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Jul
24
comment Derivation of minimum uncertainty from Squeezed Coherent State
I think you can figure it out with a hint or two. For any operator $M$ the expectation value of the operator is: $\langle M \rangle = Tr[\rho M]$ The commutation relation between canonical position and momentum operators, if we set $\hbar=1$, is $ [Q_0 ,P_0]=i$
Jul
21
comment How much computation can be performed in given time using given energy inside a ball of given volume?
This paper may be of interest: arxiv.org/abs/quant-ph/9908043
Jul
12
awarded  Commentator
Jul
12
comment Why does a measurement on one qubit force another one into a given state in Simon's algorithm?
I have opened a chat for us to continue this conversation, as this is becoming an extended discussion. Please see my above post.
Jul
12
comment Why does a measurement on one qubit force another one into a given state in Simon's algorithm?
Let us continue this discussion in chat.
Jul
12
comment Why does a measurement on one qubit force another one into a given state in Simon's algorithm?
(1) The eigenstates of the observable are not the $\psi_b$s, they are the computational basis states of the second register ((2) the computational basis is the set $\{|\{0,1\} \rangle\}$. The reason you only get $\psi_b$ is because of the specific structure of $\psi_a$.
Jul
12
comment Why does a measurement on one qubit force another one into a given state in Simon's algorithm?
Indeed, given that we are measuring $\psi_a$ in the computational basis, the only possible outcome is $\psi_b$. This is most readily observed by noting that $\psi_a$ can be expressed as a superposition of exclusively states of the form $\psi_b$.
Jul
12
comment Why does a measurement on one qubit force another one into a given state in Simon's algorithm?
Certainly there are vectors in the Hilbert space that it would be impossible to observe given $\psi_a$. Take again the bell state example, we should never expect to measure the state $|0\rangle|1\rangle$. Additionally, it is assumed that the measurement on the second register is made in the computational basis, so we should not expect to find the second register in a superposition of computational basis states (although that constraint need not be applied to the first register, since only the second register is being measured)
Jul
11
revised Bounds on dimension of a purification?
added 7 characters in body
Jul
11
answered Why does a measurement on one qubit force another one into a given state in Simon's algorithm?
Jul
11
answered Bounds on dimension of a purification?
Apr
10
answered What type of Quantum Gate is this
Apr
9
comment Is there a simple expression for the coherent information of a Pauli channel?
By $H(\Lambda)$ I mean the entropy of the Choi matrix. So in the case of a Pauli channel $H(\Lambda)=-\Sigma P_i Log(P_i)$ A couple of the places it seems like this is assumed to be true are: here here and here
Apr
8
asked Is there a simple expression for the coherent information of a Pauli channel?
Feb
20
awarded  Scholar
Feb
20
accepted Is a quantum channel well behaved under a perturbation of its Choi matrix?
Feb
18
asked Is a quantum channel well behaved under a perturbation of its Choi matrix?
Jan
12
comment Topological entanglement entropy only defined for a system in the ground state?
Here is a free version of the paper linked above (arxiv.org/abs/0704.3616)
Nov
23
revised Trace of the number operator in second quantization
corrected mathematical mistakes
Nov
23
revised Trace of the number operator in second quantization
added 129 characters in body