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Quantum computers can run classical computations using exactly the same algorithms, and hence have the same running time in terms of scaling. For example, if you look at shor’s algorithm, a major component of that is modular exponentiation, but nobody ever draws the circuit because they just say “use the classical algorithm”. In terms of absolute running ...


Yes, since the trace norm is the sum of the absolute value of the singular values, and the singular values can be found for each of the $a$ blocks independently.


Your mistake is that you assume that $\rho$ and $\sigma$ are classical-quantum in the same classical basis on $X$. However, there is no need to do so -- all which is necessary is that there exists such a basis, which can however depend on the state. As soon as you choose a different classical basis for the two states, your argument breaks down.


You seem to be mixing two very different concepts here. Quantum cloning is talking about the absolute limits of what is theoretically possible in a perfect world. In this absolute theoretical limit, yes we can derive how well quantum cloning can work, and we also know that classical cloning is nominally perfect. There is then a separate question of how well ...


In quantum information theory, the standard way to obtain what it is called reduced density operator from a quantum system composed by several quantum states is to use the so-called partial trace operation. For the case where there are two quantum states, $\rho^{AB}$ can be reduced to $\rho^A$ and $\rho ^B$ in the following way: $\rho^A=tr_B(\rho^{AB})$ $\...


Classical registers are typically used for capturing measurement results, and may also be used for conditionally applying quantum operation. See: https://github.com/Qiskit/openqasm/blob/master/spec/qasm2.rst Given the problem you described, one approach would be to have a classical program that iteratively: 1) defines and executes a quantum circuit on a ...

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