Can a leopard and tiger show love to each other?

I think you video answers the question...

Another proof could be the existence of Doglas and Tigards:
"- Dogla
The name dogla is used for a supposedly natural hybrid offspring of a tiger and a leopard or possibly a leopard with aberrant patterns.
Note: The term "panther" used here refers exclusively to the Indian leopard in either spotted or black form.
There is anecdotal evidence in India of offspring resulting from leopard to tigress matings. The supposed hybrids are called "dogla". Indian folklore claims that large male leopards sometimes mate with tigresses. A supposed dogla was reported in the early 1900s. Many reports are probably large leopards with abdominal striping or other striped shoulders and body of a tiger. One account stated, "On examining it, I found it to be a very old male hybrid. Its head and tail were purely those of a panther, but with the body, shoulders, and neck ruff of a tiger. The pattern was a combination of rosettes and stripes; the stripes were black, broad and long, though somewhat blurred and tended to break up into rosettes. The head was spotted. The stripes predominated over the rosettes." The pelt of this hybrid, if it ever existed, was lost. It was supposedly larger than a leopard and, though male, it showed some feminization of features which might be expected in a sterile male hybrid.
K Sankhala's book "Tiger" refers to large troublesome leopards as "adhabaghera" which he translated as "bastard" and suggests a dogla (tiger/leopard hybrid) belief of local people. Sankhala amongst local people that tigers and leopards naturally hybridise. There may have been plans to test this theory at New Delhi Zoo during the 1970s.
From "The Tiger, Symbol Of Freedom", edited by Nicholas Courtney: "Rare reports have been made of tigresses mating with lions in the wild. There has even been an account of the sighting of an rosettes, the stripes of the tiger being most prominent in the body. The animal was a male measuring a little over eight feet [2.44 m]." This is the same description given by Hicks.
In 1900, Carl Hagenbeck crossed a female leopard with a Bengal tiger. The stillborn offspring had a mixture of spots, rosettes and stripes. The 1951 book "Mammalian Hybrids" reported that tiger/leopard matings were infertile, producing spontaneously aborted "walnut sized foetuses".
- Tigard
A tigard is the hybrid offspring of a male tiger and a leopardess. The only known attempts to mate the two have produced stillborns.
In 1900, Carl Hagenbeck crossed a female leopard with a Bengal tiger. The stillborn offspring had a mixture of spots, rosettes and stripes. In The Field No 2887, April 25th, 1908, Henry Scherren wrote "A male tiger from Penang served two female Indian leopards, and twice with success. Details are not given and the story concludes somewhat lamely. 'The leopardess dropped her cubs prematurely, the embryos were in the first stage of development and were scarcely as big as young mice.' Of the second leopardess there is no mention. "
The 1951 book "Mammalian Hybrids" reported that tiger/leopard matings were infertile, producing spontaneously aborted "walnut sized foetuses"."
Source and further information:
http://en.wikipedia.org/wiki/Panthera_hybrid#Leopard_and_tiger_hybrids

I hope this would happen one day in the future.

Anything can show love to each other....

It could be argued that some species of animals - the ones that mate for life - love in the human sense, but generally speaking animals don't have the emotional make-up to love at all, never mind love a different species.