# Tag Info

Accepted

### Significance of The Church of the Higher Hilbert space

The church of the larger (or higher, or greater) Hilbert space is just a trick that some people like (myself included) for rewriting some operations. The most general operations that you can write ...
• 60.7k

### If all quantum gates must be unitary, what about measurement?

Unitary operations are only a special case of quantum operations, which are linear, completely positive maps ("channels") that map density operators to density operators. This becomes obvious in the ...
• 2,457

### Twirling Quantum Channels: Pauli and Clifford Twirling

Definitions Denoting the Haar measure of some function $f\left(x\right)$ over $d$-dimensional unitaries as $\int_{\mathrm U\left(d\right)}f\left(x\right)d\mu\left(x\right)$, twirling some arbitrary ...
• 3,756
Accepted

### How does the vectorization map relate to the Choi and Kraus representations of a channel?

One way to understand the relationship between the Choi representation of a channel and its possible Kraus representations is to use the vectorization map. Suppose that we have two finite-dimensional ...
• 6,227

### If all quantum gates must be unitary, what about measurement?

Short Answer Quantum operations do not need to be unitary. In fact, many quantum algorithms and protocols make use of non-unitarity. Long Answer Measurements are arguably the most obvious example of ...
• 26.3k
Accepted

### What is the "complementary map" of a channel with given Kraus decomposition?

Let's start by finding a complementary channel for any channel given by a Kraus representation $$\Phi(X) = \sum_{k=1}^n A_k X A_k^{\dagger}.$$ To make the necessary equations clear, let us assume ...
• 6,227

### Counterexamples in quantum information theory

Quantum Channels Quantum channels: general properties Not every positive map is completely positive. One may argue that this is the mother of all counterexamples in quantum information: the ...

### If all quantum gates must be unitary, what about measurement?

At risk of going off-topic from quantum computing and into physics, I'll answer what I think is a relevant subquestion of this topic, and use it to inform the discussion of unitary gates in quantum ...
• 1,097

### What is the "Stinespring Dilation"?

Not exactly sure what you find confusing, but the ultimate need for Stinespring dilation theorem is that in quantum mechanics the dynamics is in general defined by a completely positive trace ...
• 431