7
votes
Accepted
How to find the density operator of two joint systems given the density operator of the individual systems?
This is not possible in general, as both density matrices could be the reduced density matrices of several joint density operators, see e.g. here and here.
The reduced density matrices determine the ...
- 6,502
6
votes
Accepted
Understanding the probability of measurement w.r.t. density matrix
This is not derived, this is the Born rule or the Lüders-von Neumann measurement rule. Either way, it is a fundamental axiom of quantum mechanics that measurements work this way. See e.g. this, this ...
- 118k
5
votes
Are two localized single-photon states always invariant under the particle exchange?
When you write a state like $|H\rangle_a \otimes |V\rangle_b = \hat{a}^{\dagger}_H\hat{b}^{\dagger}_V|\mathrm{vac}\rangle$ you're using the formalism of second quantization. In this formalism the ...
- 423
3
votes
Are two localized single-photon states always invariant under the particle exchange?
The question is whether the photons are distinguishable in another degree of freedom. If so, then the state must not be complete symmetric.
In this case, the photons are distinguished by their ...
- 3,538
2
votes
Accepted
Does Quantum Key Distribution (QKD) guarantee perfect secrecy?
In quantum key distribution there is no message in the ordinary sense of the word. That is, no information is conveyed from A to B. Rather, it is a method whereby a random classical bitstring can be ...
- 53.1k
2
votes
Accepted
How is the measurement of the $Z_0Z_2$ error syndrome realised by these two circuits?
Two points are important to this:
The controlled Z gate is symmetric: It is irrelevant which of the qubits you call the "control" and which the "target". So you can put the Z on ...
- 18.7k
2
votes
Accepted
Gate operations for controlling Cat States
One way to do this approximately is with the displacement operator:
$$
D(i\beta) = \mathrm{exp}[i\beta(\hat{a}+\hat{a}^{\dagger})]
$$
where $\beta$ is assumed to be real. Applying this operator on the ...
- 423
1
vote
Accepted
How do physicist keep entangled particles entangled while moving them/storing them?
When experiments are performed on entangled pairs: Photons are the most common choices for entangling quanta, and Bell tests are common uses of entangled pairs. Generally, the entangled photons are ...
- 139
1
vote
Distinguishing between two sets of quantum states
You have to specify whether there is freedom in choosing the measurement. In general, the optimal probability to discriminate between two states $\rho_1,\rho_2$ with priors $p_1,p_2$ is $\frac12(1+\|...
- 13.6k
1
vote
Accepted
Solving Buck-Sukumar model for nonlinear cavity
The Hamiltonian commutes with total number of excitations defined as $\hat{n} = \sigma_z + \hat{a}^\dagger \hat{a}$. Therefore, the eigenfunctions can be found using an ansatz
\begin{equation}
|\psi\...
- 537
1
vote
Monotonicity of Relative Entropy with Respect to Temperature
Is $f$ an nondecreasing function?
No, $f$ need not be a non-decreasing function.
As a counterexample, consider e.g. two qubits with a Hamiltonian
$$
H = E_0 \lvert 01\rangle\langle01\rvert +
E_1 \...
- 18.7k
1
vote
Odd dimensional Density Matrix construction with Pauli matrices
A 3×3 hermitian matrix may be represented by a real-coefficient linear combination of the eight su(3)-basis Gell-Mann matrices,
$$
\lambda_1 = \begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ ...
- 55.4k
1
vote
Accepted
Derivation of QFT product formula
By binary decomposition, we define $y\equiv\sum_{l=0}^{n-1} y_l 2^{-l}$, where $|y\rangle=|y_0...y_{n-1}\rangle$.
Putting together your definition of the quantum Fourier transform with this binary ...
- 538
1
vote
Equivalence between magnetically perturbed Toric Code and 2D Transverse Field Ising model and Dispersion of 1 Quasiparticle spectrum?
For the Hamiltonian you cited, the toric code is only dual to the 2d transverse field Ising model (TFIM) in the limit $J_s \to \infty$. Otherwise, they are not dual. The reason is simple: under the ...
- 2,633
1
vote
Accepted
Why does one need a low resolution when trying to tell $|0\rangle^{\otimes n}$ and $|1\rangle^{\otimes n}$ apart in a coarse grained measurement?
To get more intuition about what is happening, let's start with $n=1$.
(n=1)
The observable $S_z$ you defined will be just $S_z=\sigma_z$ and we have
$$
S_z = \left | 0 \right \rangle \left \langle 0 \...
- 371
1
vote
Accepted
How is continuous variable quantum key distribution safe against tapping some photons?
In CV-QKD, we send the signal at low power. At that levels, the signal is masked by noise of quantum nature (e.g. Shot Noise i.e. uncertainty principle of the quadratures). This noise protects the ...
- 36
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