From an information perspective, are both strands of DNA necessary?
From a strictly information theoretical perspective, no, a second strand does not provide any additional information that cannot be inferred from the complementary strand. But as many comments have pointed out, there are many practical reasons for DNA's double strandedness.


DNA is biochemically more stable in a double stranded state.
The redundancy of two strands allows for maintenance and repair mechanisms to ensure the integrity of the genome.
Proteins that bind to DNA can only recognize the sequence of that strand, so even though the complementary strand can always be reconstructed from the primary strand, DNA binding proteins cannot target that complementary strand unless it physically exists. In some cases, a DNA binding site encompasses both strands simultaneously.
Proteins (such as polymerases) traverse DNA in the 5' to 3' direction, so if information from the complementary strand was required it would have to be read "backwards".