Induced Quantum Divergence: A New Lens on Communication and Source Coding

• URL: http://arxiv.org/abs/2502.13669v1
• Date: Wed, 19 Feb 2025 12:25:56 GMT
• Title: Induced Quantum Divergence: A New Lens on Communication and Source Coding
• Authors: Gilad Gour,
• Abstract summary: This paper introduces the induced divergence, a new quantum divergence measure that replaces the hypothesis testing divergence in position-based decoding. Two key applications are considered: classical communication over quantum channels, and quantum state redistribution. Results provide new insights into fundamental single-shot quantum information protocols.
• Score: 4.3512163406552
• License:
• Abstract: This paper introduces the induced divergence, a new quantum divergence measure that replaces the hypothesis testing divergence in position-based decoding, simplifying the analysis of quantum communication and state redistribution while yielding tighter achievability bounds. Derived from a parent quantum relative entropy, it retains key properties such as data processing inequality and L\"owner monotonicity. Like the hypothesis testing divergence, it depends on a smoothing parameter and interpolates between the parent relative entropy (as the smoothing parameter approaches one) and the min-relative entropy (as it approaches zero), the latter holding when applied to the sandwiched R\'enyi relative entropy of order $\alpha\in[0,2]$. This framework refines the position-based decoding lemma, extending its applicability to a broader class of states and improving decoding success probabilities. Two key applications are considered: classical communication over quantum channels, where the induced divergence improves lower bounds on the distillable communication rate, and quantum state redistribution, where it leads to sharper bounds on communication costs. These results provide new insights into fundamental single-shot quantum information protocols and enhance existing analytical techniques.

Related papers

• Generalized quantum asymptotic equipartition [11.59751616011475]
  We prove that all operationally relevant divergences converge to the quantum relative entropy between two sets of quantum states. In particular, both the smoothed min-relative entropy between two sequential processes of quantum channels can be lower bounded by the sum of the regularized minimum output channel divergences. We apply our generalized AEP to quantum resource theories and provide improved and efficient bounds for entanglement distillation, magic state distillation, and the entanglement cost of quantum states and channels.
  arXiv  Detail & Related papers  (2024-11-06T16:33:16Z)
• Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement [39.58317527488534]
  Quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application. We analyse the generation of random states in PQCs under restrictions on the qubits connectivities. We place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement.
  arXiv  Detail & Related papers  (2024-05-03T17:32:55Z)
• Near-Term Distributed Quantum Computation using Mean-Field Corrections and Auxiliary Qubits [77.04894470683776]
  We propose near-term distributed quantum computing that involve limited information transfer and conservative entanglement production. We build upon these concepts to produce an approximate circuit-cutting technique for the fragmented pre-training of variational quantum algorithms.
  arXiv  Detail & Related papers  (2023-09-11T18:00:00Z)
• Overcoming entropic limitations on asymptotic state transformations through probabilistic protocols [12.461503242570641]
  We show that it is no longer the case when one allows protocols that may only succeed with some probability. We show that this is no longer the case when one allows protocols that may only succeed with some probability.
  arXiv  Detail & Related papers  (2022-09-07T18:00:00Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification [56.61325554836984]
  The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. We derive the exact exponent for the decay of the small modification of the quantum state in smoothing the max-relative entropy based on purified distance.
  arXiv  Detail & Related papers  (2021-11-01T16:35:41Z)
• Optimized quantum f-divergences [6.345523830122166]
  I introduce the optimized quantum f-divergence as a related generalization of quantum relative entropy. I prove that it satisfies the data processing inequality, and the method of proof relies upon the operator Jensen inequality. One benefit of this approach is that there is now a single, unified approach for establishing the data processing inequality for the Petz--Renyi and sandwiched Renyi relative entropies.
  arXiv  Detail & Related papers  (2021-03-31T04:15:52Z)
• Computing conditional entropies for quantum correlations [10.549307055348596]
  In particular, we find new upper bounds on the minimal global detection efficiency required to perform device-independent quantum key distribution. We introduce the family of iterated mean quantum R'enyi divergences with parameters $alpha_k = 1+frac12k-1$ for positive integers $k$. We show that the corresponding conditional entropies admit a particularly nice form which, in the context of device-independent optimization, can be relaxed to a semidefinite programming problem.
  arXiv  Detail & Related papers  (2020-07-24T15:27:51Z)
• Improved tripartite uncertainty relation with quantum memory [5.43508370077166]
  Uncertainty principle is a striking and fundamental feature in quantum mechanics. In quantum information theory, this uncertainty principle is popularly formulized in terms of entropy. We present an improvement of tripartite quantum-memory-assisted entropic uncertainty relation.
  arXiv  Detail & Related papers  (2020-04-09T03:54:51Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.