It is greatly to be desired that Alice can create an identifier with this quality: She can use it in her business with Company, and no one can correlate what she does using that identifier with anything she does using some other identifier.

An identifier that has this quality is sometimes called a "unidirectional" identifier.

I'll make some claims (pun intended) here, looking forward to being corrected where i am missing something or am dead wrong.

1. There is no general agreement on what 'unidirectional' means.
2. One meaning, intended by some who use the term, is that a) the unidirectional identifier is used with by Alice with only one party, b) another unidirectional identifier is used by Alice with another party and c) there is no information in the two identifiers that can be used to determine that the same person is using both identifiers.
3. Another meaning, intended by others, is that a) the unidirectional identifier is used with by Alice with only one party, b) another unidirectional identifier is used by Alice with another party and c) there is no information that can be used to determine that the same person is using both identifiers.

4. I hate to write "Let's use these terms just for this argument, please," because the next thing we know these terms will be used in other contexts.

   Let's use these terms just for this argument, please: For the meaning in 2), let's use 'weakest-unidirectional' and for the meaning in 3), let's use 'strongest-unidirectional.'

5. Identifiers having the weakest-unidirectional quality are trivially easy. There is no information in these two identifiers that can be used to determine that the same person is using both identifiers:

      http://www.joaquin.net/pseudonym1
      http://www.joaquin.net/pseudonym2

   (Please do go ahead and contradict that. There are two possible outcomes: a) You demonstrate that i'm wrong. b) You agree that what you saw as information in the identifiers was not enough; that you do need more information, not in the two identifiers, to determine that the same person is using both identifiers.)

6. No identifiers have the strongest-unidirectional quality.

   (Please do go ahead and contradict that. This could be real interesting.)

7. In the absence of continuous reliable surveillance of a person, it is possible for that person to use identifiers that have the almost-strongest-unidirectional quality.

So: What do you mean, unidirectional, exactly?