3,667 research outputs found
Secret Message Transmission over Quantum Channels under Adversarial Quantum Noise: Secrecy Capacity and Super-Activation
We determine the secrecy capacities of AVQCs (arbitrarily varying quantum
channels). Both secrecy capacity with average error probability and with
maximal error probability are derived. Both derivations are based on one common
code construction. The code we construct fulfills a stringent secrecy
requirement, which is called the strong code concept. We determine when the
secrecy capacity is a continuous function of the system parameters and
completely characterize its discontinuity points both for average error
criterion and for maximal error criterion. Furthermore, we prove the phenomenon
"super-activation" for secrecy capacities of AVQCs, i.e., two quantum channels
both with zero secrecy capacity, which, if used together, allow secure
transmission with positive capacity. We also discuss the relations between the
entanglement distillation capacity, the entanglement generating capacity, and
the strong subspace transmission capacity for AVQCs.Comment: arXiv admin note: text overlap with arXiv:1702.0348
Performance of polar codes for quantum and private classical communication
We analyze the practical performance of quantum polar codes, by computing
rigorous bounds on block error probability and by numerically simulating them.
We evaluate our bounds for quantum erasure channels with coding block lengths
between 2^10 and 2^20, and we report the results of simulations for quantum
erasure channels, quantum depolarizing channels, and "BB84" channels with
coding block lengths up to N = 1024. For quantum erasure channels, we observe
that high quantum data rates can be achieved for block error rates less than
10^(-4) and that somewhat lower quantum data rates can be achieved for quantum
depolarizing and BB84 channels. Our results here also serve as bounds for and
simulations of private classical data transmission over these channels,
essentially due to Renes' duality bounds for privacy amplification and
classical data transmission of complementary observables. Future work might be
able to improve upon our numerical results for quantum depolarizing and BB84
channels by employing a polar coding rule other than the heuristic used here.Comment: 8 pages, 6 figures, submission to the 50th Annual Allerton Conference
on Communication, Control, and Computing 201
Polar codes for private classical communication
We construct a new secret-key assisted polar coding scheme for private
classical communication over a quantum or classical wiretap channel. The
security of our scheme rests on an entropic uncertainty relation, in addition
to the channel polarization effect. Our scheme achieves the symmetric private
information rate by synthesizing "amplitude" and "phase" channels from an
arbitrary quantum wiretap channel. We find that the secret-key consumption rate
of the scheme vanishes for an arbitrary degradable quantum wiretap channel.
Furthermore, we provide an additional sufficient condition for when the secret
key rate vanishes, and we suspect that satisfying this condition implies that
the scheme requires no secret key at all. Thus, this latter condition addresses
an open question from the Mahdavifar-Vardy scheme for polar coding over a
classical wiretap channel.Comment: 11 pages, 2 figures, submission to the 2012 International Symposium
on Information Theory and its Applications (ISITA 2012), Honolulu, Hawaii,
US
Quantum Geo-Encryption
In this work we introduce the concept of quantum geo-encryption - a protocol
that invokes direct quantum encryption of messages coupled to quantum location
monitoring of the intended receiver. By obfuscating the quantum information
required by both the decrypting process and the location verification process,
a communication channel is created in which the encrypted data can only be
decrypted at a specific geographic locale. Classical wireless communications
can be invoked to unlock the quantum encryption process thereby allowing for
any deployment scenario regardless of the channel conditions. Quantum
geo-encryption can also be used to realize quantum-computing instructions that
can only be implemented at a specific location, and allow for a specified
geographical data-route through a distributed network. Here we consider the
operational aspects of quantum geo-encryption in generic Rician channels,
demonstrating that the likelihood of a successful spoofing attack approaches
zero as the adversary moves away from the allowed decrypting location. The work
introduced here resolves a long-standing quest to directly deliver information
which can only be decrypted at a given location free of assumptions on the
physical security of a receiver.Comment: 3 Figure
Communicating over adversarial quantum channels using quantum list codes
We study quantum communication in the presence of adversarial noise. In this
setting, communicating with perfect fidelity requires using a quantum code of
bounded minimum distance, for which the best known rates are given by the
quantum Gilbert-Varshamov (QGV) bound. By asking only for arbitrarily high
fidelity and allowing the sender and reciever to use a secret key with length
logarithmic in the number of qubits sent, we achieve a dramatic improvement
over the QGV rates. In fact, we find protocols that achieve arbitrarily high
fidelity at noise levels for which perfect fidelity is impossible. To achieve
such communication rates, we introduce fully quantum list codes, which may be
of independent interest.Comment: 6 pages. Discussion expanded and more details provided in proofs. Far
less unclear than previous versio
Remote preparation of quantum states
Remote state preparation is the variant of quantum state teleportation in
which the sender knows the quantum state to be communicated. The original paper
introducing teleportation established minimal requirements for classical
communication and entanglement but the corresponding limits for remote state
preparation have remained unknown until now: previous work has shown, however,
that it not only requires less classical communication but also gives rise to a
trade-off between these two resources in the appropriate setting. We discuss
this problem from first principles, including the various choices one may
follow in the definitions of the actual resources. Our main result is a general
method of remote state preparation for arbitrary states of many qubits, at a
cost of 1 bit of classical communication and 1 bit of entanglement per qubit
sent. In this "universal" formulation, these ebit and cbit requirements are
shown to be simultaneously optimal by exhibiting a dichotomy. Our protocol then
yields the exact trade-off curve for arbitrary ensembles of pure states and
pure entangled states (including the case of incomplete knowledge of the
ensemble probabilities), based on the recently established quantum-classical
trade-off for quantum data compression. The paper includes an extensive
discussion of our results, including the impact of the choice of model on the
resources, the topic of obliviousness, and an application to private quantum
channels and quantum data hiding.Comment: 21 pages plus 2 figures (eps), revtex4. v2 corrects some errors and
adds obliviousness discussion. v3 has section VI C deleted and various minor
oversights correcte
A Quantum Multiparty Packing Lemma and the Relay Channel
Optimally encoding classical information in a quantum system is one of the
oldest and most fundamental challenges of quantum information theory. Holevo's
bound places a hard upper limit on such encodings, while the
Holevo-Schumacher-Westmoreland (HSW) theorem addresses the question of how many
classical messages can be "packed" into a given quantum system. In this
article, we use Sen's recent quantum joint typicality results to prove a
one-shot multiparty quantum packing lemma generalizing the HSW theorem. The
lemma is designed to be easily applicable in many network communication
scenarios. As an illustration, we use it to straightforwardly obtain quantum
generalizations of well-known classical coding schemes for the relay channel:
multihop, coherent multihop, decode-forward, and partial decode-forward. We
provide both finite blocklength and asymptotic results, the latter matching
existing classical formulas. Given the key role of the classical packing lemma
in network information theory, our packing lemma should help open the field to
direct quantum generalization.Comment: 20 page
Stochastic resonance in Gaussian quantum channels
We determine conditions for the presence of stochastic resonance in a lossy
bosonic channel with a nonlinear, threshold decoding. The stochastic resonance
effect occurs if and only if the detection threshold is outside of a "forbidden
interval". We show that it takes place in different settings: when transmitting
classical messages through a lossy bosonic channel, when transmitting over an
entanglement-assisted lossy bosonic channel, and when discriminating channels
with different loss parameters. Moreover, we consider a setting in which
stochastic resonance occurs in the transmission of a qubit over a lossy bosonic
channel with a particular encoding and decoding. In all cases, we assume the
addition of Gaussian noise to the signal and show that it does not matter who,
between sender and receiver, introduces such a noise. Remarkably, different
results are obtained when considering a setting for private communication. In
this case the symmetry between sender and receiver is broken and the "forbidden
interval" may vanish, leading to the occurrence of stochastic resonance effects
for any value of the detection threshold.Comment: 17 pages, 6 figures. Manuscript improved in many ways. New results on
private communication adde
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