Redundant implementations of phase damping channel

[viathor]

Description of the issue

We currently have two implementations of the phase damping channel: cirq.PhaseDampingChannel and cirq.PhaseFlipChannel. They implement the same channel, but use different parametrization. Also, PhaseDampingChannel fails to provide _mixture_ (even though it is unital and hence admits a mixed-unitary representation).

I propose to combine the two channel classes, but keep all existing factories. The constructor of the new class would have to support both parametrizations, but factory functions would each work with one (i.e. as it is presently). This entails deprecating one class name and keeping all function names. The two functions are useful as a convenient interface to the two popular parametrizations of the channel.

How to reproduce the issue

In [35]: cirq.has_mixture(cirq.phase_damp(0.1))
Out[35]: False

In [36]: cirq.has_mixture(cirq.phase_flip(0.1))
Out[36]: True

After the fix both calls above should return True.

Cirq version
You can get the cirq version by printing cirq.__version__. From the command line:

In [38]: cirq.__version__
Out[38]: '0.13.0.dev'

[viathor]

Context: discovered in an attempt to reproduce #1783.

[tanujkhattar]

Notes from sync:

• Mike: They are also separately listed in N & C but have an exercise asks you to prove they are the same.
• Dave: There is a difference in how you think about these two channels.
• Dave: We have other places where this happens.
• Dave: We could subclass but modifying kraus representations would be non trivial.

We should keep both the classes for now and add mixture representation to PhaseDampingChannel.