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In the paper titled "Experimental Implementation of the Quantum Baker’s Map" by Weinstein et al. (Phys. Rev. Let. 89 (2002)), the author says something like

[...] the pseudopure state corresponding to the state $ \left |000 \right \rangle$.

But, what is a pseudopure state in general ? how it is different from a pure state ? and why do they call the state $ \left |000 \right \rangle$ pseudopure, isn't it a pure state ?

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It is a state that is the starting point for a NMR quantum computation.

It is the effective pure state whose physical action is the same as the pure state.

To obtain a pseudo pure state:

  1. temporal averaging

  2. spatial averaging

  3. logical labeling

  4. cat benchmark

For example, temporal averaging[12] needs 2n 1 (n is the quantity of qubits in system) permutations, and then adds up all the results to get the pseudopure state. Its experimental steps will increase exponentially with n, which makes the experiment become more complicated. On the other hand, the S/N ratio decreases exponentially with n. For spatial averaging[13], it uses a few PFG (pulse field of gradient) in the experimental scheme, which reduces the S/N ratio. Therefore, if a method not only reduces the complication, but also increases the S/N ratio, it is an ideal method no doubt. Recently, Vandersypen et al.[7,17] have proposed an idea for preparing pseudopure state in the multi-qubit system, which we called “CNOT gates combination”. That idea is analogous with temporal averaging[12]. Both use the summation of multi-experiment results to obtain the pseudopure state. However, CNOT gates combination uses less steps in experiment than temporal averaging. That idea takes CNOT gate, the most frequently used two-qubit gate in quantum computation circuit, as the basic element to prepare pseudopure state. Vandersypen et al. have realized 5-qubit order-finding[17] and 7-qubit Shor’s factoring algorithm[7] based on the pseudopure state obtained by that method.

Please see here:

https://link.springer.com/article/10.1360/02tb9405

A pseudo-pure state is a highly mixed state.

Please see here:

https://arxiv.org/pdf/quant-ph/0012038.pdf

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  • $\begingroup$ Thanks for the answer; however, it is still not clear to me what is the difference between a pure and a pseudopure state ? $\endgroup$ – onurcanbektas Jun 27 at 17:25
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    $\begingroup$ @onurcanbektas pseudo pure states are highly mixed states. $\endgroup$ – Árpád Szendrei Jun 27 at 17:34
  • $\begingroup$ what is a mixed state ? I know what is (statistical) mixture of states, but I don't know mixed state. $\endgroup$ – onurcanbektas Jun 27 at 17:36
  • $\begingroup$ I googled it; a state choosen from a mixture of states. But if so, why are we not calling $\left |000 \right \rangle$ a mixed state ? Also, this is a pure state, how on Earth we are talking whether it is highly or not a mixed state. $\endgroup$ – onurcanbektas Jun 27 at 17:40
  • $\begingroup$ @onurcanbektas "A pure state is what one would naturally call a state of a system. Now imagine you have a qubit in a certain state, say the equal superposition of both its computational basis states, which is 2√2(|0⟩+|1⟩). Then measure it in the computational basis. What state do you get as a result? If you read the measurement result, you know which state you have. But if you discard that result, then you don't know which state the system is in (either it is in |0⟩ or in |1⟩). This is different from the superposition you had before (which was a pure state): It is a mixed state." $\endgroup$ – Árpád Szendrei Jun 27 at 17:48

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