But what if a person wants to exchange one car for another, and both of them represented by the same amount of bitcoins lets say 1 satoshi, creating single transaction would make it impossible to tell who owns what.
ECDSA keys provably demonstrate who owns what. It uses the same technology as the rest of bitcoin.
Maybe I am missing something.
Two people want to exchange cars, Alice owns Honda CRV and Bob owns Toyota RAV4.
Honda CRV represented by 1 satoshi at 1qwe...
Toyota RAV4 represented by 1 satoshi at 1rty...
Bob and Alice construct single transaction to exchange cars:
Inputs:
1 satoshi from 1qwe...
1 satoshi from 1rty...
Ouputs:
1 satoshi to 1asd... (address owned by Alice)
1 satoshi to 1fgh... (address owned by Bob)
Is it possible to know what car owned by Alice, or did I misunderstand the statement that exchanged items has to be a part of the same transaction?
They are done as part of the same transaction.