# Tag Info

Accepted

### What is the Helstrom measurement?

The Helstrom measurement is the measurement that has the minimum error probability when trying to distinguish between two states. For example, let's imagine you have two pure states $|\psi\rangle$ ...
• 48.2k
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### What is the relation between POVMs and observables (as Hermitian operators)?

One way of looking at the relationship between POVMs and observables arises from identifying their counterparts in the theory of probability of which quantum mechanics can be thought of as an ...
• 14.8k
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### Are three POVM measurements on a single qubit physically realizable?

Three outcomes amounts to more than one bit if the outcomes are all deterministic, and give you information about the original qubit. But suppose I have a coin (that is either heads or tails). I ...
• 349

### What is an example of a measurement that is LOCC but not separable?

Such an example is given in Bennett et al., Quantum Nonlocality without Entanglement, Phys. Rev. A. 59, 1070 (1999).
• 5,097
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### What are examples of extremal non-projective POVMs?

It is indeed possible to have extremal, non-projective POVMs. Examples can be drawn from SIC-POVMs, as suggested in a comment. For example, as mentioned in the Wiki page, the only possible SIC-POVM in ...
• 19.6k
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### Does a basis of maximally entangled states exist for two-qubit or two-qutrit system so that the density matrices of the basis states don't commute?

No such (orthonormal) basis can exist. An orthonormal basis $\{|\psi_i\rangle\}$ requires $\langle \psi_i | \psi_j \rangle = 0$ for $i\neq j$, and so clearly \begin{align} [\rho_i, \rho_j] &= |\...
• 5,067
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• 6,013

### What is the relation between POVMs and projective measurements?

POVMs are more general than projective measurements. Thus, every projective measurement is also a POVM, by choosing $E_i=P_i$.
• 5,097
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• 6,013