arXiv subjects

Takayuki Miyadera

Publications and source records attributed to Takayuki Miyadera.

At least 37 records · Page 2Linked to original sources

arXiv2017

Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics

We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical language to introduce and study quantum reference systems, showing that the orthodox "absolute" quantities are good representatives of observable relative quantities if the reference state is suitably localised. We use this relational formalism to critique the literature on the relationship between reference frames and superselection rules, settling a long-standing debate on the subject.

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arXiv2017

Incompatibility of quantum channels

Two quantum channels are called compatible if they can be obtained as marginals from a single broadcasting channel; otherwise they are incompatible. We derive a characterization of the compatibility relation in terms of concatenation and conjugation, and we show that all pairs of sufficiently noisy quantum channels are compatible. The complement relation of incompatibility can be seen as a unifying aspect for many quantum features. We demonstrate that several phenomena, such as impossibility of universal broadcasting and unavoidable measurement disturbance, appear naturally in this framework.

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arXiv2016

Energy-Time Uncertainty Relations in Quantum Measurements

Quantum measurement is a physical process. A system and an apparatus interact for a certain time period (measurement time), and during this interaction, information about an observable is transferred from the system to the apparatus. In this study, we quantify the energy fluctuation of the quantum apparatus required for this physical process to occur autonomously. We first examine the so-called standard model of measurement, which is free from any non-trivial energy-time uncertainty relation, to find that it needs an external system that switches on the interaction between the system and the apparatus. In such a sense this model is not closed. Therefore to treat a measurement process in a fully quantum manner we need to consider a "larger" quantum apparatus which works also as a timing device switching on the interaction. In this setting we prove that a trade-off relation (energy-time uncertainty relation), $τ\cdot ΔH_A \geq \frac{π\hbar}{4}$, holds between the energy fluctuation $ΔH_A$ of the quantum apparatus and the measurement time $τ$. We use this trade-off relation to discuss the spacetime uncertainty relation concerning the operational meaning of the microscopic structure of spacetime. In addition, we derive another trade-off inequality between the measurement time and the strength of interaction between the system and the apparatus.

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arXiv2016

Approximating relational observables by absolute quantities: A quantum accuracy-size trade-off

The notion that any physical quantity is defined and measured relative to a reference frame is traditionally not explicitly reflected in the theoretical description of physical experiments where, instead, the relevant observables are typically represented as "absolute" quantities. However, the emergence of the resource theory of quantum reference frames as a new branch of quantum information science in recent years has highlighted the need to identify the physical conditions under which a quantum system can serve as a good reference. Here we investigate the conditions under which, in quantum theory, an account in terms of absolute quantities can provide a good approximation of relative quantities. We find that this requires the reference system to be large in a suitable sense.

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arXiv2015

An Invitation to Quantum Incompatibility

In the context of a physical theory, two devices, A and B, described by the theory are called incompatible if the theory does not allow the existence of a third device C that would have both A and B as its components. Incompatibility is a fascinating aspect of physical theories, especially in the case of quantum theory. The concept of incompatibility gives a common ground for several famous impossibility statements within quantum theory, such as ``no-cloning'' and ``no information without disturbance''; these can be all seen as statements about incompatibility of certain devices. The purpose of this paper is to give a concise overview of some of the central aspects of incompatibility.

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arXiv2015

Solution to the mean king's problem using quantum error-correcting codes

We discuss the so-called mean king's problem, a retrodiction problem among non-commutative observables, in the context of error detection. Describing the king's measurement effectively by a single error operation, we give a solution of the mean king's problem using quantum error-correcting codes. The existence of a quantum error-correcting code from a solution is also presented.

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arXiv2014

Universality of Sequential Quantum Measurements

Unavoidable disturbance caused by a quantum measurement implies that the realizable subsequent measurements are getting limited after one performs some measurement. The obvious general limitation that one cannot circumvent by sequential or any other method is that the actually implemented measurements must be jointly measurable. In this work we show that any jointly measurable pair of observables can be obtained in a sequential measurement scheme, even if the second observable would be decided after the first measurement. This universality feature holds only for measurement schemes with a specific structure. As a supplementing result, we provide a characterization of all possible joint measurements obtained from a sequential measurement lacking universality.

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arXiv2014

Qualitative Noise-Disturbance Relation for Quantum Measurements

The inherent connection between noise and disturbance is one of the most fundamental features of quantum measurements. In the two well-known extreme cases a measurement either makes no disturbance but then has to be totally noisy or is as accurate as possible but then has to disturb so much that all subsequent measurements become redundant.Most of the measurements are, however, something between these two extremes.We derive a structural relation between observables and channels that properly explains the trade-off between noise and disturbance.

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arXiv2013

Strongly Incompatible Quantum Devices

The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint measurability to all kinds of possible measurement devices, and we call this relation compatibility. Two devices are incompatible if they cannot be implemented as parts of a single measurement setup. We introduce also a more stringent notion of incompatibility, strong incompatibility. Both incompatibility and strong incompatibility are rigorously characterized and their difference is demonstrated by examples.

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arXiv2011

Relation between information and disturbance in quantum key distribution protocol with classical Alice

The "semiquantum" key distribution protocol introduced by Zou et al. [Phys. Rev. A Vol.79, 052312 (2009)] is examined. The protocol while using two-way quantum communication requires only Bob to be fully quantum. We derive a trade-off inequality between information gained by Eve and the disturbance observed by legitimate users. It guarantees that Eve cannot obtain large information if the disturbance is sufficiently small.

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arXiv2011

Time-Energy Uncertainty Relation for a Quantum Clock as a Control Device

A quantum clock working as a control device is examined. The quality of the control process is characterized by the magnitude of deviation of perturbed state from unperturbed state of the controlled system. Uncertainty relations that relate the time duration of the process and energy of the clock to the quality of the control are presented.

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arXiv2011

Uncertainty Relations for Joint Localizability and Joint Measurability in Finite-Dimensional Systems

Two quantities quantifying uncertainty relations are examined. In J.Math.Phys. 48, 082103 (2007), Busch and Pearson investigated the limitation on joint localizability and joint measurement of position and momentum by introducing overall width and error bar width. In this paper, we show a simple relationship between these quantities for finite-dimensional systems. Our result indicates that if there is a bound on joint localizability, it is possible to obtain a similar bound on joint measurability. For finite-dimensional systems, uncertainty relations for a pair of general projection-valued measures are obtained as by-products.

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arXiv2011

Quantum Kolmogorov Complexity and Information-Disturbance Theorem

In this paper, a representation of the information-disturbance theorem based on the quantum Kolmogorov complexity that was defined by P. Vitanyi has been examined. In the quantum information theory, the information-disturbance relationship, which treats the trade-off relationship between information gain and its caused disturbance, is a fundamental result that is related to Heisenberg's uncertainty principle. The problem was formulated in a cryptographic setting and quantitative relationships between complexities have been derived.

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arXiv2011

Relation between strength of interaction and accuracy of measurement for a quantum measurement

The process of measuring a two-level quantum system was examined by applying Hamiltonian formalism. For the measurement of an observable that does not commute with the system Hamiltonian, a non-trivial relationship among the strength of interaction, the time interval of the process, and the accuracy of the measurement was obtained. Particularly, to achieve an error-free measurement of such an observable, a condition stating that the interaction Hamiltonian does not commute with the system Hamiltonian needs to be satisfied.

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arXiv2011

Quantum Kolmogorov Complexity and Bounded Quantum Memory

In this study, the effect of bounded quantum memory in a primitive information protocol has been examined using the quantum Kolmogorov complexity as a measure of information. We employed a toy two-party protocol in which Bob by using a bounded quantum memory and an unbounded classical memory estimates a message that was encoded in qubits by Alice in one of the bases X or Z. Our theorem gave a nontrivial effect of the memory boundedness. In addition, a generalization of the uncertainty principle in the presence of quantum memory has been obtained.

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arXiv2009

No-Cloning Theorem on Quantum Logics

This paper discusses the no-cloning theorem in a logico-algebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result indicating a relation between cloning on effect algebras and hidden variables.

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arXiv2009

Optimal Observables for Minimum-Error State Discrimination in General Probabilistic Theories

General Probabilistic Theories provide the most general mathematical framework for the theory of probability in an operationally natural manner, and generalize classical and quantum theories. In this article, we study state-discrimination problems in general probabilistic theories using a Bayesian strategy. After re-formulation of the theories with mathematical rigor, we first prove that an optimal observable to discriminate any (finite) number of states always exists in the most general setting. Next, we revisit our recently proposed geometric approach for the problem and show that, for two-state discrimination, this approach is indeed effective in arbitrary dimensional cases. Moreover, our method reveals an operational meaning of Gudder's ``intrinsic metric'' by means of the optimal success probability, which turns out to be a generalization of the trace distance for quantum systems. As its by-product, an information-disturbance theorem in general probabilistic theories is derived, generalizing its well known quantum version.

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arXiv2009

On Ping-Pong protocol and its variant

We discuss the Ping-Pong protocol which was proposed by Bostroem and Felbinger. We derive a simple trade-off inequality between distinguishability of messages for Eve and detectability of Eve for legitimate users. Our inequality holds for arbitrary initial states. That is, even if Eve prepares an initial state, she cannot distinguish messages without being detected. We show that the same inequality holds also on another protocol in which Alice and Bob use one-way quantum communication channel twice.

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