arXiv subjects

Takayuki Miyadera

Publications and source records attributed to Takayuki Miyadera.

At least 19 recordsLinked to original sources

arXiv2024

The incompatibility of quantum channels in general probabilistic theories

In quantum theory, there exist sets of operations that cannot be performed simultaneously. These sets of operations are referred to as incompatible. While this definition of incompatibility extends to general probabilistic theories (GPTs), the dependency of the set of compatible sets on the definition of composite systems has not been thoroughly investigated. For quantum channels, compatibility is defined using the tensor product of Hilbert spaces, based on the conventional composite system. However, in GPTs, composite systems are not uniquely defined, and the set of states can vary from the minimal tensor to the maximal tensor. In this paper, in addition to the usual quantum compatibility, we introduce min-tensor-compatibility using the minimal tensor on the composite system of effect spaces and investigate their relationship employing noisy identity channels on qubits. As a result, we found that the set of min-tensor-compatible channel pairs is strictly broader than the set of quantum-compatible channel pairs. Furthermore, we introduce the concept of almost quantum compatible pairs of channels from an operational perspective. This concept corresponds to cases where the correlation functions in the verification of compatibility can be realized through a channel and local reinterpretation of effects. We demonstrate that the set of all almost quantum compatible channel pairs is strictly narrower than the set of all min-tensor-compatible channel pairs.

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arXiv2024

Upper bounds on probabilities in channel measurements on qubit channels and their applications

One of the fundamental tasks in quantum information processing is to measure the quantum channels. Similar to measurements of quantum states, measurements of quantum channels are inherently stochastic, that is, quantum theory provides a formula to calculate the probability of obtaining an outcome. The upper bound on each probability associated with the measurement outcome of the quantum channels is a fundamental and important quantity. In this study, we derived the upper bounds of the probability in a channel measurement for specific classes of quantum channels. We also present two applications for the upper bounds. The first is the notion of convertibility considered by Alberti and Uhlmann and the second is the detection problem of a quantum channel. These applications demonstrate the significance of the obtained upper bounds.

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arXiv2023

Measurement disturbance and conservation laws in quantum mechanics

Measurement error and disturbance, in the presence of conservation laws, are analysed in general operational terms. We provide novel quantitative bounds demonstrating necessary conditions under which accurate or non-disturbing measurements can be achieved, highlighting an interesting interplay between incompatibility, unsharpness, and coherence. From here we obtain a substantial generalisation of the Wigner-Araki-Yanase (WAY) theorem. Our findings are further refined through the analysis of the fixed-point set of the measurement channel, some extra structure of which is characterised here for the first time.

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arXiv2023

Quantum measurements constrained by the third law of thermodynamics

In the quantum regime, the third law of thermodynamics implies the unattainability of pure states. As shown recently, such unattainability implies that a unitary interaction between the measured system and a measuring apparatus can never implement an ideal projective measurement. In this paper, we introduce an operational formulation of the third law for the most general class of physical transformations, the violation of which is both necessary and sufficient for the preparation of pure states. Subsequently, we investigate how such a law constrains measurements of general observables, or positive operator valued measures. We identify several desirable properties of measurements which are simultaneously enjoyed by ideal projective measurements -- and are hence all ruled out by the third law in such a case -- and determine if the third law allows for these properties to obtain for general measurements of general observables and, if so, under what conditions. It is shown that while the third law rules out some of these properties for all observables, others may be enjoyed by observables that are sufficiently "unsharp".

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arXiv2022

Programming of channels in generalized probabilistic theories

For a given target system and apparatus described by quantum theory, the so-called quantum no-programming theorem indicates that a family of states called programs in the apparatus with a fixed unitary operation on the total system programs distinct unitary dynamics to the target system only if the initial programs are orthogonal to each other. The current study aims at revealing whether a similar behavior can be observed in generalized probabilistic theories (GPTs). Generalizing the programming scheme to GPTs, we derive a similar theorem to the quantum no-programming theorem. We furthermore demonstrate that programming of reversible dynamics is related closely to a curious structure named a quasi-classical structure on the state space. Programming of irreversible dynamics, i.e., channels in GPTs is also investigated.

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arXiv2022

An uncertainty relation for measurements of random unitary channels acting on a qubit

By preparing an input state and measuring an observable for the output state, we can measure a quantum channel. Following the formulation given by Xiao et al., we study an uncertainty relation for ancilla-free measurements of random unitary channels acting on a qubit. We obtain an explicit formula and give a necessary and sufficient condition for this formula to be nontrivial.

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arXiv2021

Testing incompatibility of quantum devices with few states

When observations must come from incompatible devices and cannot be produced by compatible devices? This question motivates two integer valued quantifications of incompatibility, called incompatibility dimension and compatibility dimension. The first one quantifies how many states are minimally needed to detect incompatibility if the test states are chosen carefully, whereas the second one quantifies how many states one may have to use if they are randomly chosen. With concrete examples we show that these quantities have unexpected behaviour with respect to noise.

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arXiv2020

A quantum reference frame size-accuracy trade-off for quantum channels

The imposition of symmetry upon the nature and structure of quantum observables has recently been extensively studied, with quantum reference frames playing a crucial role. In this paper, we extend this work to quantum transformations, giving quantitative results showing, in direct analogy to the case of observables, that a "large" reference frame is required for non-covariant channels to be well approximated by covariant ones. We apply our findings to the concrete setting of SU(2) symmetry.

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arXiv2020

Preparation Uncertainty Implies Measurement Uncertainty in a Class of Generalized Probabilistic Theories

In quantum theory, it is known for a pair of noncommutative observables that there is no state on which they take simultaneously definite values, and that there is no joint measurement of them. They are called preparation uncertainty and measurement uncertainty respectively, and research has unveiled that they are not independent from but related with each other in a quantitative way. This study aims to reveal whether similar relations to quantum ones hold also in generalized probabilistic theories (GPTs). In particular, a certain class of GPTs is considered which can be characterized by transitivity and self-duality and regarded as extensions of quantum theory. It is proved that there are close connections expressed quantitatively between two types of uncertainty on a pair observables also in those theories: if preparation uncertainty exists, then measurement uncertainty also exists, and they are described by similar inequalities. Our results manifest that their correspondences are not specific to quantum theory but more universal ones.

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arXiv2020

Entropic Uncertainty Relations in a Class of Generalized Probabilistic Theories

Entropic uncertainty relations play an important role in both fundamentals and applications of quantum theory. Although they have been well-investigated in quantum theory, little is known about entropic uncertainty in generalized probabilistic theories (GPTs). The current study explores two types of entropic uncertainty relations, preparation and measurement uncertainty relations, in a class of GPTs which can be considered generalizations of quantum theory. Not only a method for obtaining entropic preparation uncertainty relations but also an entropic measurement uncertainty relation similar to the quantum one by Buscemi et al. [Phys. Rev. Lett., 112, 050401] are proved in those theories. It manifests that the entropic structure of uncertainty relations in quantum theory is more universal. Concrete calculations of our relations in GPTs called the regular polygon theories are also demonstrated.

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arXiv2019

Witnessing incompatibility of quantum channels

We introduce the notion of incompatibility witness for quantum channels, defined as an affine functional that is non-negative on all pairs of compatible channels and strictly negative on some incompatible pair. This notion extends the recent definition of incompatibility witnesses for quantum measurements. We utilize the general framework of channels acting on arbitrary finite dimensional von Neumann algebras, thus allowing us to investigate incompatibility witnesses on measurement-measurement, measurement-channel and channel-channel pairs. We prove that any incompatibility witness can be implemented as a state discrimination task in which some intermediate classical information is obtained before completing the task. This implies that any incompatible pair of channels gives an advantage over compatible pairs in some such state discrimination task.

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arXiv2019

Relation between state-distinction power and disturbance in quantum measurements

The measurement of an informative observable strongly disturbs a quantum state. We examine the so-called information-disturbance relation by introducing order relations based on the state distinction power of an observable and a variety of non-disturbed observables with respect to a channel, and obtain qualitative and quantitative representations.

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arXiv2019

Relative Quantum Time

The need for a time-shift invariant formulation of quantum theory arises from fundamental symmetry principles as well as heuristic cosmological considerations. Such a description then leaves open the question of how to reconcile global invariance with the perception of change, locally. By introducing relative time observables, we are able to make rigorous the Page-Wootters conditional probability formalism to show how local Heisenberg evolution is compatible with global invariance.

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arXiv2019

Noise-disturbance relation and the Galois connection of quantum measurements

The relation between noise and disturbance is investigated within the general framework of Galois connections. Within this framework, we introduce the notion of leak of information, mathematically defined as one of the two closure maps arising from the observable-channel compatibility relation. We provide a physical interpretation for it, and we give a comparison with the analogous closure maps associated with joint measurability and simulability for quantum observables.

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arXiv2017

Fundamental bound on the power of quantum machines

Giving a universal upper bound on the power output of heat engines is a long-standing open problem. We tackle this problem for generic quantum machines in self-contained formulation by carefully including the switching process of the interaction. In this way, we show a fundamental upper bound on the power associated with the energy-time uncertainty principle. As a result, the energy fluctuation of the external controller is verified as a necessary resource for producing the power. This bound implies a trade-off between the power and `noise' for work extraction, which yields an estimation on the time scale to obtain detectable work extraction. Ideal clock-driven model of autonomous quantum machine gives a concrete demonstration of our bound.

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arXiv2017

The unavoidable information flow to environment in quantum measurements

One of the basic lessons of quantum theory is that one cannot obtain information on an unknown quantum state without disturbing it. Hence, by performing a certain measurement, we limit the other possible measurements that can be effectively implemented on the original input state. It has been recently shown that one can implement sequentially any device, either channel or observable, which is compatible with the first measurement [T. Heinosaari and T. Miyadera: Phys. Rev. A Vol 91 (2015), 022110]. In this work we prove that this can be done, apart from some special cases, only when the succeeding device is implemented on a larger system than just the input system. This means that some part of the still available quantum information has been flown to the environment and cannot be gathered by accessing the input system only. We characterize the size of the post-measurement system by determining the class of measurements for the observable in question that allow the subsequent realization of any measurement process compatible with the said observable. We also study the class of measurements that allow the subsequent realization of any observable jointly measurable with the first one and show that these two classes coincide when the first observable is extreme.

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arXiv2017

Limitations on post-processing assisted quantum programming

A quantum multimeter is a programmable device that can implement measurements of different observables depending on the programming quantum state inserted into it. The advantage of this arrangement over a single purpose device is in its versatility: one can realize various measurements simply by changing the programming state. The classical manipulation of measurement output data is known as post-processing. In this work we study the post-processing assisted quantum programming, which is a protocol where quantum programming and classical post-processing are combined. We provide examples showing that these two processes combined can be more efficient than either of them used separately. Furthermore, we derive an inequality relating the programming resources to their corresponding programmed observables, thereby enabling us to study the limitations on post-processing assisted quantum programming.

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arXiv2017

Relativity of Quantum States and Observables

Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as the incorporation of a quantum reference frame, we show that the usual quantum description approximates the relative one precisely when the reference system admits an appropriate localisable quantity and a localised state. From this follows a new perspective on the nature and reality of quantum superpositions and optical coherence.

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