Is it possble to access Minecraft PE worlds on an xbox 360?

Not at all. Minecraft: Console Edition and Minecraft: Pocket Edition are, as far as the programming concerns, completely different games and are built on different platforms and architectures. Not only that, but the Pocket Edition of Minecraft has far less features than the Console Edition.

Also note that as of 20/09/2017 (release date of the Better Together Update) the Xbox 360 version remains unchanged and does not feature the update allowing this cross-compatibility.

Today, no. Unfortunately you cannot.

There may be someday, and that someday may be as soon as this year. Microsoft recently announced that the next generation Xbox, Project Scorpio, will have a new version of Minecraft. The new version will leverage Universal Windows Platform, giving it the same codebase as Minecraft Pocket Edition and Windows 10 Edition. It is expected that more information will be available at the E3 conference this year (June of 2017).

Yes, this would require a new Xbox, so I'm not suggesting that this is an 'easy solution' assuming it is available soon. Regardless, just wanted to provide this upcoming possibility in case it helps anyone. :)

The better together update allows the answer of -1. You don't need the same username, but the same network. This will allow Windows 10 to play a PE world. Then, friend request your Windows 10 PC from your XBOX and with XBOX Live Gold, you can play. VERY ADVANCED. Sorry for any confusion.

No you can't, but you can still play a multi-player game. In that multi-player game you can have one person on Pocket edition and one on the Xbox version.

Actually, this is quite possible, contrary to belief. There's a tool called Minecraft universal converter that can be run on a Windows computer.

You can then convert your PE worlds to Xbox 360 saves, you just need a USB stick.

1. Put the converted world on the USB, then unplug the USB from the computer.
2. Plug it into your 360 and power the Xbox on.
3. Go to storage and configure the USB, then once your done hit the big X button in the middle of the controller.
4. Go to System ? Storage ? Storage devices and select USB device, your converted Minecraft world should be there.
5. Select it and push "Copy to...", then go back to storage and from there find where your game is stored. Select Minecraft as an option and then it should place your converted world into your Minecraft worlds folder
6. Then just launch Minecraft Xbox 360, and your converted world appears!

I this is just a guess but i think you can if you have minecraft on both devices and log in under your microsoft username. You should find it on the menu as you open the app on your phone.

Here's why I say NO

It has a whole different world and platform plus in the new 1.0.5.54 update on mcpe there's command blocks which means a NO, just NO.