32 research outputs found
Achieving the physical limits of the bounded-storage model
Secure two-party cryptography is possible if the adversary's quantum storage
device suffers imperfections. For example, security can be achieved if the
adversary can store strictly less then half of the qubits transmitted during
the protocol. This special case is known as the bounded-storage model, and it
has long been an open question whether security can still be achieved if the
adversary's storage were any larger. Here, we answer this question positively
and demonstrate a two-party protocol which is secure as long as the adversary
cannot store even a small fraction of the transmitted pulses. We also show that
security can be extended to a larger class of noisy quantum memories.Comment: 10 pages (revtex), 2 figures, v2: published version, minor change
Simple approach to approximate quantum error correction based on the transpose channel
We demonstrate that there exists a universal, near-optimal recovery map—the transpose channel—for approximate quantum error-correcting codes, where optimality is defined using the worst-case fidelity. Using the transpose channel, we provide an alternative interpretation of the standard quantum error correction (QEC) conditions and generalize them to a set of conditions for approximate QEC (AQEC) codes. This forms the basis of a simple algorithm for finding AQEC codes. Our analytical approach is a departure from earlier work relying on exhaustive numerical search for the optimal recovery map, with optimality defined based on entanglement fidelity. For the practically useful case of codes encoding a single qubit of information, our algorithm is particularly easy to implement
Can local dynamics enhance entangling power?
It is demonstrated here that local dynamics have the ability to strongly
modify the entangling power of unitary quantum gates acting on a composite
system. The scenario is common to numerous physical systems, in which the time
evolution involves local operators and nonlocal interactions. To distinguish
between distinct classes of gates with zero entangling power we introduce a
complementary quantity called gate-typicality and study its properties.
Analyzing multiple applications of any entangling operator interlaced with
random local gates, we prove that both investigated quantities approach their
asymptotic values in a simple exponential form. This rapid convergence to
equilibrium, valid for subsystems of arbitrary size, is illustrated by studying
multiple actions of diagonal unitary gates and controlled unitary gates.Comment: 7 pages, 3 figure
Unextendible Mutually Unbiased Bases from Pauli Classes
We provide a construction of sets of (d/2+1) mutually unbiased bases (MUBs)
in dimensions d=4,8 using maximal commuting classes of Pauli operators. We show
that these incomplete sets cannot be extended further using the operators of
the Pauli group. However, specific examples of sets of MUBs obtained using our
construction are shown to be strongly unextendible; that is, there does not
exist another vector that is unbiased with respect to the elements in the set.
We conjecture the existence of such unextendible sets in higher dimensions
(d=2^{n}, n>3) as well. Furthermore, we note an interesting connection between
these unextendible sets and state-independent proofs of the Kochen-Specker
Theorem for two-qubit systems. Our construction also leads to a proof of the
tightness of a H_{2} entropic uncertainty relation for any set of three MUBs
constructed from Pauli classes in d=4.Comment: 22 pages, v2: minor changes, references added; published versio