Formally, if the nodes read from and the nodes written from together are greater than the number of nodes (r + w > n), the highest level of consistency you can achieve is Causal consistency.
If you use quorum reads and writes in Cassandra, Causal consistency is what you are getting.
This means that if you have a write on a node (w1) and a read from a different node (r1), and then a write based on the read (w2), w2 is said to be causally dependent on w1. A causually consistent system will ensure that all nodes see w1 and then w2. and this is what QUORUM reads and writes provide. Reads and writes that are not part of a casual dependency are not ordered in any particular way. We therefore say that this system has a partial order.
If you need to do things like a uniqueness check, you need to do a Compare and Set operation. A compare and set operation requires a higher level of consistency: it requires linearizability. Linearizability imposes a total order of operations (reads and writes) to an object.
In Cassandra, Lightweight transactions are the mechanism you use to ensure Linearizability to a row, and are thus how you do uniqueness checks in Cassandra. Other systems (etcd, for example) allow for linearizability on the entire database system, not just a row. Such a system is said to have Strict Serializability.