Are QSPI Interface and SPI compatible one with another?
It obviously depends on particular "an SPI device".

If you are using the Cypress S25FL064P as external memory (as per your other inquiry), it does support both standard SPI (with MISO-MOSI) and four-lane QSPI (four bi-directional wires), see specifications (!!!). 

The nrf52840 also has two distinctive interfaces, SPIM (SPI Master) and QSPI. Both are using "EasyDMA", whatever it is. Again, read specifications for God's sake please.