Skip to main content

Questions tagged [projection-operator]

A projection operator is one which when acts upon a quantum state (which is an element of a Hilbert space), "projects" it onto a subspace or onto another element of the same Hilbert space.

17 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
8 votes
0 answers
194 views

Optimal estimation of quantum state overlap - Circuit implementation?

I've been reading this paper, but don't understand what their optimal method really is, and how it can be realized as a quantum circuit. The paper mentions the "Schur transform" which has a ...
Loic Stoic's user avatar
4 votes
0 answers
133 views

Analyzing the composition of a channel with its adjoint in relation with an identical composition obtained for the channel's complement

Let us consider two quantum channels $\Phi:M_d\rightarrow M_{d_1}$ and $\Phi_c:M_d\rightarrow M_{d_2}$ that are complementary to each other, i.e., there exists an isometry $V:\mathbb{C}^d\rightarrow \...
mathwizard's user avatar
4 votes
0 answers
54 views

If $\rho \approx_{\varepsilon}\sigma$, how to find $\Pi\rho\Pi$ to ensure that $\text{supp}(\Pi\rho\Pi)\subset\text{supp}(\sigma)$?

Let $\rho$ and $\sigma$ be positive semidefinite operators with trace less than or equal to 1. Let $\rho\approx_{\varepsilon}\sigma$ i.e. they are close in some distance, such as the trace distance. ...
lolwut's user avatar
  • 41
4 votes
0 answers
74 views

Can we characterise how correlated the expectation values associated with a pair of observables are?

Consider a state $\rho$ and two observables $P$ and $Q$. Is there a good way to characterise how correlated the associated expectation values are? Be it in terms of mutual information or something ...
glS's user avatar
  • 25k
3 votes
0 answers
155 views

A question on a subset of projectors onto symmetric subspace

Use $\text{perm}_t$ to denote the set of all permutations among $t$ items. For any particular subset $S\subseteq\{0,1\}^n$ and any $\sigma\in \text{perm}_t$, we define \begin{align} P_S(\sigma) = \...
BlackHat18's user avatar
  • 1,313
3 votes
0 answers
144 views

Increasing the von Neumann entropy despite the measurement?

Background Assume we have a density matrix $\rho$ of a sub-ensemble. However, we have an imperfect measuring instrument. While it does perform a measurement, we do not know exactly when it performs ...
More Anonymous's user avatar
2 votes
0 answers
101 views

Mutual information of shared state is larger than expectation values

Im trying to prove the following identity for a special case: Alice and Bob share the Bell state \begin{align*} |\psi\rangle = \frac{1}{\sqrt{2}}(|00\rangle+|11\rangle). \end{align*} Consider the ...
user27450's user avatar
2 votes
1 answer
191 views

Qiskit implementation for projecting a hermitian operator and finding its eigenvalues

I'm brand new to quantum computing and have been learning Qiskit for a few weeks now. I am attempting to find the number of 0 eigenvalues of the following operator: $$ T = PHP$$ where $P$ is a ...
pokerfacegoatee's user avatar
2 votes
0 answers
105 views

Distinguishing $n$ pure states in an $n$ dimensional Hilbert space

Suppose we have $n$ pure states in an $n$ dimensional Hilbert space, and we would like to distinguish them using POVM or PVM. We get any one of the pure states with equal probability, and we may set ...
Stan's user avatar
  • 21
2 votes
0 answers
179 views

Applying projectors with mid-circuit measurements

I am trying to apply a non-unitary projector (see image) to my two-qubit quantum circuit using mid-circuit measurements. $$ \begin{pmatrix} 0 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 &...
edlothia's user avatar
1 vote
0 answers
56 views

Construct of a quantum circuit for the projection $|0\rangle\langle0| + |1\rangle\langle1| $ and its generalizations

We can construct a projection over $|0\rangle \langle 0|$ using a quantum circuit with two qubits via the Hadamard test circuit $$U = H_1 X_2 CZ_{1,2} X_2 H_1 X_1\,, \tag{1}$$ and by performing ...
incud's user avatar
  • 701
1 vote
0 answers
32 views

How is implemented the hamiltonian simulation of Hermitian operator multiplied by projection

The article "Quantum Topological Data Analysis with Linear Depth and Exponential Speedup" (Ubaru et al) discusses the implementation of the Hamiltonian $\Delta_\Gamma$, named the ...
incud's user avatar
  • 701
1 vote
0 answers
50 views

Motivation behind POVM and projective measurement

This is in reference to Quantum Computation and Quantum Information by Michael A. Nielsen and Isaac L. Chung [page 90, 92]. Any POVM elements $E_{m}$ are defined as $E_{m} = M_{m}^{\dagger}M_{m}$. A ...
Physkid's user avatar
  • 520
1 vote
0 answers
83 views

Can you project on an orthogonal basis for a multipartite system using only local measurements and classical communication?

Say Alice possesses one qubit, and Bob two, and that the joint state is $|\psi_{A, B_1, B_2}\rangle = \alpha|n_1\rangle + \beta |n_2\rangle$, where $|n_1\rangle$ and $|n_2\rangle$ are orthonormal ...
Abelaer's user avatar
  • 11
1 vote
0 answers
101 views

Prove that the twirling operation on a channel gives a decomposition $\int dU\, U^\dagger\mathcal E(U\rho U^\dagger)U=\alpha P+\beta Q$

The twirled operation of a quantum channel $\mathcal E$ is defined as \begin{align} \mathcal E_T(\rho) &= \int dU U^\dagger \mathcal E(U \rho U^\dagger)U, \end{align} where the integral is over ...
Michael.Andy's user avatar
1 vote
0 answers
116 views

why Hamiltonian can be expressed by sum of outer product in two level systems?

I can not figure out why Hamiltonian can be like this. Does H should be kinetic energy puls potential energy? Your help would be highly appreciated.
Ironman1965's user avatar
0 votes
0 answers
12 views

relationship between helstrom operators acting on different pairs of quantum states

Let $\rho_1, \rho_2, \rho_3, \rho_4$ be arbitrary single-qubit density matrices. Let $A$ be an Hermitian operator and its spectral decomposition as $A = \sum_i \lambda_i \lvert i \rangle \langle i \...
user185671631's user avatar