8,565 research outputs found
Strong converse rates for quantum communication
We revisit a fundamental open problem in quantum information theory, namely
whether it is possible to transmit quantum information at a rate exceeding the
channel capacity if we allow for a non-vanishing probability of decoding error.
Here we establish that the Rains information of any quantum channel is a strong
converse rate for quantum communication: For any sequence of codes with rate
exceeding the Rains information of the channel, we show that the fidelity
vanishes exponentially fast as the number of channel uses increases. This
remains true even if we consider codes that perform classical post-processing
on the transmitted quantum data. As an application of this result, for
generalized dephasing channels we show that the Rains information is also
achievable, and thereby establish the strong converse property for quantum
communication over such channels. Thus we conclusively settle the strong
converse question for a class of quantum channels that have a non-trivial
quantum capacity.Comment: v4: 13 pages, accepted for publication in IEEE Transactions on
Information Theor
Strong Converse Rates for Quantum Communication
© 1963-2012 IEEE. We revisit a fundamental open problem in quantum information theory, namely, whether it is possible to transmit quantum information at a rate exceeding the channel capacity if we allow for a non-vanishing probability of decoding error. Here, we establish that the Rains information of any quantum channel is a strong converse rate for quantum communication. For any sequence of codes with rate exceeding the Rains information of the channel, we show that the fidelity vanishes exponentially fast as the number of channel uses increases. This remains true even if we consider codes that perform classical postprocessing on the transmitted quantum data. As an application of this result, for generalized dephasing channels, we show that the Rains information is also achievable, and thereby establish the strong converse property for quantum communication over such channels. Thus, we conclusively settle the strong converse question for a class of quantum channels that have a non-trivial quantum capacity
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
Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
A strong converse theorem for the classical capacity of a quantum channel
states that the probability of correctly decoding a classical message converges
exponentially fast to zero in the limit of many channel uses if the rate of
communication exceeds the classical capacity of the channel. Along with a
corresponding achievability statement for rates below the capacity, such a
strong converse theorem enhances our understanding of the capacity as a very
sharp dividing line between achievable and unachievable rates of communication.
Here, we show that such a strong converse theorem holds for the classical
capacity of all entanglement-breaking channels and all Hadamard channels (the
complementary channels of the former). These results follow by bounding the
success probability in terms of a "sandwiched" Renyi relative entropy, by
showing that this quantity is subadditive for all entanglement-breaking and
Hadamard channels, and by relating this quantity to the Holevo capacity. Prior
results regarding strong converse theorems for particular covariant channels
emerge as a special case of our results.Comment: 33 pages; v4: minor changes throughout, accepted for publication in
Communications in Mathematical Physic
Converse bounds for private communication over quantum channels
© 1963-2012 IEEE. 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 the 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 converse bounds on the private transmission capabilities of all phase-insensitive bosonic channels
Smooth Entropy Bounds on One-Shot Quantum State Redistribution
In quantum state redistribution as introduced in [Luo and Devetak (2009)] and
[Devetak and Yard (2008)], there are four systems of interest: the system
held by Alice, the system held by Bob, the system that is to be
transmitted from Alice to Bob, and the system that holds a purification of
the state in the registers. We give upper and lower bounds on the amount
of quantum communication and entanglement required to perform the task of
quantum state redistribution in a one-shot setting. Our bounds are in terms of
the smooth conditional min- and max-entropy, and the smooth max-information.
The protocol for the upper bound has a clear structure, building on the work
[Oppenheim (2008)]: it decomposes the quantum state redistribution task into
two simpler quantum state merging tasks by introducing a coherent relay. In the
independent and identical (iid) asymptotic limit our bounds for the quantum
communication cost converge to the quantum conditional mutual information
, and our bounds for the total cost converge to the conditional
entropy . This yields an alternative proof of optimality of these rates
for quantum state redistribution in the iid asymptotic limit. In particular, we
obtain a strong converse for quantum state redistribution, which even holds
when allowing for feedback.Comment: v3: 29 pages, 1 figure, extended strong converse discussio
Strong converse for the classical capacity of optical quantum communication channels
We establish the classical capacity of optical quantum channels as a sharp
transition between two regimes---one which is an error-free regime for
communication rates below the capacity, and the other in which the probability
of correctly decoding a classical message converges exponentially fast to zero
if the communication rate exceeds the classical capacity. This result is
obtained by proving a strong converse theorem for the classical capacity of all
phase-insensitive bosonic Gaussian channels, a well-established model of
optical quantum communication channels, such as lossy optical fibers, amplifier
and free-space communication. The theorem holds under a particular
photon-number occupation constraint, which we describe in detail in the paper.
Our result bolsters the understanding of the classical capacity of these
channels and opens the path to applications, such as proving the security of
noisy quantum storage models of cryptography with optical links.Comment: 15 pages, final version accepted into IEEE Transactions on
Information Theory. arXiv admin note: text overlap with arXiv:1312.328
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 the 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 converse bounds on the private transmission capabilities of all phase-insensitive bosonic channels
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