Questions tagged [povm]

For questions related to positive-operator valued measures (POVMs), that is, sets of positive semi-definite operators summing to the identity matrix.

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How does the extremality of a POVM reflect on its Naimark dilation isometry?

Let $\mu:\Sigma\to\mathrm{Pos}(\mathcal X)$ be some POVM, with $\Sigma$ the finite set of possible outcomes, and $\mathrm{Pos}(\mathcal X)$ the set of positive semidefinite operators on a finite-...
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Is there some notion of work associated with performing a measurement?

Let a measurement be described by POVM elements $M_i$ such that probability $p(i) = Tr[\rho M_i]$ for some state $\rho$. I want to know whether there is some notion of work associated with such ...
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What does it mean to take the maximum over all POVMs?

What does it mean to take the maximum over all POVMs (in the definition of accessible information for example) ? The set of POVMs is infinite, how can we be sure that the maximum is attained by one of ...
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What are examples where the quantum discord is achieved by a non-projective POVM?

Consider the (asymmetric) quantum discord, defined as (borrowing notation from Eq. 4.13c of Zurek's review): $$\mathcal D(\mathcal S:\mathcal A) = I(\mathcal S:\mathcal A) - \chi(\rho_{\mathcal A}),$$ ...
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POVM construction with little input information

Let $E$ be part of a POVM $M = \{E,I-E\}$. Suppose that I know that $E = f(\rho_1, \rho_2)$. Suppose also that those two states are provided but we only know their type (dimension) and we also know $f$...
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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 ...
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How to define POVM measurement operators for a composite quantum state

I have an evolved quantum composite state $\hat{\rho}^{\otimes{N}}$ that I retrieved from a quantum channel $\mathcal{E}$, Now I do know how to define a POVM for the evolved states $\hat{\rho}$ that ...
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The POVM representation for 1 qubit using multiqubit Clifford group

I am studying the multiqubit Clifford group with the aim of utilizing it to generate a POVM for a single qubit. Similar to how the SIC-POVM is generated using four matrices, I aim to accomplish a ...
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When does a Hamiltonian result in the construction of an IC-POVM?

Consider a generic $d_A$-dimensional quantum system $A$, for example made of $n$ qubits. Now consider a second higher-dimensional system $B$, with $d_B=d_A^2$, and the quantum map $$ \rho_A \...
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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 ...
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How can we derive the form of POVMs on a subspace from a projective measurement on a larger space?

Suppose we have the Hilbert space $\mathcal{H}_{0}$ describing the states of the system $s$, and the Hilbert space $\mathcal{H}_{e}$ describing the states of the environment. I have seen that [1][2], ...
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Neumark dilation for qubit tetrahedron SIC-POVM

I would like to know if an analytic solution is known for the Neumark dilation of the qubit tetrahedron SIC-POVM defined by $$ M_0= \frac{1}{4\sqrt{3}} \Big( \sqrt{3}I + X +Y +Z \Big), \qquad M_1= \...
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What does it mean "the N uses of classical-quantum channel"?

I was reading a paper Quantum Polar codes by Mark M. Wilde, where he discusses the N uses of the channel in the classical-quantum channel setting. What does he mean by "multiple channel uses"...
Najeeb Ullah's user avatar