There is one main key point in the description of your question: Is $s$ meant to be a classical secret or a quantum secret? If $s$ is meant to be a classical secret, then the answer is yes, but there is not really much quantum in the positive answer. If $s_A$, $s_B$, and $s_C$ are all $d$-state digits, then there is a simple construction that works in ...


2

Aaronson and Christiano proved the security of their scheme in an oracle model, where they assume the verifier has access to a membership oracle to some subspace $A$. In order to turn this into actual quantum money, it is "sufficient" to implement "such an oracle". How would one do that? And what is "such an oracle"? Well, the simplest question is to ...


2

Quantum key distribution (QKD) is a secure communication method that enables two parties to produce a shared random secret key known only to them, which can then be used to encrypt and decrypt messages. Quantum key distribution is only used to produce and distribute a key, not to transmit any message data. The algorithm most commonly associated with QKD is ...


2

I would start from this excellent intro course by Thomas Vidick and Stephanie Wehner, available in Edx. Then take a look at some classic papers: The one that started it all: https://core.ac.uk/reader/82447194. The one that brought a whole new approach: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.67.661 The one that simplified it somewhat: ...


2

I disagree. By no means is there a scarcity of quantum algorithms. Consider for example this review on Quantum Machine Learning. Therein the term qBLAS is contained for Quantum Linear Algebra Subroutines. This term describes all the quantum algorithms that exist for basic linear algebra tasks. Together with the (in)famous Grover Algorithm that gives a ...


2

This is an example of a controlled gate. It means that the gate is applied to the target qubit (the one with the gate on) when the control qubit (the one with the small circle on) is 1. Another example of a gate like this you might have seen is the CNOT gate, that applies an x gate to the target qubit when the control is 1. This gate works in exactly the ...


2

RSA is based on high computational complexity of integer factorization. In simple words you prepare two large prime numbers $p$ and $q$. These composed your private key which is used for decryption. The public key used for encryption is simply product $m = pq$. If you were able to factorize public key, you would get private key and break the cypher. Since ...


1

Quantum computation is a (reversible) unitary transformation and theoretically it does not require energy to perform, at all. In other words, the theoretical energy cost of quantum computation is zero. Theoretically, the energy is needed to erase information (see Landauer's principle), but unitary transformations do not erase information.


1

There absolutely is. In fact, even in classical, there is the notion of computational security against polynomial time quantum adversaries. This is the whole point of post-quantum cryptography. This would let us keep using existing, classical, technology, but hopefully be secure against quantum-powered eavesdropping.


1

As far as I know a cipher with random key cannot be broken, however, in classical realm it is problematic to distribute the key without being eavesdropped. Probably physical exchange of the key would be necessary which impractical for digital communication. As to break random key cipher is not possible according to theory, it is not possible to do so even ...


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

So first, let's define a bit your notations. I guess (correct me if I'm wrong) that you consider Bob honest, and that what you denote by $\Psi_{a_k,b_k}$ is the BB84 qubit in basis $\{0,1\}$ if $b_k = 0$, and in basis $\{+,-\}$ if $b_k = 1$, whose "value" bit is $a_k$, i.e.: $$\Psi_{a_k,b_k} = H^{b_k}X^{a_k}|0\rangle$$ Then, Bob will measure in basis $b'_k$...


1

These are two separate questions, so I will (try to) answer them separately as well. Concerning the (reduction of) privacy in remote or cloud computing. Without any alterations, the instructions for a quantum computation that is to be run on a remote computer can be seen by that remote computer. That is to say, if you want to conceal the computations that ...


1

I think there's some confusion here, so I'll try to explain the principle of QKD (Quantum Key Distribution) instead. Say Alice and Bob want to communicate in a secure fashion using symmetric encryption. To do so, they require a shared secret, a key. One of them generates it and he must somehow get it to the other person without an eavesdropper, say Eve, ...


1

I think that there are many interesting answers to your question, but I would like to point out what I personally find the most mesmerizing consequence of quantum theory to cryptography. One of the most fascinating quantum phenomena that has no classical counterpart is no cloning. This essentially means that if you don't have enough information about some ...


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