  Many quantum key distribution (QKD) schemes are based on sending and
measuring qubits -- two-dimensional quantum systems. Yet, in practical
realizations and experiments, the measuring devices at the receiver's (Bob)
site commonly do not measure a two-dimensional system but rather a quantum
space of a larger dimension. Such an enlargement sometimes results from
imperfect devices. However, in various QKD protocols such enlargement exists
even in the ideal scenario when all devices are assumed to be perfect. This
issue is common, for instance, in QKD schemes implemented via photons, where
the parties' devices are based on Mach-Zehnder interferometers, as these
inherently enlarge the quantum space in use.
  We show how space enlargement at Bob's site exposes the implemented protocol
to new kinds of attacks, attacks that have not yet been explicitly pinpointed
nor rigorously analyzed. We name these the "reversed space attacks". A key
insight in formalizing our attacks, is the idea of taking all states defining
Bob's (large) measured space and reversing them in time in order to identify
precisely the space that an eavesdropper may attack. We employ such attacks on
two variants of intereferometric-based QKD recently experimented by several
groups, and show how to get full information on the qubit sent by Alice, while
inducing no errors at all. The technique we develop here has subsequently been
used in a closely related work (Boyer, Gelles, and Mor, Physical Review A,
2014) to demonstrate a (weaker variant of) reversed-space attack on both
interferometric-based and polarization-based QKD.
