58,199 research outputs found
Can non-private channels transmit quantum information?
We study the power of quantum channels with little or no capacity for private
communication. Because privacy is a necessary condition for quantum
communication, one might expect that such channels would be of little use for
transmitting quantum states. Nevertheless, we find strong evidence that there
are pairs of such channels that, when used together, can transmit far more
quantum information than the sum of their individual private capacities.
Because quantum transmissions are necessarily private, this would imply a large
violation of additivity for the private capacity. Specifically, we present
channels which display either (1) A large joint quantum capacity but very small
individual private capacities or (2) a severe violation of additivity for the
Holevo information.Comment: We both think so. 4 pages and 3 figures explain wh
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
Maximal Privacy Without Coherence
Privacy lies at the fundament of quantum mechanics. A coherently transmitted
quantum state is inherently private. Remarkably, coherent quantum communication
is not a prerequisite for privacy: there are quantum channels that are too
noisy to transmit any quantum information reliably that can nevertheless send
private classical information. Here, we ask how much private classical
information a channel can transmit if it has little quantum capacity. We
present a class of channels N_d with input dimension d^2, quantum capacity
Q(N_d) <= 1, and private capacity P(N_d) = log d. These channels asymptotically
saturate an interesting inequality P(N) <= (log d_A + Q(N))/2 for any channel N
with input dimension d_A, and capture the essence of privacy stripped of the
confounding influence of coherence.Comment: 6 pages. Proof of Eq.(13) slightly revise
Converse bounds for private communication over quantum channels
This paper establishes several converse bounds on the private transmission
capabilities of a quantum channel. The main conceptual development builds
firmly on the notion of a private state, which is a powerful, uniquely quantum
method for simplifying the tripartite picture of privacy involving local
operations and public classical communication to a bipartite picture of quantum
privacy involving local operations and classical communication. This approach
has previously led to some of the strongest upper bounds on secret key rates,
including the squashed entanglement and the relative entropy of entanglement.
Here we use this approach along with a "privacy test" to establish a general
meta-converse bound for private communication, which has a number of
applications. The meta-converse allows for proving that any quantum channel's
relative entropy of entanglement is a strong converse rate for private
communication. For covariant channels, the meta-converse also leads to
second-order expansions of relative entropy of entanglement bounds for private
communication rates. For such channels, the bounds also apply to the private
communication setting in which the sender and receiver are assisted by
unlimited public classical communication, and as such, they are relevant for
establishing various converse bounds for quantum key distribution protocols
conducted over these channels. We find precise characterizations for several
channels of interest and apply the methods to establish several converse bounds
on the private transmission capabilities of all phase-insensitive bosonic
channels.Comment: v3: 53 pages, 3 figures, final version accepted for publication in
IEEE Transactions on Information Theor
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