Let us consider two quantum systems: system $A$ and system $B$ . Suppose that some classical information is encoded to quantum states of the system $A$ and we distribute this information to both systems by making them interact with each other. We show that it is impossible to achieve this goal perfectly if the strength of interaction between the quantum systems is smaller than a quantity that is determined by noncommutativity between a Hamiltonian of the system $A$ and the states (density operators) used for the information encoding. This is a consequence of a generalized Winger-Araki-Yanase theorem which enables us to treat conserved quantities other than additive ones.Let us consider two quantum systems: system $A$ and system $B$. Suppose that some classical information is encoded to quantum states of the system $A$ and we distribute this information to both systems by making them interact with each other. We show that it is impossible to achieve this goal perfectly if the strength of interaction between the quantum systems is smaller than a quantity that is determined by noncommutativity between a Hamiltonian of the system $A$ and the states (density operators) used for the information encoding. This is a consequence of a generalized Winger-Araki-Yanase theorem which enables us to treat conserved quantities other than additive ones.

arXiv:quant-ph/0608218Physical Review ADec 7, 20064 citations

Information in Quantum Theory

Andrew Whitaker

Advanced information and knowledge processingJan 1, 20170 citations

On the Hidden-Variables Issue

Enrico G. Beltrametti, Gianni Cassinelli, Peter Carruthers

The Question of the Completeness of Quantum Mechanics When a classical system is in a pure state, that is, when its preparation represents maximal information, the value of every physical quantity is uniquely predicted. In other words, classical pure states are dispersion-free, and classical mechanics is deterministic. Only in case the state is nonpure, thus representing nonmaximal information about the system, does probability enter into the theory. Things are different with quantum systems. Even in case the state of the system is pure, it is impossible to predict a definite value of every physical quantity: only the probability distributions of the physical quantities are given. Pure quantum states have dispersion (though, of course, they can be dispersion-free for particular physical quantities), and probability enters into quantum theory at a much more fundamental level. The basic idea of so-called hidden-variable theories is to reject the fundamental role of probability in quantum theory and to argue that probability arises because quantum states, even the pure ones, do not represent the ultimate information about the system. Accordingly, it is conjectured that there are certain hidden variables, not yet subject to experimental detection, which would complete the information carried by the quantum states, thus giving rise to so precise a knowledge of the system that probabilities would disappear and precise values of all physical quantities would be uniquely determined.The Question of the Completeness of Quantum Mechanics When a classical system is in a pure state, that is, when its preparation represents maximal information, the value of every physical quantity is uniquely predicted. In other words, classical pure states are dispersion-free, and classical mechanics is deterministic. Only in case the state is nonpure, thus representing nonmaximal information about the system, does probability enter into the theory. Things are different with quantum systems. Even in case the state of the system is pure, it is impossible to predict a definite value of every physical quantity: only the probability distributions of the physical quantities are given. Pure quantum states have dispersion (though, of course, they can be dispersion-free for particular physical quantities), and probability enters into quantum theory at a much more fundamental level. The basic idea of so-called hidden-variable theories is to reject the fundamental role of probability in quantum theory and to argue that probability arises because quantum states, even the pure ones, do not represent the ultimate information about the system. Accordingly, it is conjectured that there are certain hidden variables, not yet subject to experimental detection, which would complete the information carried by the quantum states, thus giving rise to so precise a knowledge of the system that probabilities would disappear and precise values of all physical quantities would be uniquely determined.

Cambridge University Press eBooksDec 28, 19840 citations

Information measures in quantum mechanics

Evan Harris Walker

Physica B+CJul 1, 19886 citations

A Quantification of Disturbance

Lorenzo Maccone

I introduce the “entropic disturbance” D that measures the quantity of disturbance induced by an arbitrary evolution of a quantum system. The quantity D satisfies the requirements that a disturbance should possess, as long as one focuses on the irreversibility of any disturbance. Other quantities customarily introduced to gauge disturbance do not weight irreversibility appropriately. An information‐disturbance tradeoff is introduced. It states that I ⩽ D, where I quantifies the information contained in the state of the system, i.e. the mutual information between the eigenvalues of the initial state and the measurement results.I introduce the “entropic disturbance” D that measures the quantity of disturbance induced by an arbitrary evolution of a quantum system. The quantity D satisfies the requirements that a disturbance should possess, as long as one focuses on the irreversibility of any disturbance. Other quantities customarily introduced to gauge disturbance do not weight irreversibility appropriately. An information‐disturbance tradeoff is introduced. It states that I ⩽ D, where I quantifies the information contained in the state of the system, i.e. the mutual information between the eigenvalues of the initial state and the measurement results.

AIP conference proceedingsJan 1, 20070 citations

Let us consider two quantum systems: system

A

and system

B

. Suppose that some classical information is encoded to quantum states of the system

A

and we distribute this information to both systems by making them interact with each other. We show that it is impossible to achieve this goal perfectly if the strength of interaction between the quantum systems is smaller than a quantity that is determined by noncommutativity between a Hamiltonian of the system

A

and the states (density operators) used for the information encoding. This is a consequence of a generalized Winger-Araki-Yanase theorem which enables us to treat conserved quantities other than additive ones.