Conquer Mount Qaf with these Prince of Persia guides
Prince of Persia sidequests: Where to find each
Prince of Persia Amulets: Powerful trinkets
Prince of Persia The Deserter quest: Help the lost soldier
Prince of Persia Sacred Archive puzzles: Each solution
The fast travel feature in Prince of Persia: The Lost Crown is one of the later ones you unlock during the game, and you'll already have explored a fair few areas across Mount Qaf before you're able to zip freely between them. The ancient city is pretty expansive, and as with any metroidvania worth its salt, you can expect multiple regions to discover.
As you unlock more abilities and progress the main quest, you'll open up new routes to traverse throughout Mount Qaf, which will make getting around that much easier. Still, the easiest way to get between regions quickly is fast travel, so here's how to unlock it in game.
How to unlock fast travel
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You won't be able to access fast travel until you're well into the game's second chapter; The Abducted Prince. You'll already have travelled to the Hyrcanian Forest to find a way to progress in the Lower City, and you'll have fought the Jahandar boss to unlock the Rush of the Simurgh power.
Using this midair dash, you can cross the spiked traps through the corridor to the west of the big open area with the statue, and travel towards the previously inaccessible west side of the Lower City and the Sacred Archives. After you've crossed the spiked traps, keep heading left to find a Wak-Wak Tree, and just a little further beyond it, a purple time rift. If you smash this rift, it'll rebuild a ruined statue.
These Homa Statues are fast travel points, which, once rebuilt by smashing the time rift, will let you teleport between them. Since this is the first you'll find, the only other fast travel point available is the one in The Haven locked behind an iron gate. I suggest travelling there straight away to unlock it from the inside so you can use it in future next time you're there. While exploring, keep an eye out for the corners of your screen turning purple and cracked, since this indicates there's a purple time rift nearby that likely unlocks a statue.