3 research outputs found
Optimality of private quantum channels
We addressed the question of optimality of private quantum channels. We have
shown that the Shannon entropy of the classical key necessary to securely
transfer the quantum information is lower bounded by the entropy exchange of
the private quantum channel and von Neumann entropy of the ciphertext
state . Based on these bounds we have shown that decomposition
of private quantum channels into orthogonal unitaries (if exists) is optimizing
the entropy. For non-ancillary single qubit PQC we have derived the optimal
entropy for arbitrary set of plaintexts. In particular, we have shown that
except when the (closure of the) set of plaintexts contains all states, one bit
key is sufficient. We characterized and analyzed all the possible single qubit
private quantum channels for arbitrary set of plaintexts. For the set of
plaintexts consisting of all qubit states we have characterized all possible
approximate private quantum channels and we have derived the relation between
the security parameter and the corresponding minimal entropy.Comment: no commen
Private quantum decoupling and secure disposal of information
Given a bipartite system, correlations between its subsystems can be
understood as information that each one carries about the other. In order to
give a model-independent description of secure information disposal, we propose
the paradigm of private quantum decoupling, corresponding to locally reducing
correlations in a given bipartite quantum state without transferring them to
the environment. In this framework, the concept of private local randomness
naturally arises as a resource, and total correlations get divided into
eliminable and ineliminable ones. We prove upper and lower bounds on the amount
of ineliminable correlations present in an arbitrary bipartite state, and show
that, in tripartite pure states, ineliminable correlations satisfy a monogamy
constraint, making apparent their quantum nature. A relation with entanglement
theory is provided by showing that ineliminable correlations constitute an
entanglement parameter. In the limit of infinitely many copies of the initial
state provided, we compute the regularized ineliminable correlations to be
measured by the coherent information, which is thus equipped with a new
operational interpretation. In particular, our results imply that two
subsystems can be privately decoupled if their joint state is separable.Comment: Child of 0807.3594 v2: minor changes v3: presentation improved, one
figure added v4: extended version with a lot of discussions and examples v5:
published versio