# Tag Info

Accepted

### Generating random, but non-uniform state

Rejection sampling is a good fit and works without any changes, simply by plugging the desired distribution $p(\psi)$ into the standard algorithm. Let$^1$ $M:=\max_{\psi\in\mathbb{CP}^1} p(\psi)$. To ...
Accepted

### How do I get correct measurement probabilities in ZX calculus?

OK, I made two mistakes. Both were corrected by a closer reading of the paper "Simulating quantum circuits with ZX-calculus reduced stabiliser decompositions". First, as was pointed out by ...

### Simultaneous measurements and Bell basis measurements to estimate $\lvert\text{Tr}(\sigma \rho)\rvert^2$ in Huang et al. paper

Here, "simultaneous measurement" of an observable does not refer to simultaneously in time, but rather the ability to estimate several observables from the same measurement setting acting on ...
Accepted

### Conditional expectation for Haar random states

Intuitively, that's the case: the vector being random, there is no reason to prefer $|0\rangle$ over $|1\rangle$ on the first qubit. I don't think it requires to compute some integrals other than ...
Accepted

### Survival probability quantum circuit

We can calculate this survival probability $P(t) = |\langle \psi | e^{-i \mathcal{H}t} | \psi \rangle|^2$ in two ways. The first corresponds to the so-called Hadamard test, as shown in the figure ...
Accepted

### Why is $|P_0- P_1|=1$?

If you are promised that you will receive a qubit in a classical state and you also know the basis it is in, then it is certain that when you perform a measurement in that basis, the resulting ...
Accepted

### How to write post-measurement states when the measurement apparatus measures one of two observables?

Let's assume that that both observables $A$ and $B$ have projectors $P^{A/B}_i$. I'm going to assume that the set of outcomes for the two is the same (and therefore, implicitly, that I don't know ...
Accepted

### How to get exact measurement probabilities when having intermediate measurements with Qiskit?

To do what you want in Qiskit, you could replace each measurement operation in your circuit by a simple call to the Statevector.probabilities(qargs) method, where ...

### Stabilizer States - Calculating measurement probabilities with the rank of the stabilizer table's X-block

The issue is that numpy.linalg.matrix_rank is assuming you want the rank over real numbers, when actually you want the rank over integers modulo 2. For example, ...

### How do you find the possible measurement values of an observable?

Unfortunately, some parts of this question are unclear to me as currently written. I will do my best to try and answer, in the sense of addressing some aspects of your below statement Attempt at ...
1 vote

### How to compute marginal probabilities of Alice's qubit (in density operator language)?

Using pure states and kets, as you described, you compute the marginal probabilities by computing the squared norm of the projection on the states you're interested in. In this case, this means ...
1 vote

### How to compute marginal probabilities of Alice's qubit (in density operator language)?

Let's first see how projective measurements work in 'density operator language'. If you perform a measurement on your density operator $\rho$, corresponding to a set of projective measurement ...
1 vote

### Why are probabilities represented with alpha^2 and beta^2?

The issue is that coefficients $\alpha$ and $\beta$ are complex numbers representing both probability of measuring certain basis state and so-called quantum phase. Note that the phase can be used for ...
1 vote

### How to get exact measurement probabilities when having intermediate measurements with Qiskit?

You can use save_probabilities() function to save the measurement outcome probabilities anywhere in your quantum circuit when using ...
1 vote

### How to get exact measurement probabilities when having intermediate measurements with Qiskit?

Alternatively, you can use Quirk for small circuits. Especially it's chance and amplitude displays are useful for visualizing measurement probabilities.
1 vote

### Simultaneous measurements and Bell basis measurements to estimate $\lvert\text{Tr}(\sigma \rho)\rvert^2$ in Huang et al. paper

I am not sure what you mean with Bell measurement (haven't read the paper in detail). Maybe this demo can help understand the concept of simultaneous measurement in the Pauli basis. This is a general ...
1 vote
Accepted

### Sum of probability in non-orthogonal basis

In Quantum Computing, a measurement projects a vector onto an eigenspace of an observable $A$, which is an Hermitian matrix. Since it is Hermitian, its eigenvectors form an orthonormal basis of the ...

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