492 research outputs found
Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way post-processing
We derive a bound for the security of QKD with finite resources under one-way
post-processing, based on a definition of security that is composable and has
an operational meaning. While our proof relies on the assumption of collective
attacks, unconditional security follows immediately for standard protocols like
Bennett-Brassard 1984 and six-states. For single-qubit implementations of such
protocols, we find that the secret key rate becomes positive when at least
N\sim 10^5 signals are exchanged and processed. For any other discrete-variable
protocol, unconditional security can be obtained using the exponential de
Finetti theorem, but the additional overhead leads to very pessimistic
estimates
Secure quantum key distribution using squeezed states
We prove the security of a quantum key distribution scheme based on
transmission of squeezed quantum states of a harmonic oscillator. Our proof
employs quantum error-correcting codes that encode a finite-dimensional quantum
system in the infinite-dimensional Hilbert space of an oscillator, and protect
against errors that shift the canonical variables p and q. If the noise in the
quantum channel is weak, squeezing signal states by 2.51 dB (a squeeze factor
e^r=1.34) is sufficient in principle to ensure the security of a protocol that
is suitably enhanced by classical error correction and privacy amplification.
Secure key distribution can be achieved over distances comparable to the
attenuation length of the quantum channel.Comment: 19 pages, 3 figures, RevTeX and epsf, new section on channel losse
Tight Finite-Key Analysis for Quantum Cryptography
Despite enormous progress both in theoretical and experimental quantum
cryptography, the security of most current implementations of quantum key
distribution is still not established rigorously. One of the main problems is
that the security of the final key is highly dependent on the number, M, of
signals exchanged between the legitimate parties. While, in any practical
implementation, M is limited by the available resources, existing security
proofs are often only valid asymptotically for unrealistically large values of
M. Here, we demonstrate that this gap between theory and practice can be
overcome using a recently developed proof technique based on the uncertainty
relation for smooth entropies. Specifically, we consider a family of
Bennett-Brassard 1984 quantum key distribution protocols and show that security
against general attacks can be guaranteed already for moderate values of M.Comment: 11 pages, 2 figure
Secure Coherent-state Quantum Key Distribution Protocols with Efficient Reconciliation
We study the equivalence between a realistic quantum key distribution
protocol using coherent states and homodyne detection and a formal entanglement
purification protocol. Maximally-entangled qubit pairs that one can extract in
the formal protocol correspond to secret key bits in the realistic protocol.
More specifically, we define a qubit encoding scheme that allows the formal
protocol to produce more than one entangled qubit pair per coherent state, or
equivalently for the realistic protocol, more than one secret key bit. The
entanglement parameters are estimated using quantum tomography. We analyze the
properties of the encoding scheme and investigate its application to the
important case of the attenuation channel.Comment: REVTeX, 11 pages, 2 figure
Security Against Collective Attacks of a Modified BB84 QKD Protocol with Information only in One Basis
The Quantum Key Distribution (QKD) protocol BB84 has been proven secure
against several important types of attacks: the collective attacks and the
joint attacks. Here we analyze the security of a modified BB84 protocol, for
which information is sent only in the z basis while testing is done in both the
z and the x bases, against collective attacks. The proof follows the framework
of a previous paper (Boyer, Gelles, and Mor, 2009), but it avoids the classical
information-theoretical analysis that caused problems with composability. We
show that this modified BB84 protocol is as secure against collective attacks
as the original BB84 protocol, and that it requires more bits for testing.Comment: 6 pages; 1 figur
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