Approximate Quantum Markov Chains

Sutter, David

doi:10.1007/978-3-319-78732-9_5

Cited by 24 publications

(28 citation statements)

References 121 publications

(216 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We will suppress the state in the subscript when it is clear from context. We also make use of the (quantum) conditional mutual information [16], defined for a state ρ on a system containing subsystems X, Y, Z, as…”

Section: Proofsmentioning

confidence: 99%

Emergent classicality in general multipartite states and channels

Ranard

2021

Quantum

View full text Add to dashboard Cite

In a quantum measurement process, classical information about the measured system spreads throughout the environment. Meanwhile, quantum information about the system becomes inaccessible to local observers. Here we prove a result about quantum channels indicating that an aspect of this phenomenon is completely general. We show that for any evolution of the system and environment, for everywhere in the environment excluding an O(1)-sized region we call the "quantum Markov blanket," any locally accessible information about the system must be approximately classical, i.e. obtainable from some fixed measurement. The result strengthens the earlier result of Brandão et al. (Nat. comm. 6:7908) in which the excluded region was allowed to grow with total environment size. It may also be seen as a new consequence of the principles of no-cloning or monogamy of entanglement. Our proof offers a constructive optimization procedure for determining the "quantum Markov blanket" region, as well as the effective measurement induced by the evolution. Alternatively, under channel-state duality, our result characterizes the marginals of multipartite states.

show abstract

Section: Proofsmentioning

confidence: 99%

Emergent classicality in general multipartite states and channels

Ranard

2021

Quantum

View full text Add to dashboard Cite

show abstract

“…We note that optimization problems of the form we consider have recently been studied in the context of recovery measures (i.e., the fidelity of recovery and generalizations of this measure) [FR15, SW15, BHOS15, CHM + 16, BT16, BFT17]. Expositions of this topic can be found in [Sut18] and Chapter 12 of [Wil17].…”

Section: Introductionmentioning

confidence: 99%

Certifying optimality for convex quantum channel optimization problems

Coutts,

Girard,

Watrous

2018

Preprint

View full text Add to dashboard Cite

We identify necessary and sufficient conditions for a quantum channel to be optimal for any convex optimization problem in which the optimization is taken over the set of all quantum channels of a fixed size. Optimality conditions for convex optimization problems over the set of all quantum measurements of a given system having a fixed number of measurement outcomes are obtained as a special case. In the case of linear objective functions for measurement optimization problems, our conditions reduce to the well-known Holevo-Yuen-Kennedy-Lax measurement optimality conditions. We illustrate how our conditions can be applied to various state transformation problems having non-linear objective functions based on the fidelity, trace distance, and quantum relative entropy.

show abstract

“…A quantum Markov chain is defined as follows. The quantum systems A B C form a Markov chain if there exists a recovery channel P B→BC such that ρ ABC = (id A ⊗ P B→BC )(ρ AB ) [52]. In general, this holds if and only if…”

Section: A Notation States and Information Measuresmentioning

confidence: 99%

The Quantum Multiple-Access Channel with Cribbing Encoders

Pereg,

Deppe,

Boche

2021

Preprint

View full text Add to dashboard Cite

Communication over a quantum multiple-access channel (MAC) with cribbing encoders is considered, whereby Transmitter 2 performs a measurement on a system that is entangled with Transmitter 1. Based on the no-cloning theorem, perfect cribbing is impossible. This leads to the introduction of a MAC model with noisy cribbing. In the causal and non-causal cribbing scenarios, Transmitter 2 performs the measurement before the input of Transmitter 1 is sent through the channel. Hence, Transmitter 2's cribbing may inflict a "state collapse" for Transmitter 1. Achievable regions are derived for each setting. Furthermore, a regularized capacity characterization is established for robust cribbing, i.e. when the cribbing system contains all the information of the channel input. Building on the analogy between the noisy cribbing model and the relay channel, a partial decode-forward region is derived for a quantum MAC with non-robust cribbing. For the classical-quantum MAC with cribbing encoders, the capacity region is determined with perfect cribbing of the classical input, and a cutset region is derived for noisy cribbing. In the special case of a classical-quantum MAC with a deterministic cribbing channel, the inner and outer bounds coincide.

show abstract

Approximate Quantum Markov Chains

Cited by 24 publications

References 121 publications

Emergent classicality in general multipartite states and channels

Emergent classicality in general multipartite states and channels

Certifying optimality for convex quantum channel optimization problems

The Quantum Multiple-Access Channel with Cribbing Encoders

Contact Info

Product

Resources

About