Superluminal communication is the term used to describe the hypothetical process by which one might send information at faster-than-light (FTL) speeds. Scientific investigation has thus far produced no empirical evidence for superluminal communication.
Some theories and experiments include:
According to the currently accepted theory three out of those four phenomena do not produce superluminal communication, although they may give that appearance under some conditions. Only tachyons (which are generally thought to be theoretically impossible) produce truly superluminal communication.
If wormholes are possible, then ordinary subluminal methods of communication could be sent through them to achieve superluminal transmission speeds. Considering the immense energy that current theories suggest would be required to open a wormhole large enough to pass spacecraft through it may be that only atomic-scale wormholes would be practical to build, limiting their use solely to information transmission. Some theories of wormhole formation would prevent them from ever becoming "timeholes", allowing superluminal communication without the additional complication of allowing communication with the past.
The no cloning theorem prevents superluminal communication via quantum entanglement. Consider the EPR thought experiment, and suppose quantum states could be cloned. Alice could send bits to Bob in the following way:
If Alice wishes to transmit a '0', she measures the spin of her electron in the z direction, collapsing Bob's state to either |z+>B or |z->B. If Alice wishes to transmit a '1', she measures the spin of her electron in the x direction, collapsing Bob's state to either |x+>B or |x->B. Bob creates many copies of his electron's state, and measures the spin of each copy in the z direction. If Alice transmitted a '0', all his measurements will produce the same result; otherwise, his measurements will be split evenly between +1/2 and -1/2. This would allow Alice and Bob to communicate across space-like separations, potentially violating causality.