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# 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.

13 questions with no upvoted or accepted answers
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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-...
• 25.4k
56 views

### 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 ...
• 191
72 views

### 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 ...
• 127
65 views

### 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): $$\mathcal D(\mathcal S:\mathcal A) = I(\mathcal S:\mathcal A) - \chi(\rho_{\mathcal A}),$$ ...
• 25.4k
46 views

### 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 $f$...
• 2,337
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 ...
• 21
134 views

### 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 ...
1 vote
23 views

### 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 ...
• 11
1 vote