Quantum Computation Toward Quantum Gravity

The aim of this paper is to enlighten the emerging relevance of Quantum Information Theory in the field of Quantum Gravity. As it was suggested by J. A. Wheeler, information theory must play a relevant role in understanding the foundations of Quantum Mechanics (the "It from bit" proposal). Here we suggest that quantum information must play a relevant role in Quantum Gravity (the "It from qubit" proposal). The conjecture is that Quantum Gravity, the theory which will reconcile Quantum Mechanics with General Relativity, can be formulated in terms of quantum bits of information (qubits) stored in space at the Planck scale. This conjecture is based on the following arguments: a) The holographic principle, b) The loop quantum gravity approach and spin networks, c) Quantum geometry and black hole entropy. From the above arguments, as they stand in the literature, it follows that the edges of spin networks pierce the black hole horizon and excite curvature degrees of freedom on the surface. These excitations are micro-states of Chern-Simons theory and account of the black hole entropy which turns out to be a quarter of the area of the horizon, (in units of Planck area), in accordance with the holographic principle. Moreover, the states which dominate the counting correspond to punctures of spin j = 1/2 and one can in fact visualize each micro-state as a bit of information. The obvious generalization of this result is to consider open spin networks with edges labeled by the spin –1/ 2 representation of SU(2) in a superposed state of spin "on" and spin "down." The micro-state corresponding to such a puncture will be a pixel of area which is "on" and "off" at the same time, and it will encode a qubit of information. This picture, when applied to quantum cosmology, describes an early inflationary universe which is a discrete version of the de Sitter universe.     

Quantum World with Quantum Time

Since the beginning of quantum mechanics there have been a lot of attempts to quantize time. In this paper we refer to the little known concept of quantum time proposed by E.Kapuscik [Hadronic J. 8 (1985) 75]. We analyze some properties of systems with quantum time. Moreover we comment and discuss the idea of quantum time.     

Quantum Logic for Quantum Computers

The following results obtained within a project of finding the algebra of statesin a general-purpose quantum computer are reported: (1) All operations of anorthomodular lattice, including the identity, are fivefold-defined; (2) there arenonorthomodular models for both quantum and classical logics; (3) there is afour-variable orthoarguesian lattice condition which contains all known orthoarguesianlattice conditions including six- and five-variable ones. Repercussions to quantumcomputers operating as quantum simulators are discussed.     

Multiparty Quantum Secret Sharing of Quantum States with Quantum Registers

A quantum secret sharing scheme is proposed by making use of quantum registers. In the proposed scheme, secret message state is encoded into multipartite entangled states. Several identical multi-particle entanglement states are generated and each particle of the entanglement state is filled in different quantum registers which act as shares of the secret message. Two modes, i.e. the detecting mode and the message mode, are employed so that the eavesdropping can be detected easily and the secret message may be recovered. The security analysis shows that the proposed scheme is secure against eavesdropping of eavesdropper and cheating of participants.     

Quantum Gate-Based Quantum Private Comparison

International Journal of Theoretical Physics - Many existing protocols of quantum private comparison (QPC) are often made up of quantum part and classical part, because they employ quantum...     

Quantum Secure Dialogue with Quantum Encryption

How to solve the information leakage problem has become the research focus of quantum dialogue. In this paper, in order to overcome the information leakage problem in quantum dialogue, a novel approach for sharing the initial quantum state privately between communicators, i.e., quantum encryption sharing, is proposed by utilizing the idea of quantum encryption. The proposed protocol uses EPR pairs as the private quantum key to encrypt and decrypt the traveling photons, which can be repeatedly used after rotation. Due to quantum encryption sharing, the public announcement on the state of the initial quantum state is omitted, thus the information leakage problem is overcome. The information-theoretical efficiency of the proposed protocol is nearly 100%, much higher than previous information leakage resistant quantum dialogue protocols. Moreover, the proposed protocol only needs single-photon measurements and nearly uses single photons as quantum resource so that it is convenient to implement in practice.     

Quantum Mechanics is About Quantum Information

I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitive---just as, following Einsteins special theory of relativity, a field is no longer regarded as the physical manifestation of vibrations in a mechanical medium, but recognized as a new physical entity in its own right.     

Quantum Secure Dialogue with Quantum Encryption

How to solve the information leakage problem has become the research focus of quantum dialogue. In this paper, in order to overcome the information leakage problem in quantum dialogue, a novel approach for sharing the initial quantum state privately between communicators, i.e., quantum encryption sharing, is proposed by utilizing the idea of quantum encryption. The proposed protocol uses EPR pairs as the private quantum key to encrypt and decrypt the traveling photons, which can be repeatedly used after rotation. Due to quantum encryption sharing, the public announcement on the state of the initial quantum state is omitted, thus the information leakage problem is overcome.The information-theoretical efficiency of the proposed protocol is nearly 100%, much higher than previous information leakage resistant quantum dialogue protocols. Moreover, the proposed protocol only needs single-photon measurements and nearly uses single photons as quantum resource so that it is convenient to implement in practice.     

Duality Quantum Computers and Quantum Operations

We present a mathematical theory for a new type of quantum computer called a duality quantum computer that is similar to one that has recently been proposed. We discuss the nonunitarity of certain circuits of a duality quantum computer. We then discuss the relevance of this work to quantum operations and their convexity theory. This discussion is based upon isomorphism theorems for completely positive maps.     

From Quantum Probabilities to Quantum Amplitudes

The task of reconstructing the system’s state from the measurements results, known as the Pauli problem, usually requires repetition of two successive steps. Preparation in an initial state to be determined is followed by an accurate measurement of one of the several chosen operators in order to provide the necessary “Pauli data”. We consider a similar yet more general problem of recovering Feynman’s transition (path) amplitudes from the results of at least three consecutive measurements. The three-step histories of a pre- and post-selected quantum system are subjected to a type of interference not available to their two-step counterparts. We show that this interference can be exploited, and if the intermediate measurement is “fuzzy”, the path amplitudes can be successfully recovered. The simplest case of a two-level system is analysed in detail. The “weak measurement” limit and the usefulness of the path amplitudes are also discussed.     

Quantum Parallelism in Quantum Information Processing

We investigate distinguishability (measured by fidelity) of the initial and the final state of a qubit, which is an object of the so-called nonideal quantum measurement of the first kind. We show that the fidelity of a nonideal measurement can be greater than the fidelity of the corresponding ideal measurement. This result is somewhat counterintuitive, and can be traced back to the quantum parallelism in quantum operations, in analogy with the quantum parallelism manifested in the quantum computing theory. In particular, as the quantum parallelism in quantum computing underlies efficient quantum algorithms, the quantum parallelism in quantum information theory underlies the classically unexpected increase of fidelity.     

Quantum Ratchet in Disordered Quantum Walk

Symmetrically evolving discrete quantum walk results in dynamic localization with zero mean displacement when the standard evolution operations are replaced by a temporal disorder evolution operation. In this work we show that the quantum ratchet action, that is, a directed transport in standard or disordered discrete‐time quantum walk can be realized by introducing a pawl like effect realized by using a fixed coin operation at marked positions that is, different from the ones used for evolution at other positions. We also show that the combination of standard and disordered evolution operations can be optimized to get the mean displacement of order ∝ t (number of walk steps). This model of quantum ratchet in quantum walk is defined using only a set of entangling unitary operators resulting in the coherent quantum transport.     

Quantum Coherence in Non-Markovian Quantum Channels

We numerically simulate quantum coherence in a system of two qubits interacting with a reservoir for non-Markovian channels. The explicit form of the master equation is taken in terms of density-operator elements and is solved according to the initial conditions. In particular, we consider the effect of an Ohmic reservoir (OR) with Lorentz–Drude regularization (LDR) on the extent of coherence during dynamics. We describe the dynamical behavior of the coherence for low, intermediate, and high-temperature reservoirs. We explain the effect of the ratio of the cutoff frequency (CF) to the quantum system frequency and the effect of temperature on the quantum coherence. We show that a decreasing ratio enhances coherence, while an increasing temperature decreases it.

     

Quantum Covers in Quantum Measure Theory

Sorkin’s recent proposal for a realist interpretation of quantum theory, the anhomomorphic logic or coevent approach, is based on the idea of a “quantum measure” on the space of histories. This is a generalisation of the classical measure to one which admits pair-wise interference and satisfies a modified version of the Kolmogorov probability sum rule. In standard measure theory the measure on the base set Ω is normalised to one, which encodes the statement that “Ω happens”. Moreover, the Kolmogorov sum rule implies that the measure of any subset A is strictly positive if and only if A cannot be covered by a countable collection of subsets of zero measure. In quantum measure theory on the other hand, simple examples suffice to demonstrate that this is no longer true. We propose an appropriate generalisation, the quantum cover, which in addition to being a cover of A, satisfies the property that if the quantum measure of A is non-zero then this is also the case for at least one of the elements in the cover. Our work implies a non-triviality result for the coevent interpretation for Ω of finite cardinality, and allows us to cast the Peres-Kochen-Specker theorem in terms of quantum covers.     

Quantum Capacity under Adversarial Quantum Noise: Arbitrarily Varying Quantum Channels

We investigate entanglement transmission over an unknown channel in the presence of a third party (called the adversary), which is enabled to choose the channel from a given set of memoryless but non-stationary channels without informing the legitimate sender and receiver about the particular choice that he made. This channel model is called an arbitrarily varying quantum channel (AVQC). We derive a quantum version of Ahlswede’s dichotomy for classical arbitrarily varying channels. This includes a regularized formula for the common randomness-assisted capacity for entanglement transmission of an AVQC. Quite surprisingly and in contrast to the classical analog of the problem involving the maximal and average error probability, we find that the capacity for entanglement transmission of an AVQC always equals its strong subspace transmission capacity. These results are accompanied by different notions of symmetrizability (zero-capacity conditions) as well as by conditions for an AVQC to have a capacity described by a single-letter formula. In the final part of the paper the capacity of the erasure-AVQC is computed and some light shed on the connection between AVQCs and zero-error capacities. Additionally, we show by entirely elementary and operational arguments motivated by the theory of AVQCs that the quantum, classical, and entanglement-assisted zero-error capacities of quantum channels are generically zero and are discontinuous at every positivity point.     

量子噪音与量子Langevin方程

介绍了量子噪音和量子Langevin方程 ,并与经典噪音和经典Langevin方程进行了比较 .量子噪音来源于两种途径 ,第一种与经典噪音相似 ,第二种则起源于Heisengberg测不准原理 .同时 ,也简略给出了量子Langevin方程的推导.The properties of quantum noise and Langevin equation are discussed. Comparisons between the quantum noise and Langevin eqution and the classic one are presented. A brief derivation for quantum Langevin equation is showed. The quantum noise comes from two ways, namely, the way as same as that of classic noise and the Heisenberg uncertainty.     

Quantum Spinor Structures for Quantum Spaces

A general theory of quantum spinor structures on quantum spaces is presented within the formalism of quantum principal bundles. Quantum analogs of basic objects of the classical theory are constructed: Laplace and Dirac operators, quantum versions of Clifford and spinor bundles, a Hodge *-operator, integration operators. Quantum phenomena are discussed, including an example of the Dirac operator associated to a quantum Hopf fibration.     

Quantum Charged Non-Linear Nano-String and Quantum Vacuum

The classical and quantum dynamic of a non-linear charged vibrating string and its interaction with quantum vacuum field is investigated. Some probability amplitudes for transitions between vacuum field and quantum states of the string are obtained. The effect of non-linearity on some probability amplitudes is investigated and finally the correct equation for string containing the vacuum and radiation reaction field is obtained.