Are there any applications of Quantum Computation to Cryptography? (besides Cryptanalysis) I know that people may be yelling "of course!" at the title of the question, but my concern is not about how to construct quantum-resistant primitives, but rather how to use the power of quantum computers to develop secure and efficient cryptographic primitives and protocols.

For example, in post-quantum Cryptography people are concerned about the power of quantum computing as an adversarial situation, and the main use of such power is to solve problems like factoring or discrete logarithm (whereas the quantum-resilient primitives involve classical algorithms).

Are there primitives that use this power as an advantage (for instance, to improve efficiency)? 

If quantum computers are going to become a reality then I agree we should prepare and deploy quantum-resistant schemes, but besides using the quantum power to perform cryptanalysis on certain classical cryptosystems, we could also use it to develop primitives involving quantum algorithms in their implementation (these may not be deployable before we live in a post-quantum world, but they could be used once scalable quantum computers exist). 

Have this been studied? are there any proposals? In other words,does having quantum computers improve the Crypto world somehow?
As noted by kodlu, you are basically asking about the existence of the whole field of quantum cryptography (which is different from post-quantum cryptography).
All the field was arguably started by Stephen Wiesner’s invention of Conjugate Coding in 1969, but which was rejected remained unpublished until 1983. He proposed a theoretical way to use quantum mechanics to construct unforgeable banknotes. This stayed a pedagogical example until (roughly) the last decade, which saw a renewed interest in quantum money schemes.
The main and best-known application is quantum key distribution (QKD), for which many protocols and have been studied since Charles Bennett and Gilles Brassard’s seminal paper in 1984. These protocols need the capacity to exchange attenuated light pulses (typically single photons or coherent states) between the partners, a capacity which has been recently demonstrated over 400 km. There is currently research going on to build quantum relay, some experimental networks using “trusted relay” are operational, and a satellite has been sent by China last year to serve as a quantum communication relay. Beyond this line of work optimizing the “practicality” of these protocols, theoreticians work to improve the security proofs, going in some cases until device-independent security (the protocol is secure even if the physical device you need has been built by the adversary).
Bit commitment (BC) schemes have been proposed since 1984, in the same paper as QKD, but attacks were always found. In 1997, Dominique Mayers, and, independently, Hoi-Kwong Lo and H.F. Chau showed that unconditionally secure quantum bit commitment was impossible. Since secure  BC protocols have been found in specific scenarios:

Protocols secure against adversaries with limited noisy quantum memories
Non-composable secure protocols in a relativistic setting, where the fact that no information can propagate faster than light is a key part of the security proof.

Other relativistic quantum protocols have been studied for position verification since 2010, but security proofs remain hard to be found. We know that we will be limited to computational security, but the best generic attack is known is currently exponential, which leaves hope for security protocols.
Another line of research is blind quantum computing, the quantum analog of completely homomorphic encryption: it is possible to make a quantum computer (if you have one) perform a commutation on encrypted data in a completely blind way, at a small extra cost. The operator of the computer has no way to know anything about the computation (except its size), while the client, which only needs a small quantum apparatus (similar to the QKD one) gets the result of the said computation.
There are of course other avenues of research in quantum cryptography. If you want to have an idea of some of the subjects of this community, you can look on the web the program of the annual QCrypt conferences, where the slides of many talks are online.