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votes
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Weak Schur sampling and state distinguishability
Consider the task of distinguishing between the following two $n$ qubit quantum states.
$$ \rho = \frac{\mathbb{I}}{2^{n}}.$$
$$ \sigma = \frac{1}{2^{n/2}}\sum_{x \in \{0, 1\}^{n/2}} |x\rangle\langle x| \otimes |x\rangle\langle x|.$$
We can see that…
BlackHat18
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6
votes
1 answer
Random quantum states and Schur-Weyl duality
Consider the following density matrix over $n$ qubits, with $C$ being a single qubit operator:
$$
\rho_{n} = \int_{C \sim \text{Haar}} \big(C|0\rangle\langle0|C^\dagger\big)^{\otimes n} dC.
$$
Let's say I measure the qubit with respect to orthogonal…
BlackHat18
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1 answer
What does the partial trace of $|W\rangle$ states represent physically?
Given the W-state $|W\rangle = |001\rangle + |010\rangle + |100\rangle$, where $|ijk \rangle $implies $|i\rangle_A \otimes |j\rangle_B \otimes |k \rangle_C$, the partial trace over first qubit turns out to be
$$Tr_A\left[|W\rangle \langle W| \right]…
User101
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6
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1 answer
Does a photonic quantum computer control a single photon?
Does a photonic quantum computer control a single photon and use it to represent a single qubit?
I think ion trapped quantum computers use a single ion to represent a qubit. I would like to know how a photonic quantum computer represents each qubit.
david
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6
votes
1 answer
BB84 Protocol Alice Choice to Bob
The image is taken from this link.
Here Alice is using random bases to encode 0 or 1. After the process is completed, Bob has similarly polarized photons as Alice. These polarization can be any of the $\lvert 0 \rangle , \lvert 1 \rangle, \lvert +…
QuestionEverything
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6
votes
3 answers
Why does a quantum operation being trace-preserving imply that $\sum_k E_k^\dagger E_k=I$?
I am reading Nielsen Chuang Chapter 8. They say that if a quantum operation is trace-preserving, then
\begin{equation}
Tr\left(\sum_k E_k^{\dagger}E_k \rho\right) = 1
\end{equation}
which I understand. They however then claim that as this is true…
alpha
- 109
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6
votes
1 answer
How to show mathematically the equivalency between Ising Model and QUBO?
It is said that the Ising Model using spin variables $s ∈ \{−1, 1\}$
$$H(s)=\sum_{i}h_is_i+\sum_{i
26118in
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6
votes
3 answers
When can pairs of states be transformed into other pairs of states via unitary mapping?
The states $|+\rangle, |-\rangle$ can be mapped to $|0\rangle, |1\rangle$ by a simple rotation.
But if I now have other states ($|\psi_0\rangle, |\psi_1\rangle$) which are not orthogonal, does a unitary transformation of these states to two other…
Johny Dow
- 157
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6
votes
1 answer
Oblivious Amplitude Amplification & Eigenstate decomposition
Looking at the oblivious AA (OAA) : https://docs.microsoft.com/en-us/azure/quantum/user-guide/libraries/standard/algorithms
I am trying to figure out the eigendecomposition of Q, which leads to below. Any help or suggestion on how to derive these…
John Parker
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6
votes
1 answer
Do entangled measurements across multiple copies help in state distinguishability?
Consider two density matrices $\rho$ and $\sigma$. The task is to distinguish between these two states, given one of them --- you do not know beforehand which one.
There is an optimal measurement to distinguish between these two states --- the…
BlackHat18
- 1,313
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6
votes
1 answer
Implement the classical shadow coding error?
I'm trying to reproduce the basic method of classical shadow, which is based on the tutorial of pennylane. However, I've met some realization problems here when I finish reading the tutorial of pennylane, and trying to finish the method myself, just…
narip
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6
votes
2 answers
Quantum communications and "knowledge" of receiving a qubit
Question from a computer scientist (not a physicist).
Imagine two nodes on a quantum network.
Alice sends Bob a qubit in some state of superposition over a quantum channel.
Is Bob able to sense that he's received a qubit without measuring it?
If so,…
6
votes
1 answer
What does it mean for a channel to be independent of the input state?
A 2007 paper shows how to construct quantum channels on finite-dimensional Hilbert spaces
$$\sigma=\Phi(\rho)=\sum_i K_i \rho K_i^\dagger,\qquad \sum_i K_i^\dagger K_i=\mathbb{I}$$ for which $\Phi(\rho)=\sigma$ is independent of $\rho$. This seems…
Quantum Mechanic
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6
votes
3 answers
Interpretation of the unitaries involved in the eigenvalue decomposition of a density operator
If $\rho=\sum_{i}p_{i}|\psi_{i}\rangle\langle \psi_{i}|$, this ensemble doesn't require $\langle \psi_{i}|\psi_{j}\rangle$=0. Given that $\rho$ is positive semi-definite, by the spectral theorem it can be expressed in diagonal form…
GaussStrife
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6
votes
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Do individual qubits on IBM quantum processors share the same control unit?
I want to investigate the maximum possible parallelism of quantum operations on a specific IBM device (such as the latest heavy-hex architecture), which requires a basic knowledge of their control electronics. I want to know whether individual…
jojo
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