Optimal control of overdamped systems.

Necessary and sufficient conditions on n-qudit state for perfect teleportation of an arbitrary single qudit state

Information erasure inevitably leads to the generation of heat. Minimizing this dissipation will be crucial for developing small-scale information processing systems, but little is known about the optimal procedures required. We have obtained closed-form expressions for maximally efficient erasure cycles for deletion of a classical bit of information stored by the position of a particle diffusing in a double-well potential. We find that the extra heat generated beyond the Landauer bound is proportional to the square of the Hellinger distance between the initial and final states divided by the cycle duration, which quantifies how far out of equilibrium the system is driven. Finally, we demonstrate close agreement between the exact optimal cycle and the protocol found using a linear response framework.

Recently, a quantum secure direct communication (QSDC) protocol based on the mixture of Bell state particles and single photons[Acta Phys. Sin. 65 230301(2016)] was put forward. In this QSDC protocol, the single photons and the Bell states were both used as information carriers. To be specific, each Bell state as well as single photon was encoded by three bits of classical information. After the sender told the receiver how to measure the particles, the receiver could read out the secret message sent by the sender. Speciously, the information transmission efficiency of this protocol was high. Unfortunately, there exists the information leakage problem in this protocol. When the sender announces that the receiver uses the Z-basis to measure a single photon, everyone knows that the sent secret message is 000 or 001, that is, the first two bits are leaked out; when the sender announces that the receiver uses the X-basis to measure a single photon, everyone knows that the sent secret message is 010 or 011, that is, the first two bits are leaked out too; when the sender announces that the receiver uses the Bell-basis to measure a pair of particles from a Bell state, everyone knows that the sent secret message is 100, 101, 110 or 111, that is, the first bit is leaked out. In a word, two of the three bits of classical information encoded in a single photon, and one of the three bits of classical information encoded in a Bell state are leaked out. Therefore, this scheme is not secure. On the basis of keeping the original idea and changing the contents of the protocol as less as possible, we put forward an improved message encoding rule to solve the information leakage problem, that is, the single photon is only encoded by one bit of classical information, and the Bell state is only encoded by two bits of classical information. In fact, this makes the information capacity of the improved protocol achieves the Helovo bound. So it has high coding capacity. We hope researchers pay more attention to the information leakage problem in quantum secure communication protocols, and thus design truly secure ones.

Can quantum communication be more efficient than its classical counterpart? Holevo's theorem rules out the possibility of communicating more than n bits of classical information by the transmission of n quantum bits—unless the two parties are entangled, in which case twice as many classical bits can be communicated but no more. In apparent contradiction, there are distributed computational tasks for which quantum communication cannot be simulated efficiently by classical means. In some cases, the effect of transmitting quantum bits cannot be achieved classically short of transmitting an exponentially larger number of bits. In a similar vein, can entanglement be used to save on classical communication? It is well known that entanglement on its own is useless for the transmission of information. Yet, there are distributed tasks that cannot be accomplished at all in a classical world when communication is not allowed, but that become possible if the non-communicating parties share prior entanglement. This leads to the question of how expensive it is, in terms of classical communication, to provide an exact simulation of the spooky power of entanglement.

The exploitation of nature's machinery at length scales below the dimensions of a cell is an exciting challenge for biologists, chemists and physicists, while advances in our understanding of these biological motifs are now providing an opportunity to develop real single molecule devices for technological applications. Single molecule studies are already well advanced and biological molecular motors are being used to guide the design of nano-scale machines. However, controlling the specific functions of these devices in biological systems under changing conditions is difficult. In this review we describe the principles underlying the development of a molecular motor with numerous potential applications in nanotechnology and the use of specific synthetic polymers as prototypic molecular switches for control of the motor function. The molecular motor is a derivative of a TypeI Restriction-Modification (R-M) enzyme and the synthetic polymer is drawn from the class of materials that exhibit a temperature-dependent phase transition.The potential exploitation of single molecules as functional devices has been heralded as the dawn of new era in biotechnology and medicine. It is not surprising, therefore, that the efforts of numerous multidisciplinary teams [1,2]. have been focused in attempts to develop these systems. as machines capable of functioning at the low sub-micron and nanometre length-scales [3]. However, one of the obstacles for the practical application of single molecule devices is the lack of functional control methods in biological media, under changing conditions. In this review we describe the conceptual basis for a molecular motor (a derivative of a TypeI Restriction-Modification enzyme) with numerous potential applications in nanotechnology and the use of specific synthetic polymers as prototypic molecular switches for controlling the motor function [4].

Automating the search of molecular motor templates by evolutionary methods

Biological molecular motors are high-performance nanomachines that convert chemical energy into mechanical motion via chemomechanical coupling. Their reaction cycles typically comprise a series of intermediate chemical states between the initial and final primary states. However, the influence of these intermediate states on motor performance has not yet been fully explored. In this study, we investigate the impact of intermediate states on the motor kinetics using a reaction-diffusion model. In most cases, the intermediate states accelerate the motor by lowering the effective barrier height. This acceleration is particularly pronounced when an external load is applied to the motor, implying the practical importance of the intermediate states. The intermediate states can also slow down the reaction in some cases, such as the slow reaction limit with asymmetric kinetics. Our findings provide practical insights into the design principles behind the high performance of biological molecular motors, as well as the development of efficient artificial molecular motors.

<sec>Biological molecular motors exist in cells widely. They can make use of intracellular free energy to complete all kinds of internal biological transports by transforming chemical energy into mechanical energy. The kind of directional movement of biological molecular motors plays a very important role in intracellular material transportation. In order to study the transport mechanism of molecular motors further, a large number of ratchet models are proposed, such as rocking ratchets and flashing ratchets. By investigating various kinds of ratchets we can not only understand the directional movement mechanism of Brownian particles, but can find suitable conditions in which the performance of Brownian motors’ directional transportation could be enhanced. Meanwhile, the investigation of ratchets could also be applied in manufacturing nanometer devices.</sec><sec>At present, the directional transportation of Brownian ratchet has attracted extensive interests of researchers. In general, most friction factors of Brownian ratchet models are considered unit. In fact, the concentration of solutions and cell fluid impurity affect the actual frictional damping conditions, so the real frictional coefficient of Brownian motors is often changed. In addition, lots of experimental studies have shown that the movement of Brownian motors is collectively directed motion and the kind of directional movement is induced by intermolecular coupling interaction. As a result, it is more valuable to investigate the transporting performance of coupled Brownian particles that existed in different frictional damping conditions. In order to enhance the transporting performance of Brownian ratchet in different frictional damping conditions, we discuss how the frictional damping factor influences the directional movement of coupled Brownian particles deeply when Brownian particles drag loads.</sec><sec> In this paper, we established the overdamped frictional ratchets, and then we investigated how frictional damping coefficient ratio, coupling strength and external force amplitude affect the transportation of coupled Brownian ratchets. On the basis of the investigation, some interesting results are found. The directional transport of frictional ratchets can be promoted by adjusting the frictional damping factor. Besides, the transportation can obtain the maximum under the appropriate friction factor case. In addition, under certain frictional damping condition, the directional transportation of the friction ratchets present multi-peak structure as the external force amplitude increases. Meanwhile, the appropriate free length and coupling strength can also enhance the transportation characteristic of frictional ratchets. All conclusions obtained in this paper can not be applied in selecting suitable frictional damping conditions experimentally to improve the directional transportation of coupled Brownian ratchets, but they can also be used in developing and manufacturing nanometer devices.</sec>

The bacterial flagellar motor is a complex biological rotary molecular motor which is situated in the cell envelopes of bacteria. Whereas most biological motors use adenosine triphosphate (ATP) as their energy source, the rotation of the flagellar motor is driven by a flow of charged ions across the bacterial plasma membrane. The motor powers the rotation of helical flagellar filaments at speeds of up to several hundred hertz. These rotating filaments act like propellers, pushing the cells through their environment. The motors are regulated by one of the best‐characterized biological signalling pathways, the chemotaxis pathway. This pathway changes the swimming pattern of the bacteria in response to changes in the concentration of external chemicals so that they move into environments which are optimal for their growth. Key concepts: Bacteria swim using a small biological rotary motor which is powered by the movement of charged ions across the plasma membrane. The flagellar motor consists of a rotor which rotates against stator units that are anchored to the peptidoglycan cell wall. Torque is generated by the interaction of the stator units, MotA and MotB, with FliG in the rotor. Despite the fact that the driving ions always flow in one direction through the stator units, many flagellar motors can switch between clockwise and counterclockwise rotation. A complex signalling pathway regulates the motor output in response to environmental signals ensuring that bacteria swim towards nutrient rich environments.

The ability to transfer information securely is essential in the modern world we live in. While the field of cryptography has long researched ways to do this, events over the last couple of years have brought the issues of secure information transfer squarely into the public eye. As a consequence, security and cryptography have quickly become issues of social and political importance, sparking debates about the values of privacy and the role of government. An essential ingredient of modern cryptography is the generation of randomness: cryptographic techniques are built on the premise that one has access to random bits. It is well known, however, that computers cannot produce algorithmically random sequences – that is, sequences with maximal algorithmic information content – but are doomed to produce 'pseudorandomness'. This lack of randomness can be, and has been, exploited to compromise security, see [4]. The active field of quantum information theory has proposed approaches to provide supposedly 'unbreakable' security by exploiting various quantum phenomena. This security unfortunately relies on assumptions about the nature of quantum measurements and their ability to generate random bits. Anton Zeilinger summarises this by postulating that the simplest quantum systems, qubit, can hold only one bit of classical information [6]. This foundational principle is in line with a wider paradigm shift to view quantum information as an extension of classical information, but it is nonetheless unsatisfying to simply postulate this principle, given its importance in determining the practical advantages of quantum information theory. In order to understand better how quantum mechanics can help generate meaningful information, we instead look to relate the outcomes of quantum measurements to formal properties of the system based on more fundamental assumptions. Indeed, we have shown that a) some of the postulated properties of quantum information follow from the formal structure of the theory and b) a purely formal notion of information within a quantum world can generate, via measurement, meaningful and useful information in the macroscopic world (for example, in cryptography). The indeterminism of quantum measurements can be formalised via the notion of value indefiniteness. To explain this concept, let us consider an arbitrary quantum system and ask whether the outcome of a measurement of any observable quantity A (such as the energy of the system, its angular momentum (spin), etc.) is determined prior to the measurement. If this is the case, then we say the observable is value definite with value v(A); otherwise, the observable is value indefinite and v(A) is undefined. Mathematically, one can reduce all observable quantities to so-called projection observables, which can only take the values 0 or 1. Thus, the question of whether the outcome of several measurements can be simultaneously determined in advance can be rephrased in terms of the information 'carried' by a particular system in a definite quantum state. Classically, one expects that all quantities are determined in advance, and hence all observables are value definite. Quantum mechanically, however, the belief is that this is not the case, and the information content of quantum systems is limited. Formulating carefully the notion of value indefiniteness allows us to formalise the notion of (quantum) indeterminism; however, this doesn't help clarify whether quantum systems are indeed value indefinite or not. Staying in this formal framework, the Kochen-Specker theorem [5] provides a first positive result, showing that at least some observables must be value indefinite if one makes the assumption known as non-contextuality, which states that any definite values that exist must be independent of other compatible measurements that may or may not be performed on the system. Under the same assumption, this theorem can be strengthened to show that only one single observable can have the definite value 1 (see [2]). Furthermore, only observables that can be measured simultaneously with this single one can have the definite value 0; the rest must all be value indefinite. Since the preparation of a system involves precisely ensuring that, usually via measurement, the system is in a definite state with respect to some desired observable, this result shows that no other incompatible observable can be value definite. That is, preparing a system in a definite state by making the 'preparation' observable value definite specifies completely the information content of the quantum system. This is an example of syntactical quantum information acquiring meaning at the level of the quantum itself. Can the syntactical information at the level of the quantum generate meaning outside the quantum, that is, at the macroscopic level? The results cited above hold in the Hilbert-space framework of quantum mechanics and are formulated only in terms of a syntactical notion of information. Their real importance becomes evident when one interprets them in the context of quantum measurements. Specifically, if we prepare a quantum system in a known state, they allow us to 'locate' observables which we can measure, but which are value indefinite; that is, observables whose measurement results are not specified by any pre-existing property of the quantum system. Furthermore, with respect to a mathematical model of unpredictability which we developed in [3], the results of these measurements can be shown to be absolutely unpredictable. In this way we get a mathematical explanation and justification of the largely accepted intuition that quantum mechanics is inherently unpredictable, and that this unpredictability arises from the phenomenon of indefiniteness within the quantum world. Furthermore, if one considers a hypothetical infinite sequence generated by the repeated measurement of a quantum value indefinite observable, one can prove that these sequences must be strongly incomputable, technically 'bi-immune' [1]. Such sequences cannot be generated by any Turing machine or classical computer, showing that value indefiniteness leads to a clear classical/quantum split in a purely algorithmic context. Importantly, bi-immunity is a property of observed, macroscopic quantities, quite separate from the quantum framework in which the value indefiniteness is formalised. This form of macroscopic meaning created from the lack of syntactic information is precisely the scenario that quantum random number generators try to create, and which is essential for the development and certification of quantum cryptographic systems. The fact that the macroscopic information created goes beyond anything classically obtainable serves as a valuable practical resource, outside of and removed from the quantum formalism. To conclude, quantum information creates meaning within the quantum and via measure- ment, the lack of information within the quantum, creates meaning and valuable information at the macroscopic level. Acknowledgments The second author thanks Prof. S. Marcus for useful conversations on quantum information theory. This work was supported in part by Marie Curie FP7-PEOPLE-2010-IRSES Grant RANPHYS. References and Notes Abbott, A.A.; Calude, C.S.; Svozil, K. Strong Kochen-Specker theorem and incomputability of quantum randomness. Physical Review A 2012, 86, 062109. Abbott, A.A.; Calude, C.S.; Svozil, K. Value-indefinite observables are almost everywhere. Physical Review A 2013, 89, 032109. Abbott, A.A.; Calude, C.S.; Svozil, K. On the unpredictability of individual quantum measurement outcomes. CDMTCS Research Report 2014, 458. Calude, C.S. Quantum randomness & cryptology. CyberTalk 2013, 3, 42–43. Kochen, S.; Specker, E. The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics 1967, 17, 59–87. Zeilinger, A. A foundational principle for quantum mechanics. Foundations of Physics 1999, 29(4),631–643.

With the assistance of auxiliary two-dimensional polarization entanglement, we theoretically present an efficient Bell state measurement (BSM) method for photonic four-dimensional entanglement in the path degree of freedom, in which just simple linear optical elements and common single-photon detectors are utilized. With this approach, the 16 mutually orthogonal four-dimensional path Bell states can be classified into eight distinguishable groups, which allows the transmission of 3 bits of classical information by just sending one photon in our quantum superdense coding protocol. Compared with previous quantum dense coding protocols that are also based on linear-optical BSM, our protocol has certain advantages and will be useful for other quantum communication protocols based on high-dimensional entanglement.

Ideal dense coding protocols allow one to use prior maximal entanglement to send two bits of classical information by the physical transfer of a single encoded qubit. We investigate the case when the prior entanglement is not maximal and the initial state of the entangled pair of qubits being used for the dense coding is a mixed state. We find upper and lower bounds on the capability to do dense coding in terms of the various measures of entanglement and in terms of the average mutual distinguishability of the signal states.

By means of Temperley---Lieb Algebra and topological basis, we make a new realization of topological basis, and get sixteen complete orthonormal topological basis states which are all maximally entangled for four quasi-particles. Then we present an explicit protocol for teleporting an arbitrary two-qubit state via a topological basis entanglement channel. We also show that four bits of classical information can be encoded into a topological basis state by two-particle unitary operations.

The famous superdense coding protocol of Bennett and Wiesner demonstrates that it is possible to communicate two bits of classical information by sending only one qubit and using a shared EPR pair. Our first result is that an arbitrary protocol for achieving this task (where there are no assumptions on the sender’s encoding operations or the dimension of the shared entangled state) is locally equivalent to the canonical Bennett-Wiesner protocol. In other words, the superdense coding task is rigid . In particular, we show that the sender and receiver only use additional entanglement (beyond the EPR pair) as a source of classical randomness. We also investigate several questions about higher-dimensional superdense coding, where the goal is to communicate one of d 2 possible messages by sending a d -dimensional quantum state, for general dimensions d . Unlike the d =2 case (i.e., sending a single qubit), there can be inequivalent superdense coding protocols for higher d . We present concrete constructions of inequivalent protocols, based on constructions of inequivalent orthogonal unitary bases for all d > 2. Finally, we analyze the performance of superdense coding protocols where the encoding operators are independently sampled from the Haar measure on the unitary group. Our analysis involves bounding the distinguishability of random maximally entangled states, which may be of independent interest.

Most physicists have kept their distance from living cells for good reason; they are just too complex. It is a long jump from a two body problem to cellular mechanics. However, the enormous advances made in polymer physics in recent years has greatly narrowed the distance between these two fields. As can be seen from the accompanying chapters in this volume, highly talented physicists are now working with biological polymers and molecular motors and are finding that the behavior of these complex systems are no longer beyond their reach. This is tremendously exciting because we will never fully understand life without defining its physical basis. At the same time, enormous advances have been made in the area of molecular cell biology. For example, the human genome project has led to the discovery of incredible numbers of new molecules and genes as well as many useful chemical reagents. However, we still do not understand how these molecules join together to form living cells that can change shape, grow, and move. This question of how life is structured is the ultimate problem in biology and solving this riddle will likely require the effort of physicists as well as biologists.