Quantum Rate-Distortion Coding of Relevant Information

Salek, Sina; Cadamuro, Daniela; Kammerlander, Philipp; Wiesner, Karoline

doi:10.1109/tit.2018.2878412

Cited by 19 publications

(28 citation statements)

References 15 publications

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“…concluding the proof. ∎ This not only serves to complete the proof of the operational interpretation of the quantum IB function given in [15], but is also of independent interest.…”

Section: Convexity Of the Qib Functionmentioning

confidence: 76%

“…However, the operational significance of this task remained unclear. Later, Salek et al [15] attempted to give an operational interpretation to the quantum IB function. They showed that it is the optimal asymptotic rate of a certain informationtheoretic task, under the assumption that the quantum IB function is convex.…”

Section: Quantum Information Bottleneckmentioning

confidence: 99%

“…In this section we discuss some examples in order to give an intuition for the information bottleneck and privacy funnel functions and their properties. For better comparison, we choose to normalize the IB function in the following way (as is done in [15]):…”

Section: Numerics and Examplesmentioning

confidence: 99%

“…For the numerical examples, we use an improved version of the algorithm described in the supplemental material of [15]. We implemented two main features that are not present in the original code:…”

Section: Numerics and Examplesmentioning

confidence: 99%

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Convexity and Operational Interpretation of the Quantum Information Bottleneck Function

Datta

Hirche

Winter

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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In classical information theory, the information bottleneck method (IBM) can be regarded as a method of lossy data compression which focusses on preserving meaningful (or relevant) information. As such it has of late gained a lot of attention, primarily for its applications in machine learning and neural networks. A quantum analogue of the IBM has recently been defined, and an attempt at providing an operational interpretation of the so-called quantum IB function as an optimal rate of an information-theoretic task, has recently been made by Salek et al. The interpretation given by these authors is however incomplete, as its proof is based on the conjecture that the quantum IB function is convex. Our first contribution is the proof of this conjecture.Secondly, the expression for the rate function involves certain entropic quantities which occur explicitly in the very definition of the underlying information-theoretic task, thus making the latter somewhat contrived. We overcome this drawback by pointing out an alternative operational interpretation of it as the optimal rate of a bona fide information-theoretic task, namely that of quantum source coding with quantum side information at the decoder, which has recently been solved by Hsieh and Watanabe. We show that the quantum IB function characterizes the rate region of this task,We similarly show that the related privacy funnel function is concave (both in the classical and quantum case). However, we comment that it is unlikely that the quantum privacy funnel function can characterize the optimal asymptotic rate of an information theoretic task, since even its classical version lacks a certain essential additivity property.

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“…concluding the proof. ∎ This not only serves to complete the proof of the operational interpretation of the quantum IB function given in [15], but is also of independent interest.…”

Section: Convexity Of the Qib Functionmentioning

confidence: 76%

Section: Quantum Information Bottleneckmentioning

confidence: 99%

Section: Numerics and Examplesmentioning

confidence: 99%

Section: Numerics and Examplesmentioning

confidence: 99%

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Convexity and Operational Interpretation of the Quantum Information Bottleneck Function

Datta

Hirche

Winter

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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“…We stop here briefly to remark on the curious resemblance of our function I δ with the so-called information bottleneck function introduced by Tishby et al [13], whose generalization to quantum information theory is recently being discussed [14,15]. Indeed, the concavity and additivity properties of the two functions are proved by the same principles, although it is not evident to us, what -if any-, the information theoretic link between I δ and the information bottleneck is.…”

Section: A Converse Boundmentioning

confidence: 90%

Distributed Compression of Correlated Classical-Quantum Sources or: The Price of Ignorance

Khanian

Winter

2020

IEEE Trans. Inform. Theory

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We resume the investigation of the problem of independent local compression of correlated quantum sources, the classical case of which is covered by the celebrated Slepian-Wolf theorem. We focus specifically on classical-quantum (cq) sources, for which one edge of the rate region, corresponding to the compression of the classical part, using the quantum part as side information at the decoder, was previously determined by Devetak and Winter [Phys. Rev. A 68, 042301 (2003)]. Whereas the Devetak-Winter protocol attains a rate-sum equal to the von Neumann entropy of the joint source, here we show that the full rate region is much more complex, due to the partially quantum nature of the source. In particular, in the opposite case of compressing the quantum part of the source, using the classical part as side information at the decoder, typically the rate sum is strictly larger than the von Neumann entropy of the total source.We determine the full rate region in the generic case, showing that, apart from the Devetak-Winter point, all other points in the achievable region have a rate sum strictly larger than the joint entropy. We can interpret the difference as the price paid for the quantum encoder being ignorant of the classical side information. In the general case, we give an achievable rate region, via protocols that are built on the decoupling principle, and the principles of quantum state merging and quantum state redistribution. Our achievable region is matched almost by a single-letter converse, which however still involves asymptotic errors and an unbounded auxiliary system. I. SOURCE AND COMPRESSION MODELData compression can be regarded as the foundation of information theory in the treatment of Shannon [1], and it remains one of the most fruitful problems to be considered, especially when additional constraints on the source, the encoders or the decoder are imposed. In particular, the Slepian-Wolf problem of two sources correlated in a known way, but subject to separate, local compression [2] has proved to provide a unifying principle for much of Shannon theory, giving rise to natural information theoretic interpretations of entropy and conditional entropy, and exhibiting deep connections with error correction, channel capacities and mutual information (cf. [3]). The quantum case has been investigated for two decades, starting with the second author's PhD thesis [4] and subsequently in [5], up to the systematic study [6], and while we still do not have a complete understanding of the rate region, it has become clear that the problem is of much higher complexity than the classical case. The quantum Slepian-Wolf problem, and specifically quantum data compression with side information at the decoder, has resulted in many fundamental advances in quantum information theory, including the protocols of quantum state merging [7,8] and quantum state redistribution [9], which have given operational meaning to the conditional von Neumann entropy, the mutual information and the conditional quantum mutual information, r...

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Quantum Optimal Transport with Quantum Channels

Palma

Trevisan

2021

Ann. Henri Poincaré

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Quantum Rate-Distortion Coding of Relevant Information

Cited by 19 publications

References 15 publications

Convexity and Operational Interpretation of the Quantum Information Bottleneck Function

Convexity and Operational Interpretation of the Quantum Information Bottleneck Function

Distributed Compression of Correlated Classical-Quantum Sources or: The Price of Ignorance

Quantum Optimal Transport with Quantum Channels

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