52 research outputs found
Tomographic Quantum Cryptography
We present a protocol for quantum cryptography in which the data obtained for
mismatched bases are used in full for the purpose of quantum state tomography.
Eavesdropping on the quantum channel is seriously impeded by requiring that the
outcome of the tomography is consistent with unbiased noise in the channel. We
study the incoherent eavesdropping attacks that are still permissible and
establish under which conditions a secure cryptographic key can be generated.
The whole analysis is carried out for channels that transmit quantum systems of
any finite dimension.Comment: REVTeX4, 9 pages, 3 figures, 1 tabl
Quantum Key Distribution using Multilevel Encoding: Security Analysis
We present security proofs for a protocol for Quantum Key Distribution (QKD)
based on encoding in finite high-dimensional Hilbert spaces. This protocol is
an extension of Bennett's and Brassard's basic protocol from two bases, two
state encoding to a multi bases, multi state encoding. We analyze the mutual
information between the legitimate parties and the eavesdropper, and the error
rate, as function of the dimension of the Hilbert space, while considering
optimal incoherent and coherent eavesdropping attacks. We obtain the upper
limit for the legitimate party error rate to ensure unconditional security when
the eavesdropper uses incoherent and coherent eavesdropping strategies. We have
also consider realistic noise caused by detector's noise.Comment: 8 pages, 3 figures, REVTe
Tomographic Quantum Cryptography: Equivalence of Quantum and Classical Key Distillation
The security of a cryptographic key that is generated by communication
through a noisy quantum channel relies on the ability to distill a shorter
secure key sequence from a longer insecure one. For an important class of
protocols, which exploit tomographically complete measurements on entangled
pairs of any dimension, we show that the noise threshold for classical
advantage distillation is identical with the threshold for quantum entanglement
distillation. As a consequence, the two distillation procedures are equivalent:
neither offers a security advantage over the other.Comment: 4 pages, 1 figur
Encoding a qubit in an oscillator
Quantum error-correcting codes are constructed that embed a
finite-dimensional code space in the infinite-dimensional Hilbert space of a
system described by continuous quantum variables. These codes exploit the
noncommutative geometry of phase space to protect against errors that shift the
values of the canonical variables q and p. In the setting of quantum optics,
fault-tolerant universal quantum computation can be executed on the protected
code subspace using linear optical operations, squeezing, homodyne detection,
and photon counting; however, nonlinear mode coupling is required for the
preparation of the encoded states. Finite-dimensional versions of these codes
can be constructed that protect encoded quantum information against shifts in
the amplitude or phase of a d-state system. Continuous-variable codes can be
invoked to establish lower bounds on the quantum capacity of Gaussian quantum
channels.Comment: 22 pages, 8 figures, REVTeX, title change (qudit -> qubit) requested
by Phys. Rev. A, minor correction
Unitary quantum gates, perfect entanglers and unistochastic maps
Non-local properties of ensembles of quantum gates induced by the Haar
measure on the unitary group are investigated. We analyze the entropy of
entanglement of a unitary matrix U equal to the Shannon entropy of the vector
of singular values of the reshuffled matrix. Averaging the entropy over the
Haar measure on U(N^2) we find its asymptotic behaviour. For two--qubit quantum
gates we derive the induced probability distribution of the interaction content
and show that the relative volume of the set of perfect entanglers reads 8/3
\pi \approx 0.85. We establish explicit conditions under which a given
one-qubit bistochastic map is unistochastic, so it can be obtained by partial
trace over a one--qubit environment initially prepared in the maximally mixed
state.Comment: 14 pages including 6 figures in eps, version 4, title changed
according to a suggestion of the editor
Extremal spacings between eigenphases of random unitary matrices and their tensor products
Extremal spacings between eigenvalues of random unitary matrices of size N
pertaining to circular ensembles are investigated. Explicit probability
distributions for the minimal spacing for various ensembles are derived for N =
4. We study ensembles of tensor product of k random unitary matrices of size n
which describe independent evolution of a composite quantum system consisting
of k subsystems. In the asymptotic case, as the total dimension N = n^k becomes
large, the nearest neighbor distribution P(s) becomes Poissonian, but
statistics of extreme spacings P(s_min) and P(s_max) reveal certain deviations
from the Poissonian behavior
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