Quantum Channel Marginal Problem

Hsieh, Chung-Yun; Lostaglio, Matteo; Acín, Antonio

doi:10.48550/arxiv.2102.10926

Cited by 6 publications

(25 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To define the free operations, let us first recall the notion of channel compatibility recently introduced in Ref. [65]. Throughout, we use E A→B to represent a channel mapping from systems A to B.…”

Section: E Completing the Resource Theory Of 𝑅-Free Incompatibilitymentioning

confidence: 99%

“…Then, a global channel E S →S mapping from S to S is said to have a well-defined marginal in the input-output pair X → X (with X ⊆ S and X ⊆ S) if there exists a marginal channel E X →X from X to X such that the following commutation relation holds [65]:…”

Section: E Completing the Resource Theory Of 𝑅-Free Incompatibilitymentioning

confidence: 99%

“…In Section IV we provide several applications of our framework and demonstrate how some of the aforementioned problems can be recovered accordingly. After that, in Section V, we generalize-using the results recently established in [65]-our framework to the dynamical regime, thereby allowing us to analyze various channel resource theories and channel marginal problems within the same setting. The corresponding witness for incompatibility is then shown to admit an operational interpretation in terms of a state-discrimination task.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Resource Marginal Problems

Hsieh¹,

Tabia²,

Yin³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

We introduce the resource marginal problems, which concern the possibility of having a resource-free target subsystem compatible with a given collection of marginal density matrices. By identifying an appropriate choice of resource 𝑅 and target subsystem T, our problems reduce, respectively, to the well-known marginal problems for quantum states and the problem of determining if a given quantum system is a resource. More generally, we define a set of marginal states to be resource-free incompatible with a target subsystem T if all global states compatible with this set must result in a resourceful state in T. We show that this incompatibility induces a resource theory that can be quantified by a monotone. We derive necessary and sufficient conditions for this monotone to be a finite conic program and further show, via the corresponding witnesses, that resourcefree incompatibility is equivalent to an operational advantage in some subchannel discrimination task. Via our framework, a clear connection can be established between any marginal problem (that involves some notion of incompatibility) for quantum states and a resource theory for quantum states. In addition, the universality of our framework leads, for example, to an immediate, quantitative understanding of the incompatibility associated with the recently-proposed entanglement marginal problems. As further applications, we provide the first example showing a form of transitivity of nonlocality (steerability) for quantum states. We discuss also the analogous framework in the dynamical regime and establish a set of theoretical results that closely mirror those obtained for a resource theory for quantum states. Again, they allow us to recover a wide variety of results related to the studies of channel marginal problems, channel resource theories, etc.

show abstract

Section: E Completing the Resource Theory Of 𝑅-Free Incompatibilitymentioning

confidence: 99%

Section: E Completing the Resource Theory Of 𝑅-Free Incompatibilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Resource Marginal Problems

Hsieh¹,

Tabia²,

Yin³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Given this, we can ask if one can construct a correlation measure related to the unitarity similar to the covariance of two random variables. However, while there is a clear notion of a marginal distribution for a joint probability distribution the situation is more complex for a bipartite quantum channel where the reduction to 'marginal channels' depends on the structure of the initial state considered [34].…”

Section: Defining a Tractable Measure Of Correlation For Bipartite Qu...mentioning

confidence: 99%

Estimation of correlations and non-separability in quantum channels via unitarity benchmarking

Girling,

Cirstoiu,

Jennings

2021

Preprint

View full text Add to dashboard Cite

The ability to transfer coherent quantum information between systems is a fundamental component of quantum technologies and leads to coherent correlations within the global quantum process. However correlation structures in quantum channels are less studied than those in quantum states. Motivated by recent techniques in randomized benchmarking, we develop a range of results for efficient estimation of correlations within a bipartite quantum channel. We introduce sub-unitarity measures that are invariant under local changes of basis, generalize the unitarity of a channel, and allow for the analysis of coherent information exchange within channels. Using these, we show that unitarity is monogamous, and provide a novel information-disturbance relation. We then define a notion of correlated unitarity that quantifies the correlations within a given channel. Crucially, we show that this measure is strictly bounded on the set of separable channels and therefore provides a witness of non-separability. Finally, we describe how such measures for effective noise channels can be efficiently estimated within different randomized benchmarking protocols. We find that the correlated unitarity can be estimated in a SPAM-robust manner for any separable quantum channel, and show that a benchmarking/tomography protocol with mid-circuit resets can reliably witness nonseparability for sufficiently small reset errors. The tools we develop provide information beyond that obtained via simultaneous randomized benchmarking and so could find application in the analysis of cross-talk and coherent errors in quantum devices.

show abstract

“…A marginal of a quantum channel is also a quantum channel. This gives rise to the question of compatibility of quantum channels [HMZ16,HLA21].…”

Section: Asymmetric Quantum Cloningmentioning

confidence: 99%

A geometrical description of the universal $1 \to 2$ asymmetric quantum cloning region

Nechita¹,

Pellegrini²,

Rochette³

2021

Preprint

View full text Add to dashboard Cite

We consider the problem of determining the achievable region of parameters for universal 1 → 2 asymmetric quantum cloning. Measuring the cloning performance with the figure of merit of singlet fraction, we show that the physical region is a union of ellipses in the plane. Equivalently, we characterize the parameter region of quantum state compatibility of two possibly different isotropic states, considering, for the first time, negative singlet fractions.

show abstract

Quantum Channel Marginal Problem

Cited by 6 publications

References 30 publications

Resource Marginal Problems

Resource Marginal Problems

Estimation of correlations and non-separability in quantum channels via unitarity benchmarking

A geometrical description of the universal $1 \to 2$ asymmetric quantum cloning region

Contact Info

Product

Resources

About