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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1answer
89 views

How do I efficiently implement a POVM using a fixed universal gate set and the ability to measure in the standard basis?

Let's say I am given a Hamiltonian \begin{equation} H = \sum_{i = 1}^{m} H_{i}, \end{equation} where $H$ acts on $n$-qubits, and each $H_{i}$ acts non-trivially on at most $k$ qubits. The eigenvalues ...
2
votes
1answer
67 views

How to construct a non-trivial (non-projective) POVM measurement example?

We know that generalized (POVM) measurement is defined by matrices $M_i$ which are Positive semidefinite Add up to a unit matrix, $\sum_i M_i = \mathbb{I}$ and the probability of obtaining outcome $...
3
votes
1answer
74 views

How do you embed a POVM matrix in a Unitary?

In QuantumKatas Measurement Task 2.3 - Peres-Wooter's Game, we are given 3 states A,B and C. We construct a POVM of these states. But how do we convert that POVM into a Unitary that we can apply. ...
3
votes
1answer
129 views

Why are POVMs useful? Are they just an axiomatic way to define measurement?

I know the definition of projective measurement, generalized measurement, POVM. I understand the usage of generalized measurement for the reason that it can model experiments "easier" (for example ...
4
votes
2answers
162 views

Give an explicit example of a $d = 4$ SIC-POVM

For $q=e^{2 \pi i/3}$, the set of $d^2$ vectors ($d=3$) \begin{equation} \left( \begin{array}{ccc} 0 & 1 & -1 \\ 0 & 1 & -q \\ 0 & 1 & -q^2 \\ -1 & 0 & 1 \\ -q &...
4
votes
2answers
227 views

Are three POVM measurements on a single qubit physically realizable?

In Nielsen and Chuang Quantum Computation and Quantum Information book section 2.2.6, a POVM of three elements are used to measure a single qubit in order to know for sure whether the state is $|0\...
3
votes
2answers
93 views

Confusion about the relation between POVMs and projective measurements

I'm a little confused about the terminology of measurement. So say that we have the single qubit state $|\phi \rangle=c_0|0\rangle+c_1|1\rangle$. If we perform the projective measurement $P_0=|0\...
1
vote
1answer
104 views

Does the dilation in Naimark's theorem produce a state?

A POVM, as defined for example in (Peres and Wooters 1991), is defined by a set of positive operators $\mu(a)$ satisfying $\sum_a \mu(a)=\mathbb 1$. We do not require the $\mu(a)$ to be projectors, ...
4
votes
2answers
152 views

POVM three-qubit circuit for symmetric quantum states

I have been reading this paper but don't yet understand how to implement a circuit to determine in which state the qubit is not for a cyclic POVM. More specifically, I want to implement a cyclic POVM ...
11
votes
1answer
880 views

What is the Helstrom measurement?

I have been reading the paper Belief propagation decoding of quantum channels by passing quantum messages by Joseph Renes for decoding Classical-Quantum channels and I have crossed with the concept of ...