180,082 research outputs found
Generalized entropic measures of quantum correlations
We propose a general measure of non-classical correlations for bipartite
systems based on generalized entropic functions and majorization properties.
Defined as the minimum information loss due to a local measurement, in the case
of pure states it reduces to the generalized entanglement entropy, i.e., the
generalized entropy of the reduced state. However, in the case of mixed states
it can be non-zero in separable states, vanishing just for states diagonal in a
general product basis, like the Quantum Discord. Simple quadratic measures of
quantum correlations arise as a particular case of the present formalism. The
minimum information loss due to a joint local measurement is also discussed.
The evaluation of these measures in a few simple relevant cases is as well
provided, together with comparison with the corresponding entanglement
monotones.Comment: 9 pages, 2 figure
Error Free Perfect Secrecy Systems
Shannon's fundamental bound for perfect secrecy says that the entropy of the
secret message cannot be larger than the entropy of the secret key initially
shared by the sender and the legitimate receiver. Massey gave an information
theoretic proof of this result, however this proof does not require
independence of the key and ciphertext. By further assuming independence, we
obtain a tighter lower bound, namely that the key entropy is not less than the
logarithm of the message sample size in any cipher achieving perfect secrecy,
even if the source distribution is fixed. The same bound also applies to the
entropy of the ciphertext. The bounds still hold if the secret message has been
compressed before encryption.
This paper also illustrates that the lower bound only gives the minimum size
of the pre-shared secret key. When a cipher system is used multiple times, this
is no longer a reasonable measure for the portion of key consumed in each
round. Instead, this paper proposes and justifies a new measure for key
consumption rate. The existence of a fundamental tradeoff between the expected
key consumption and the number of channel uses for conveying a ciphertext is
shown. Optimal and nearly optimal secure codes are designed.Comment: Submitted to the IEEE Trans. Info. Theor
Towards an Entanglement Measure for Mixed States in CFTs Based on Relative Entropy
Relative entropy of entanglement (REE) is an entanglement measure of
bipartite mixed states, defined by the minimum of the relative entropy
between a given mixed state and an
arbitrary separable state . The REE is always bounded by the
mutual information because
the latter measures not only quantum entanglement but also classical
correlations. In this paper we address the question of to what extent REE can
be small compared to the mutual information in conformal field theories (CFTs).
For this purpose, we perturbatively compute the relative entropy between the
vacuum reduced density matrix on disjoint subsystems
and arbitrarily separable state in the limit where two subsystems
A and B are well separated, then minimize the relative entropy with respect to
the separable states. We argue that the result highly depends on the spectrum
of CFT on the subsystems. When we have a few low energy spectrum of operators
as in the case where the subsystems consist of a finite number of spins in spin
chain models, the REE is considerably smaller than the mutual information.
However in general our perturbative scheme breaks down, and the REE can be as
large as the mutual information.Comment: 35 pages, 2 figure
- …