There are several ways to root Sony Ericsson Xperia 2011 phones, i am showing you the easiest one.
There are 2 steps, unlocking bootloader and then rooting the phone.
Unlocking Bootloader source
[this method was actually for neo v, but it worked for my mini pro sk17i]
Before you proceed, please check if your phone’s boot loader can be unlocked or not?
How to check unlockability:
In your device, open the dialler and enter *#*#7378423#*#* to access the service menu. Tap Service info > Configuration > Rooting Status. If Bootloader unlock allowed says Yes, then you can continue with the next step. If it says Bootloader unlocked: Yes, then your bootloader already unlocked, you can now root your xperia easily. If it says No, or if the status is missing, your device cannot be unlocked hence you cant root your device following this thread.
For better understanding, I highly recommend you to watch the above video along with the instructions below:
2)Extract the file you downloaded above on your PC. You’ll get the following three files:
3)Click/DoubleClick on the internet shortcut file you got in Step 2.3 “unlockbootloader.sonyericsson.com”.
This will open a web page in your default browser. Scroll to the bottom of the Instructions on the page and you’ll see a link like “Continue”, click on it.
In the pop-up window click “Yes, I’m sure” and then in the next window click on both the checkboxes, and then click “I accept”.
4)Now insert the details as per the instructions:
First 14 digits of your IMEI No. Do NOT enter the last digit (15th) in the box. To know your IMEI No. dial *#06# on your Xperia Arc.
Your Email address.
Then click on “Submit”
5)You’ll get a KEY in your email account to unlock boot loader. Write it down somewhere you can remember, it will be used later.
Switch off your phone.
Now extract the “fastboot_with_Android_USB_file.zip” file you got in Step 2.2.
8)Pick up your phone (it must be switched off) and hold the “FASTBOOT” button (the key at the bottom right of your phone), now while holding the “FASTBOOT” button connect your phone to your PC with an USB cable.
9)Once connected — the LED light near the phone’s USB plug will turn blue. If it doesn’t — repeat the Step 8.
10)Now to install the drivers do the following:
Extract the “drivers.zip” file you got in Step 2.1
11)Open “Device Manager” on your PC and look for “S1Boot Fastboot” under the head “Other devices”
Right-click on “S1Boot Fastboot” and select “Update Driver Software…”
Now select “Browse my computer for driver software” and select the folder where you’ve extracted all the three files you got in Step 2. Once done — click Ok.
12)Now click Next (Make sure you’ve ticked the “Include subfolders” checkbox).
If you see any Windows security warning box, don’t worry . Just select “Install this driver software anyway”
Wait for “Windows has successfully updated your driver software” message to appear on your screen. Now click Close.
Open the “fastboot” folder from the file we extracted in Step 7.
13)Now hold Shift and press mouse right click (Shift + Mouse Right Click) anywhere on the empty white space inside the “fastboot” folder. And then select “Open command window here” from the context menu.
14)Now in the command prompt window type/paste the following:
fastboot.exe -i 0x0fce getvar version
It should return a value like “0.3”. This ensures that your device is correctly connected.
15)Now type/paste the following line in the command prompt window:
fastboot.exe -i 0x0fce oem unlock 0xKEY
IMPORTANT! Replace the word “KEY” from the above line with the KEY that you received in Step 5. Then hit Enter.
Now wait for the process to complete. Command prompt will show a “Finished” message when it will be completed. Once it’s done, disconnect the USB cable from your phone and switch it ON.Your phone’s boot loader should now be unlocked.