Barna was born in Hungary and immigrated to Canada with his family in the late 1950s as a result of the Hungarian Uprising. His parents were Holocaust survivors who had been imprisoned in Auschwitz concentration camp. Barna and his parents arrived in Canada at Pier 21 in Halifax, Nova Scotia. As part of a 2006 portrait photography exhibit in which Barna was featured, he stated that his parents "had suffered under both fascism and communism, and they said they were looking for a country where politicians retire rather than being executed"