Is it possible that diesel engine has less efficiency than petrol engine for the same compression ratio and same heat input, if yes then why?

Diesel engine is high compression engine, if its compression ratio is kept as low as petrol engine then the air which is to be compressed and heated up by compression doesnot reach to its appropraite temperature to burn fuel properly and completly which will cause fall of efficiency

 

first allow me to correct one part of your question i would like to clear that Diesel engine and patrol/Gasoline engine are not the same compression ratio ..
and here why they are not the same .
- patrol/Gasoline engine .
in said the cylinder the cycle during the movement down with the opening valve it Suction or withdrawal process oxygen is mixed with the air and fuel and here the amount of space in the cylinder are increasing in which creating enough amount of mixture air and fuel to be compressed ..
following the compression the spark plug to spark and ignite.
both air and fuel.
in this cycle the compression are lower or less in temperature and pressure then the diesel .
so here is the different in gas engine compression ratio temperature and compression are less then Diesel - Diesel engine instead of withdraw mixture of air and fuel ( gasoline Engine ) it withdraw only air in the cylinder chamber room and then compressed it in higher volume of compression and temperature ..
unlike the gasoline engine use spark plug to ignite ..
here the diesel engine spray diesel to the extreme hot compressed air to ignite ..
and that help more on fuel economy and more torque to the wheels .
i hope i did deliver in my answer to your question ...
thank you

because it has to be compress the air to ignite the diesel , whereas the petrol is ignited by sparkplug.
petrol is more volatile than diesel , it is light and diesel is little viscous & dense

Both engine has different velumetric efficiency,but in petrole engin the air and petrole mix then deliver to the inlet manifold,after that as per engibie timing it ignited by the spark plug,but in other hand in diesel engine,the air are copressed in cylinder,during his compression stroke from BDC TO TDC,and diesel spray with pressure as maintain by manufacturer,as per engine timing.it move in heet and fire.there is not the same working ratio.