Showing papers on "Coherent information published in 2005"
IBM1
TL;DR: In this paper, the capacity of a quantum channel for transmitting private classical information is derived, which is shown to be equal to the capacity for generating a secret key, and neither capacity is enhanced by forward public classical communication.
Abstract: A formula for the capacity of a quantum channel for transmitting private classical information is derived. This is shown to be equal to the capacity of the channel for generating a secret key, and neither capacity is enhanced by forward public classical communication. Motivated by the work of Schumacher and Westmoreland on quantum privacy and quantum coherence, parallels between private classical information and quantum information are exploited to obtain an expression for the capacity of a quantum channel for generating pure bipartite entanglement. The latter implies a new proof of the quantum channel coding theorem and a simple proof of the converse. The coherent information plays a role in all of the above mentioned capacities
833 citations
TL;DR: The concept of prior quantum information is explored: given an unknown quantum state distributed over two systems, how much quantum communication is needed to transfer the full state to one system is determined, conditioned on its prior information.
Abstract: Information—be it classical1 or quantum2—is measured by the amount of communication needed to convey it. In the classical case, if the receiver has some prior information about the messages being conveyed, less communication is needed3. Here we explore the concept of prior quantum information: given an unknown quantum state distributed over two systems, we determine how much quantum communication is needed to transfer the full state to one system. This communication measures the partial information one system needs, conditioned on its prior information. We find that it is given by the conditional entropy—a quantity that was known previously, but lacked an operational meaning. In the classical case, partial information must always be positive, but we find that in the quantum world this physical quantity can be negative. If the partial information is positive, its sender needs to communicate this number of quantum bits to the receiver; if it is negative, then sender and receiver instead gain the corresponding potential for future quantum communication. We introduce a protocol that we term ‘quantum state merging’ which optimally transfers partial information. We show how it enables a systematic understanding of quantum network theory, and discuss several important applications including distributed compression, noiseless coding with side information, multiple access channels and assisted entanglement distillation.
445 citations
TL;DR: In this article, a multiparty quantum state sharing scheme for an arbitrary two-particle state is presented with Einstein-Podolsky-Rosen pairs, where any one of the agents has the access to regenerate the original state with two local unitary operations if he collaborates with the other agents, say the controllers.
Abstract: A scheme for multiparty quantum state sharing of an arbitrary two-particle state is presented with Einstein-Podolsky-Rosen pairs. Any one of the $N$ agents has the access to regenerate the original state with two local unitary operations if he collaborates with the other agents, say the controllers. Moreover, each of the controllers is required to take only a product measurement ${\ensuremath{\sigma}}_{x}\ensuremath{\bigotimes}{\ensuremath{\sigma}}_{x}$ on his two particles, which makes this scheme more convenient for the agents in the applications on a network than others. As all the quantum source can be used to carry the useful information, the intrinsic efficiency of qubits approaches the maximal value. With a new notation for the multipartite entanglement, the sender need only publish two bits of classical information for each measurement, which reduces the information exchanged largely.
436 citations
TL;DR: A limit on the average fidelity achievable when the states are transmitted or stored by a classical channel, i.e., a measure and repreparation scheme which sends or stores classical information only is proved.
Abstract: We consider the storage and transmission of a Gaussian distributed set of coherent states of continuous variable systems. We prove a limit on the average fidelity achievable when the states are transmitted or stored by a classical channel, i.e., a measure and repreparation scheme which sends or stores classical information only. The obtained bound is tight and serves as a benchmark which has to be surpassed by quantum channels in order to outperform any classical strategy. The success in experimental demonstrations of quantum memories as well as quantum teleportation has to be judged on this footing.
146 citations
Book•
12 Sep 2005
TL;DR: The goal of this book is to contribute towards the realization of quantum information processing in a more efficient manner than is currently possible in the literature.
Abstract: Preface 1 Introduction 2 Quantum Theory 3 Quantum Communication and Information 4 Quantum Computing 5 Physical Realization of Quantum Information Processing References Index
109 citations
Book•
01 Jan 2005
TL;DR: Elements of Classical Information Theory, Elements of Quantum Information Theory and Information and the Brain are presented.
Abstract: Elements of Classical Information Theory.- Elements of Quantum Information Theory.- Classical, Quantum and Information-Driven Interactions.- The "Active" Role of Information in Biological Systems.- The 'Passive' Role of Information in Physics.- Information and the Brain.
91 citations
TL;DR: This paper examines how many-qubit (or many-spin) environments can store information about a single system and shows that randomly chosen states of the environment almost always encode the information so that an observer must capture a majority of the Environment to deduce the system’s state.
Abstract: As quantum information science approaches the goal of constructing quantum computers, understanding loss of information through decoherence becomes increasingly important. The information about a system that can be obtained from its environment can facilitate quantum control and error correction. Moreover, observers gain most of their information indirectly, by monitoring (primarily photon) environments of the “objects of interest.” Exactly how this information is inscribed in the environment is essential for the emergence of “the classical” from the quantum substrate. In this paper, we examine how many-qubit (or many-spin) environments can store information about a single system. The information lost to the environment can be stored redundantly, or it can be encoded in entangled modes of the environment. We go on to show that randomly chosen states of the environment almost always encode the information so that an observer must capture a majority of the environment to deduce the system’s state. Conversely, in the states produced by a typical decoherence process, information about a particular observable of the system is stored redundantly. This selective proliferation of “the fittest information” (known as Quantum Darwinism) plays a key role in choosing the preferred, effectively classical observables of macroscopic systems. The developing appreciation that the environment functions not just as a garbage dump, but as a communication channel, is extending our understanding of the environment’s role in the quantum-classical transition beyond the traditional paradigm of decoherence.
89 citations
TL;DR: These conceptions of entropy, which have been successively assimilated to different concepts such as disorder and information, are revisited, and disorder or agitation is shown to be more appropriately linked with temperature.
Abstract: Entropy is a basic physical quantity that led to various, and sometimes apparently conflicting interpretations. It has been successively assimilated to different concepts such as disorder and information. In this paper we're going to revisit these conceptions, and establish the three following results: Entropy measures lack of information; it also measures information. These two conceptions are complementary. Entropy measures freedom, and this allows a coherent interpretation of entropy formulas and of experimental facts. To associate entropy and disorder implies defining order as absence of freedom. Disorder or agitation is shown to be more appropriately linked with temperature.
81 citations
TL;DR: In this article, the authors consider quantum channels with two senders and one receiver and give multi-letter characterizations of two different two-dimensional capacity regions, the first region is comprised of the rates at which it is possible for one sender to send classical information, while the other sends quantum information.
Abstract: We consider quantum channels with two senders and one receiver. For an arbitrary such channel, we give multi-letter characterizations of two different two-dimensional capacity regions. The first region is comprised of the rates at which it is possible for one sender to send classical information, while the other sends quantum information. The second region consists of the rates at which each sender can send quantum information. For each region, we give an example of a channel for which the corresponding region has a single-letter description. One of our examples relies on a new result proved here, perhaps of independent interest, stating that the coherent information over any degradable channel is concave in the input density operator. We conclude with connections to other work and a discussion on generalizations where each user simultaneously sends classical and quantum information.
75 citations
TL;DR: The additivity of the minimal output Renyi entropies with entropic parameters α [0, 2], generalizing an argument by Alicki and Fannes, is proved and a weak form of covariance of a channel is introduced in order to relate these results to the classical information capacity.
Abstract: We consider the additivity of the minimal output entropy and the classical information capacity of a class of quantum channels. For this class of channels, the norm of the output is maximized for the output being a normalized projection. We prove the additivity of the minimal output Renyi entropies with entropic parameters α [0, 2], generalizing an argument by Alicki and Fannes, and present a number of examples in detail. In order to relate these results to the classical information capacity, we introduce a weak form of covariance of a channel. We then identify various instances of weakly covariant channels for which we can infer the additivity of the classical information capacity. Both additivity results apply to the case of an arbitrary number of different channels. Finally, we relate the obtained results to instances of bi-partite quantum states for which the entanglement cost can be calculated.
62 citations
TL;DR: In this paper, a general analytic approach is proposed for a three-level trapped ion system in the presence of the time-dependent couplings, which conclusively analyzes the general properties of the von Neumann entropy and quantum information entropy.
Abstract: Trapped and laser-cooled ions are increasingly used for a variety of modern high-precision experiments, frequency standard applications and quantum information processing. Therefore, in this communication we present a comprehensive analysis of the pattern of information entropy arising in the time evolution of an ion interacting with a laser field. A general analytic approach is proposed for a three-level trapped-ion system in the presence of the time-dependent couplings. By working out an exact analytic solution, we conclusively analyse the general properties of the von Neumann entropy and quantum information entropy. It is shown that the information entropy is affected strongly by the time-dependent coupling and exhibits long time periodic oscillations. This feature attributed to the fact that in the time-dependent region Rabi oscillation is time dependent. Using parameters corresponding to a specific three-level ionic system, a single beryllium ion in a RF-(Paul) trap, we obtain illustrative examples of some novel aspects of this system in the dynamical evolution. Our results establish an explicit relation between the exact information entropy and the entanglement between the multi-level ion and the laser field. We show that different nonclassical effects arise in the dynamics of the ionic population inversion, depending on the initial states of the vibrational motion/field and on the values of Lamb–Dicke parameter η.
Book•
01 Jan 2005
TL;DR: The rates at which classical and quantum information can be simultaneously transmitted from two spatially separated senders to a single receiver over an arbitrary quantum channel are characterized and two main results are proved.
Abstract: The rates at which classical and quantum information can be simultaneously transmitted from two spatially separated senders to a single receiver over an arbitrary quantum channel are characterized. Two main results are proved in detail. The first describes the region of rates at which one sender can send classical information while the other sends quantum information. The second describes those rates at which both senders can send quantum information. For each of these situations, an example of a channel is given for which the associated region admits a single-letter description. This is the author's Ph.D. dissertation, submitted to the Department of Electrical Engineering at Stanford University in March, 2005. It represents an expanded version of the paper quant-ph/0501045, containing a number of tutorial chapters which may be of independent interest for those learning about quantum Shannon theory.
TL;DR: In this paper, it was shown that the quantum capacity is lower bounded by the limit of coherent information maximized over the set of input density operators which are proportional to the projections onto the code spaces of symplectic stabilizer codes.
Abstract: The highest information rate at which quantum error-correction schemes work reliably on a channel is called the quantum capacity. Here this is proven to be lower-bounded by the limit of coherent information maximized over the set of input density operators which are proportional to the projections onto the code spaces of symplectic stabilizer codes. The quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a completely positive linear map on a Hilbert space of finite dimension. The codes that are proven to have the desired performance are symplectic stabilizer codes. On the depolarizing channel, the bound proven here is actually the highest possible rate at which symplectic stabilizer codes work reliably
TL;DR: It is shown that matter arises from quantum–mechanical processes through the constitution of larger ensembles that share some information while living organisms make use of a special form of information selection.
Abstract: Quantum–mechanical systems may be understood in terms of information. When they interact, they modify the information they carry or represent in two, and only two, ways: by selecting a part of the initial amount of (potential) information and by sharing information with other systems. As a consequence, quantum systems are informationally shielded. These features are shown to be general features of nature. In particular, it is shown that matter arises from quantum–mechanical processes through the constitution of larger ensembles that share some information while living organisms make use of a special form of information selection.
31 Oct 2005
TL;DR: In this article, the authors show that unconditional oblivious transfer can be achieved from a single realization of PR, and vice versa, and also show a simple and optimal protocol allowing for inverting the direction of OT.
Abstract: Oblivious transfer, a central functionality in modern cryptography, allows a party to send two one-bit messages to another who can choose one of them to read, remaining ignorant about the other, whereas the sender does not learn the receiver's choice. Oblivious transfer the security of which is information-theoretic for both parties is known impossible to achieve from scratch. The joint behavior of certain bi-partite quantum states is non-local, i.e., cannot be explained by shared classical information. In order to better understand such behavior, which is classically explainable only by communication, but does not allow for it, Popescu and Rohrlich have described a "non-locality machine": Two parties both input a bit, and both get a random output bit the XOR of which is the AND of the input bits. We show a close connection, in a cryptographic sense, between OT and the "PR primitive." More specifically, unconditional OT can be achieved from a single realization of PR, and vice versa. Our reductions, which are single-copy, information-theoretic, and perfect, also lead to a simple and optimal protocol allowing for inverting the direction of OT
TL;DR: In this article, it was proposed that both channel and entanglement problems can be classified in terms of pure states more than 2 parts, and the dimensions of the Hilbert spaces of the component parts, along with other criteria still to be determined.
Abstract: The well-known duality relating entangled states and noisy quantum channels is expressed in terms of a channel ket, a pure state on a suitable tripartite system, which functions as a pre-probability allowing the calculation of statistical correlations between, for example, the entrance and exit of a channel, once a framework has been chosen so as to allow a consistent set of probabilities. In each framework the standard notions of ordinary (classical) information theory apply, and it makes sense to ask whether information of a particular sort about one system is or is not present in another system. Quantum effects arise when a single pre-probability is used to compute statistical correlations in different incompatible frameworks, and various constraints on the presence and absence of different kinds of information are expressed in a set of all-or-nothing theorems which generalize or give a precise meaning to the concept of 'no-cloning'. These theorems are used to discuss the location of information in quantum channels modeled using a mixed-state environment, the classical-quantum channels introduced by Holevo, and the location of information in the physical carriers of a quantum code. It is proposed that both channel and entanglement problems be classified in terms of pure statesmore » (functioning as pre-probabilities) on systems of p{>=}2 parts, with mixed bipartite entanglement and simple noisy channels belonging to the category p=3, a five-qubit code to the category p=6, etc., then by the dimensions of the Hilbert spaces of the component parts, along with other criteria yet to be determined.« less
TL;DR: A unified theory of information transfer is presented, which naturally incorporates Shannon's theories of information transmission and the theory of identification in the presence of noise as extremal cases and provides several novel coding theorems.
TL;DR: In this paper, it is shown that it is possible to obtain the Quantum Mechanics principles using Information and Game Theory (IGT) and that the principles are universal invariant among human behavior, universe physical laws and ordered and complex biological systems.
Abstract: Rationality is the universal invariant among human behavior, universe physical laws and ordered and complex biological systems. Econophysics isboth the use of physical concepts in Finance and Economics, and the use of Information Economics in Physics. In special, we will show that it is possible to obtain the Quantum Mechanics principles using Information and Game Theory.
TL;DR: Classical privacy theory is presented as a particular case of information theory with adversaries, where similar general laws hold as in entanglement theory and the result of Renner and Wolf is placed into this general formalism.
Abstract: There are aspects of privacy theory that are analogous to quantum theory. In particular one can define distillable key and key cost in parallel to distillable entanglement and entanglement cost. We present here classical privacy theory as a particular case of information theory with adversaries, where similar general laws hold as in entanglement theory. We place the result of Renner and Wolf—that intrinsic information is lower bound for key cost—into this general formalism. Then we show that the question of whether intrinsic information is equal to key cost is equivalent to the question of whether Alice and Bob can create a distribution product with Eve using I
M
bits of secret key. We also propose a natural analogue of relative entropy of entanglement in privacy theory and show that it is equal to the intrinsic information. We also provide a formula analogous to the entanglement of formation for classical distributions.
TL;DR: This work studies two-player quantum games of incomplete information in which both the sides have partial information and the game exhibits many interesting features.
Abstract: We study two-player quantum games of incomplete information in which both the sides have partial information. The previous results of Du et al. [Phys. Rev. E 68 (2003) 016124] are incorporated in our more general formalism. Because of different roles played by the total information uncertainty and the information asymmetry, the game exhibits many interesting features.
TL;DR: In this paper, it was shown that if any post-quantum physics should allow more information storage it could still be under the umbrella of thermodynamics, and that thermodynamics implies a weaker bound on it than the quantum mechanical one (the Holevo bound).
Abstract: Thermodynamics is a macroscopic physical theory whose two very general laws are independent of any underlying dynamical laws and structures. Nevertheless, its generality enables us to understand a broad spectrum of phenomena in physics, information science and biology. Does thermodynamics then imply any results in quantum information theory? Taking accessible information in a system as an example, we show that thermodynamics implies a weaker bound on it than the quantum mechanical one (the Holevo bound). In other words, if any post-quantum physics should allow more information storage it could still be under the umbrella of thermodynamics.
TL;DR: This paper gives a sufficient condition for additivity of the minimum output entropy for a pair of given channels and an analytic verification of this condition for specific quantum channels breaking a closely related multiplicativity property yields validity of the additivity conjecture.
Abstract: In this paper we give a sufficient condition for additivity of the minimum output entropy for a pair of given channels and an analytic verification of this condition for specific quantum channels breaking a closely related multiplicativity property [1, 2]. This yields validity of the additivity conjecture for these channels, a result obtained by a different method in [3]. Our proof relies heavily upon certain concavity properties of the output entropy, which are of independent interest.
TL;DR: In this paper, it was shown that perfect quantum sealing is not possible for perfectly retrievable information, due to the possibility of performing a perfect measurement without disturbance, even on unknown states.
Abstract: Sealing information means making it publicly available, but with the possibility of knowing if it has been read. Commenting on Ref. 1, we will show that perfect quantum sealing is not possible for perfectly retrievable information, due to the possibility of performing a perfect measurement without disturbance, even on unknown states. The measurement is a collective one, and this makes the protocol of quantum sealing very interesting as the only example of the power of collective measurements in breaking security.
Posted Content•
TL;DR: This work derives the nonlinear evolution equations of dynamic information density and dynamic information entropy density, and obtains the dynamic mutual information and dynamic channel capacity reflecting the dynamic dissipation character in the transmission process.
Abstract: We extend present Shannon's static statistical information theory to dynamic processes and establish a dynamic statistical information theory. We derive the nonlinear evolution equations of dynamic information density and dynamic information entropy density. We present the expressions of drift information flow and diffusion information flow, the formulas of information entropy production rate and information dissipation rate. The information dissipation rate is equal to the information entropy production rate in a same dynamic system. Information diffusion and information dissipation occur at the same time. We obtain the dynamic mutual information and dynamic channel capacity reflecting the dynamic dissipation character in the transmission process. These derivations and results are unified and rigorous from evolution equations of dynamic information and dynamic information entropy without adding any extra assumption. Two actual dynamic topics are discussed.
TL;DR: It is argued that this fundamental aspect of nature can be seen as a resource for quantum information processing and presented examples showing how it is possible to do useful and efficient quantum informationprocessing using only the effects of particle statistics.
Abstract: Particle statistics is a fundamental part of quantum physics, and yet its role and use in the context of quantum information have been poorly explored so far. After briefly introducing particle statistics and the Symmetrization Postulate, we argue that this fundamental aspect of nature can be seen as a resource for quantum information processing and present examples showing how it is possible to do useful and efficient quantum information processing using only the effects of particle statistics.
Posted Content•
TL;DR: In this paper, it is shown that collapse of the wave function on a quantum system A may be brought about by an interaction with another quantum system B, and that this is not just a possible but a necessary consequence of information transfer from A to B. The authors generalize this to explain why coherences are normally not observed in macroscopic quantum systems.
Abstract: It is widely known that `collapse of the wave function' on a quantum system A may be brought about by an interaction with another quantum system B. We will prove that this is not just a possible, but a necessary consequence of information transfer from A to B. We generalize this in order to explain why coherences are normally not observed in macroscopic quantum systems. Finally, we provide a quantitative insight into the balance between information gain and state disturbance. We define the quality of an information transfer. For all information transfers of a certain quality, we find a minimum amount of state collapse. Along the way, we obtain generalizations of the Joint Measurement Theorem and of the Heisenberg Principle.
12 Dec 2005
TL;DR: New formulae for the mutual information between jointly observed analog signals and point processes are developed allowing also that there may be an underlying unobserved state.
Abstract: We develop new formulae for the mutual information between jointly observed analog signals and point processes allowing also that there may be an underlying unobserved state. Our derivation method delivers existing results as special cases while throwing new light on them.
TL;DR: This paper discusses two problems studied recently that concerns a quantum algorithm in a generalized sense solving the SAT problem (one of NP complete problems) and another concerns quantum mutual entropy properly describing quantum communication processes.
TL;DR: In this article, the degree of entanglement in a two-level atom and two electromagnetic fields injected simultaneously within a cavity, with the interaction between the fields in parametric frequency-converter form, was measured under certain conditions and consequently the density matrix was obtained.
Abstract: We consider the interaction between a two-level atom and two electromagnetic fields injected simultaneously within a cavity, with the interaction between the fields in parametric frequency-converter form. The wave function in Schr odinger picture is obtained under certain conditions and consequently the density matrix. By employing a generalization of the von Neumann mutual information (in the context of Tsallis' nonextensive statistics) we measure the degree of entanglement for the present system. An important change is observed in the generalized mutual information depending on the entropic index. We also measure the minimum degree of entanglement during the transition from collapse to revival and vice-versa. Successive revival peaks show a lowering of the local maximum point indicating a dissipative irreversible change in the atomic state.
TL;DR: Liouville equation, SKE and quantum Fokker-Planck equation for information density or entropy operator share the same formalisms as that of density operator, which allows one to apply QID directly to perform quantum information as discussed by the authors.
Abstract: We study several kinetic equations for quantum information density (QID) based on the classical dynamical statistical information theory (Trans. Beijing Inst. Technol. 24 (2004) 1; Acta Phys. Scinica 53 (2004) 2852). We find that the Liouville equation, SKE and quantum Fokker–Planck equation for information density or entropy operator share the same formalisms as that of density operator. This allows one to apply QID directly to perform quantum information. Furthermore, we also obtain a quantum Fokker–Planck equation for information density which exposes that flow of shift and diffusion for information density introduce change of total derivative of information density with respect to time. As an application, the complex spectrum of SKE for information density has been discussed, which can be used to study stability of quantum computing in a spin-boson model.