arXiv subjects

Igor Devetak

Publications and source records attributed to Igor Devetak.

24 records · Page 2Linked to original sources

arXiv2004

Bounds on classical information capacities for a class of quantum memory channels

The maximum rates for information transmission through noisy quantum channels has primarily been developed for memoryless channels, where the noise on each transmitted state is treated as independent. Many real world communication channels experience noise which is modelled better by errors that are correlated between separate channel uses. In this paper, upper bounds on the classical information capacities of a class of quantum memory channels are derived. The class of channels consists of indecomposable quantum memory channels, a generalization of classical indecomposable finite-state channels.

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arXiv2003

Relating quantum privacy and quantum coherence: an operational approach

We describe how to achieve optimal entanglement generation and one-way entanglement distillation rates by coherent implementation of a class of secret key generation and secret key distillation protocols, respectively. This short paper is a high-level descrioption of our detailed papers [8] and [10].

quant-ph↗

arXiv2003

Distillation of secret key and entanglement from quantum states

We study and solve the problem of distilling secret key from quantum states representing correlation between two parties (Alice and Bob) and an eavesdropper (Eve) via one-way public discussion: we prove a coding theorem to achieve the "wire-tapper" bound, the difference of the mutual information Alice-Bob and that of Alice-Eve, for so-called cqq-correlations, via one-way public communication. This result yields information--theoretic formulas for the distillable secret key, giving ``ultimate'' key rate bounds if Eve is assumed to possess a purification of Alice and Bob's joint state. Specialising our protocol somewhat and making it coherent leads us to a protocol of entanglement distillation via one-way LOCC (local operations and classical communication) which is asymptotically optimal: in fact we prove the so-called "hashing inequality" which says that the coherent information (i.e., the negative conditional von Neumann entropy) is an achievable EPR rate. This result is well--known to imply a whole set of distillation and capacity formulas which we briefly review.

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arXiv2002

Quantum Rate-Distortion Theory for I.I.D. Sources

We formulate quantum rate-distortion theory in the most general setting where classical side information is included in the tradeoff. Using a natural distortion measure based on entanglement fidelity and specializing to the case of an unrestricted classical side channel, we find the exact quantum rate-distortion function for a source of isotropic qubits. An upper bound we believe to be exact is found in the case of biased sources. We establish that in this scenario optimal rate-distortion codes produce no entropy exchange with the environment of any individual qubit.

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arXiv2002

Low-Entanglement Remote State Preparation

An upper bound on the low-entanglement remote state preparation (RSP) ebits vs. bits tradeoff curve (Bennett et al.,quant-ph/0006044) is found using techniques of classical information theory. We prove our coding scheme to be optimal amongst an important class of protocols, and conjecture the bound to be tight.

quant-ph↗

arXiv2001

Fidelity trade-off for finite ensembles of identically prepared qubits

We calculate the trade-off between the quality of estimating the quantum state of an ensemble of identically prepared qubits and the minimum level of disturbance that has to be introduced by this procedure in quantum mechanics. The trade-off is quantified using two mean fidelities: the operation fidelity which characterizes the average resemblance of the final qubit state to the initial one, and the estimation fidelity describing the quality of the obtained estimate. We analyze properties of quantum operations saturating the achievability bound for the operation fidelity versus the estimation fidelity, which allows us to reduce substantially the complexity of the problem of finding the trade-off curve. The reduced optimization problem has the form of an eigenvalue problem for a set of tridiagonal matrices, and it can be easily solved using standard numerical tools.

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