Picking out Noun Phrases

I have found the key to his secret.

There are actually three noun phrases present:

(1) "I"

(2) "the key to his secret"

(3) "his secret"

The pronoun "I" is a noun phrase functioning as subject. The larger noun phrase (2) is object of "found". Note that the preposition phrase "to his secret" is complement of "key" and hence part of the noun phrase.

Finally, within the preposition phrase, "his secret" is also a noun phrase functioning as complement of the preposition "to".

This sentence can be analysed as follows:

I have found the key to his secret.

Noun Phrase

1. I (functions as the subject)
2. the key to his secret (functions as the object of the verb)
3. his secret (object of the preposition to)

Verb Phrase

have found the key to his secret

("In linguistics, a verb phrase (VP) is a syntactic unit composed of at least one verb and its dependents—objects, complements and other modifiers—but not always including the subject". - Wikipedia.)

Verb

have found (have = auxiliary verb; found= main verb)

Prepositional Phrase

to his secret (a prepositional phrase is comprised of a preposition and a noun phrase - Preposition = to; noun phrase = his secret)

Head Noun

1. I (the subject)
2. key (the object of the verb)
3. secret (the object of the preposition)