One-Shot Yield-Cost Relations in General Quantum Resource Theories

  title={One-Shot Yield-Cost Relations in General Quantum Resource Theories},
  author={Ryuji Takagi and Bartosz Regula and Mark M. Wilde},
  journal={PRX Quantum},
Although itis wellknown that the amount of resources that can be asymptotically distilledfrom a quantum state orchanneldoesnotexceedtheresourcecostneededtoproduceit, thecorrespondingrelationinthenon-asymptotic regime hitherto has not been well understood. Here, we establish a quantitative relation between the one-shot distillable resource yield and dilution cost in terms of transformation errors involved in these processes. Notably, our bound is applicable to quantum state and channel… 

Tight constraints on probabilistic convertibility of quantum states

The monotone is used to tightly characterise single-shot probabilistic distillation in broad types of resource theories, allowing an exact analysis of the trade-offs between the probabilities and errors in distilling maximally resourceful states.

Quantifying dynamical magic with completely stabilizer preserving operations as free

The resource theory of magic is extended to the channel case by considering completely stabilizer preserving operations (CSPOs) as free and a classical simulation algorithm whose runtime is related to the generalized robustness of magic for channels is given.



Benchmarking one-shot distillation in general quantum resource theories

It is shown that every convex quantum resource theory admits a meaningful notion of a pure maximally resourceful state which maximizes several monotones of operational relevance and finds use in distillation.

One-Shot Manipulation of Dynamical Quantum Resources.

We develop a unified framework to characterize one-shot transformations of dynamical quantum resources in terms of resource quantifiers, establishing universal conditions for exact and approximate

No-Go Theorems for Quantum Resource Purification: New Approach and Channel Theory

A novel and powerful method is developed for analyzing the limitations of quantum resource purification, which not only leads to improved bounds that rule out exact purification for a broader range of noisy states and are tight in certain cases, but also allow us to establish a no-purification theory for quantum channel (dynamical) resources.

One-shot dynamical resource theory

This work establishes a universal strategy to determine upper and lower bounds on rates that convert between any given resource and the target, and shows that the rates are related to resource measures based on the channel robustness and the channel hypothesis testing entropy, with regularization factors of the target resource measures.

General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures

This work proves the corresponding uniqueness inequality for the consistent resource measures of a quantum state take values between the distillable resource and the resource cost of the state, and establishes a foundation of QRTs applicable to mathematically intractable but physically motivated quantum resources in a unified way.

Quantum resource theories in the single-shot regime

One of the main goals of any resource theory such as entanglement, quantum thermodynamics, quantum coherence, and asymmetry, is to find necessary and sufficient conditions (NSC) that determine

Operational Interpretation of Weight-Based Resource Quantifiers in Convex Quantum Resource Theories.

The resource quantifier of weight of resource for convex quantum resource theories of states and measurements with arbitrary resources captures the advantage that a resourceful state offers over all possible free states (measurements) in the operational task of exclusion of subchannels (states).

Simple bounds for one-shot pure-state distillation in general resource theories

Borders for distilling many copies of a pure state from an arbitrary initial state in a general quantum resource theory are presented and known results in coherence and entanglement theory are reproduced in this more general framework.

Operational Quantification of Continuous-Variable Quantum Resources.

It is shown that the robustness constitutes a well-behaved, bona fide resource quantifier in any convex resource theory, contrary to a related negativity-based measure known as the standard robustness.

Fundamental limitations on distillation of quantum channel resources

This work establishes universal limitations on the processing of both quantum states and channels, expressed in the form of no-go theorems and quantitative bounds for the manipulation of general quantum channel resources under the most general transformation protocols.