Showing papers on "Coherent information published in 1996"

Quantum data processing and error correction

Abstract: This paper investigates properties of noisy quantum information channels We define a quantity called coherent information, which measures the amount of quantum information conveyed in the noisy channel This quantity can never be increased by quantum information processing, and it yields a simple necessary and sufficient condition for the existence of perfect quantum error correction \textcopyright{} 1996 The American Physical Society

Classical information capacity of a quantum channel

Abstract: We consider the transmission of classical information over a quantum channel. The channel is defined by an ``alphabet'' of quantum states, e.g., certain photon polarizations, together with a specified set of probabilities with which these states must be sent. If the receiver is restricted to making separate measurements on the received ``letter'' states, then the Kholevo theorem implies that the amount of information transmitted per letter cannot be greater than the von Neumann entropy H of the letter ensemble. In fact the actual amount of transmitted information will usually be significantly less than H. We show, however, that if the sender uses a block coding scheme consisting of a choice of code words that respects the a priori probabilities of the letter states, and the receiver distinguishes whole words rather than individual letters, then the information transmitted per letter can be made arbitrarily close to H and never exceeds H. This provides a precise information-theoretic interpretation of von Neumann entropy in quantum mechanics. We apply this result to ``superdense'' coding, and we consider its extension to noisy channels. \textcopyright{} 1996 The American Physical Society.

Quantum-state disturbance versus information gain: Uncertainty relations for quantum information

Abstract: When an observer wants to identify a quantum state, which is known to be one of a given set of nonorthogonal states, the act of observation causes a disturbance to that state. We investigate the trade-off between the information gain and that disturbance. This issue has important applications in quantum cryptography. The optimal detection method, for a given tolerated disturbance, is explicitly found in the case of two equiprobable nonorthogonal pure states. \textcopyright{} 1996 The American Physical Society.

Information as a basic property of the universe

Abstract: A theory is proposed which considers information to be a basic property of the universe the way matter and energy are. Operationally — just as energy is defined in terms of its capacity to perform work — so is information defined in terms of its capacity to organize a system. Pure energy can perform no ‘useful’ (entropy reducing) work without a concomitant input of information. Conversely, all expenditures of energy lead to a reorganization of the universe, hence to a change in its information status. Energy and information are interconvertible; physicists have been able to ignore the information parameter principally for two major reasons. First, historically, just as there was no need to define energy prior to the advent of increasingly complex, powered machinery and cannons (Galileo was a military engineer), so was there no need until the 20th Century to define information. It was the telephone engineers who first preoccupied themselves with developing a theory of information. The second reason is that physicists invented accounting devices such as potential energy and entropy to explain the apparent disappearance of energy yet maintain the law of the conservation of energy. The proposed theory would consider that what is conserved is the sum of information and energy. The mathematical relationship between information and entropy is provided by the equation: I = (I o ) e −S K while the conversion of energy into information involves the relationship: 1 J /° K = 10 23 bits (approximately) Acceptance of the theory would require paradigm shifts in a number of interrelated areas.

Limitation on the Amount of Accessible Information in a Quantum Channel

Abstract: We prove a new result limiting the amount of accessible information in a quantum channel This generalizes Kholevo's theorem and implies it as a simple corollary Our proof uses the strong subadditivity of the von Neumann entropy functional $S(\ensuremath{\rho})$ and a specific physical analysis of the measurement process The result presented here has application in information obtained from ``weak'' measurements, such as those sometimes considered in quantum cryptography

Physical interpretation of information entropy: Numerical evidence of the Collins conjecture.

Abstract: The conjecture by Collins that the correlation energy ${\mathit{E}}_{\mathrm{corr}}$ is proportional to the information entropy as defined by Jaynes is examined. We present numerical evidence supporting this conjecture by computing atomic information entropies from highly correlated wave functions of configuration-interaction (CI) type for members of the lithium isoelectronic series. Sequences of increasingly larger basis sets are used to show how ${\mathit{E}}_{\mathrm{corr}}^{\mathrm{CI}}$ (CI correlation energy) is related to ${\mathit{S}}_{\mathrm{Jaynes}}$. \textcopyright{} 1996 The American Physical Society.

Sending quantum entanglement through noisy channels

Abstract: This paper addresses some general questions of quantum information theory arising from the transmission of quantum entanglement through (possibly noisy) quantum channels. A pure entangled state is prepared of a pair of systems $R$ and $Q$, after which $Q$ is subjected to a dynamical evolution given by the superoperator $\superop^{Q}$. Two interesting quantities can be defined for this process: the entanglement fidelity $F_{e}$ and the entropy production $S_{e}$. It turns out that neither of these quantities depends in any way on the system $R$, but only on the initial state and dynamical evolution of $Q$. $F_{e}$ and $S_{e}$ are related to various other fidelities and entropies, and are connected by an inequality reminiscent of the Fano inequality of classical information theory. Some insight can be gained from these techniques into the security of quantum cryptographic protocols and the nature of quantum error-correcting codes.

Quantum teleportation without irreversible detection.

Abstract: We show that the teleportation of an unknown quantum state can be achieved without the irreversible amplification of an intermediate detector, as required in the original scheme. This allows us to show how the quantum information is ``hidden'' within the correlations between the system and the environment while being wholly absent from any of the individual subsystems. This revival of correlations from the environment is quite surprising since it seems to go against the usual intuition of the environment irreversibly destroying information. By developing a description of quantum teleportation at the amplitude level we can see why the relevant information is robust to such irreversible actions of the environment. \textcopyright{} 1996 The American Physical Society.

Coherent states for quantum systems with a trilinear boson Hamiltonian

Abstract: We introduce a set of coherent states which are associated with quantum systems governed by a trilinear boson Hamiltonian. These states are produced by the action of a nonunitary displacement operator on a reference state and can be equivalently defined by some eigenvalue equations. The system prepared initially in the reference state will evolve into the coherent state during the first instants of the interaction process. Some properties of the coherent states are discussed. In particular, the resolution of the identity is derived and the related analytic representation in the complex plane is developed. It is shown that this analytic representation coincides with a double representation based on the Glauber coherent states of the pump mode and on the SU(1,1) Perelomov coherent states of the signal-idler system. Entanglement between the field modes and photon statistics of the coherent states are studied. Connections between the coherent states and the long-time evolution induced by the trilinear Hamiltonian are considered.

Information flow and chaotic dynamics

Abstract: We introduce an information-theory-based concept for the characterization of the information flow in chaotic systems in the framework of symbolic dynamics. The information flow characterizes the loss of information about the initial conditions, i.e. the decay of statistical correlations between the entire past and a point p steps ahead into the future as a function of p. In the case where the partition generating the symbolic dynamics is finite the information loss is measured by an entropy. This entropy which we call "source-p-step-mutual information" is an extension of the source-entropy. More relevant is the study of the evolution of information loss for the cases of infinitesimal partitions which characterize the intrinsic behaviour of the dynamics on an extremely fine scale. The intrinsic information flow is characterized by the evolution of a conditional entropy which generalizes the Kolmogorov-Sinai entropy for the case of observing the uncertainty more than one step ahead into the future. In order to characterize the dynamics on fine scale and to describe the true and intrinsic information flow of chaotic systems an infinitesimal partition were used. The zeta function formalism is applied.