A simple proof of unconditional security of relativistic quantum cryptography

A simple proof of the unconditional security of a relativistic quantum cryptosystem based on orthogonal states is given. Limitations imposed by the special relativity theory allow the proof to be markedly simplified as compared to the case of nonrelativistic cryptosystems based on nonorthogonal states. An important point in the proposed protocol is a space-time structure of the quantum states, which is ignored in the non-relativistic protocols using only the properties of the space of states of the information carriers. As a consequence, the simplification is related to the inefficacy of using the collective measurements against an eavesdropper, the allowance for which is an especially difficult task in the nonrelativistic case.     

A new approach to relativistic multi-configuration quantum mechanics in titanium

Multiply-ionized atoms in plasmas and astronomical systems are predominantly of intermediate atomic numbers with open electron shells. The spectra seen in laboratory plasmas and astrophysical plasmas are dominated by characteristic Kα1,2 photoemission lines. Modelling these transitions requires advanced relativistic frameworks to begin to formulate solutions. We present a new approach to relativistic multi-configuration determination of Kα1,2 diagram and satellite energies in titanium to a high level of convergence, allowing accurate fitting of satellite contributions and the first agreement with profile to negligible residuals. These developments also apply to exciting frontiers including temporal variation of fundamental constants, theoretical chemistry and laboratory astrophysics.     

The role of causality in ensuring the ultimate security of relativistic quantum cryptography

One of the central points of quantum information theory is the problem of ultimate security of quantum cryptography; i.e., the security that is due only to the fundamental laws of nature rather than to technical restrictions. It is shown that a relativistic quantum cryptosystem proposed in this paper is ultimately secure against any eavesdropping attempts. The application of relativistic causality makes it possible to simply prove the security of the cryptosystem. Moreover, because the scheme does not involve collective measurements and quantum codes, it can be experimentally implemented even at the current level of optical fiber technologies.     

Device-independent security of quantum cryptography against collective attacks

We present the optimal collective attack on a quantum key distribution protocol in the "device-independent" security scenario, where no assumptions are made about the way the quantum key distribution devices work or on what quantum system they operate. Our main result is a tight bound on the Holevo information between one of the authorized parties and the eavesdropper, as a function of the amount of violation of a Bell-type inequality.     

Collective attacks and unconditional security in continuous variable quantum key distribution

We present here an information theoretic study of Gaussian collective attacks on the continuous variable key distribution protocols based on Gaussian modulation of coherent states. These attacks, overlooked in previous security studies, give a finite advantage to the eavesdropper in the experimentally relevant lossy channel, but are not powerful enough to reduce the range of the reverse reconciliation protocols. Secret key rates are given for the ideal case where Bob performs optimal collective measurements, as well as for the realistic cases where he performs homodyne or heterodyne measurements. We also apply the generic security proof of Christiandl et al. to obtain unconditionally secure rates for these protocols.     

A real-time approach to nonequilibrium quantum field theory of relativistic fields

Summary The basic ingredients of a real-time nonequilibrium quantumfield theoretical approach, based on a generalization of thermofield dynamics, are briefly reviewed. In particular, the possible advantages of its application to relativistic models, as the φ⁴-model for the Higgs field are pointed out. Also the differences between the above approach and others using the Feynman's path integral method are underlined. ?Angelo della Riccia? Fellow.     

Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way postprocessing

We derive a bound for the security of quantum key distribution with finite resources under one-way postprocessing, based on a definition of security that is composable and has an operational meaning. While our proof relies on the assumption of collective attacks, unconditional security follows immediately for standard protocols such as Bennett-Brassard 1984 and six-states protocol. For single-qubit implementations of such protocols, we find that the secret key rate becomes positive when at least N approximately 10(5) signals are exchanged and processed. For any other discrete-variable protocol, unconditional security can be obtained using the exponential de Finetti theorem, but the additional overhead leads to very pessimistic estimates.     

Classical noise-based cryptography similar to two-state quantum cryptography

A scheme of cryptographic key agreement via classical noise is introduced. The principle underlying its security is similar to that of the two-state quantum cryptosystem, but it has the advantage that signal amplification can be applied. Radio and optical implementations of the scheme are suggested.     

On the resistance of relativistic quantum cryptography in open space at finite resources

The security of keys for the basic nonrelativistic BB84 protocol has been examined for more than 15 years. A simple proof of security for the case of a single-photon source of quantum states and finite sequences has been only recently obtained using entropy uncertainty relations. However, the existing sources of states are not strictly single-photon. Since sources are not single-photon and losses in a quantum channel??open space??are not a priori known and vary, nonrelativistic quantum cryptographic systems in open space cannot guarantee the unconditional security of keys. Recently proposed relativistic quantum cryptography removes fundamental constraints associated with non-single-photon sources and losses in open space. The resistance of a fundamentally new family of protocols for relativistic quantum key distribution through open space has been analyzed for the real situation with finite lengths of transmitted sequences of quantum states. This system is stable with real sources of non-single-photon states (weakened laser radiation) and arbitrary losses in open space.     

Trajectories and causal phase-space approach to relativistic quantum mechanics

We analyze phase-space approaches to relativistic quantum mechanics from the viewpoint of the causal interpretation. In particular, we discuss the canonical phase space associated with stochastic quantization, its relation to Hilbert space, and the Wigner-Moyal formalism. We then consider the nature of Feynman paths, and the problem of nonlocality, and conclude that a perfectly consistent relativistically covariant interpretation of quantum mechanics which retains the notion of particle trajectory is possible.     

A new experimental approach to Mach's principle and relativistic graviation

As noted many years ago by Sciama, and more recently by Nordtvedt, Lorentz invariant (relativistic) gravitation at linear order involves a vector potential that is required to properly account for large inertial effects as well as the correct prediction of the classical tests of general relativity theory (GRT). It is pointed out that the linear-order vector aspect of the gravitational potential makes possible a simple, powerful and inexpensive technique for testing the predictions of GRT and associated issues. An experiment using this technique gives preliminary results that, to order of magnitude, corroborate GRT.1. If one demands a theory that satisfies Mach's Principle irrespective of the particular value of _c, one must go to a theory that contains GRT with critical cosmic matter density as a special case. Such a theory (an Einstein-Cartan theory with teleparallelism) has been developed by Treder [2].2. Equation (4) here is Nordtvedt's Eq. (14), in Ref. 3, with GRT PPN parameters chosen.3. The exact value of this correction factor that depends on the way in which energy is distributed between field and sources in turn depends on how the source term for the gravitational field equations is constructed. At least two different source terms that give correct predictions for the various tests of GRT exist. In this connection see Peters [4]. This ambiguity does not mean that it is impossible in principle to determine how energy is distributed between sources and field. Indeed, if one posits the existence of critical cosmic matter density, this experiment can decide the issue.     

On a two-pass scheme without a faraday mirror for free-space relativistic quantum cryptography

The stability of destructive interference independent of the input polarization and the state of a quantum communication channel in fiber optic systems used in quantum cryptography plays a principal role in providing the security of communicated keys. A novel optical scheme is proposed that can be used both in relativistic quantum cryptography for communicating keys in open space and for communicating them over fiber optic lines. The scheme ensures stability of destructive interference and admits simple automatic balancing of a fiber interferometer.     

Principles of the new quantum cryptography protocols building

The main aim of the quantum cryptography protocols is the maximal secrecy under the conditions of the real experiment. This work presents the result of the new protocol building with the use of the secrecy maximization. While using some well known approaches this method has allowed to achieve the completely new results in quantum cryptography. The process of the protocol elaboration develops from the standard BB84 protocol upgrading to the building of completely new protocol with arbitrary large bases number. The secrecy proofs of the elaborated protocol appear to be natural continuation of the protocol building process. This approach reveals possibility to reach extremely high parameters of the protocol. It suits both the restrictions of contemporary technologies and requirements for high bit rate while being absolutely secret.     

A standing-wave approach for discussing electron transport in relativistic quantum conductors

Electron transport through a generic one-dimensional relativistic quantum conductor is discussed by calculating the quantized electron velocity as well as the quantized energy for sufficiently large values of the involved quantum number in the framework of a standing-wave approach. Fermi velocity and Fermi energy are discussed near the classical limit.     

A fundamental threat to quantum cryptography: gravitational attacks

An attack on the “Bennett-Brassard 84” (BB84) quantum key-exchange protocol in which Eve exploits the action of gravitation to infer information about the quantum-mechanical state of the qubit exchanged between Alice and Bob, is described. It is demonstrated that the known laws of physics do not allow to describe the attack. Without making assumptions that are not based on broad consensus, the laws of quantum gravity, unknown up to now, would be needed even for an approximate treatment. Therefore, it is currently not possible to predict with any confidence if information gained in this attack will allow to break BB84. Contrary to previous belief, a proof of the perfect security of BB84 cannot be based on the assumption that the known laws of physics are strictly correct, yet. A speculative parameterization that characterizes the time-evolution operator of quantum gravity for the gravitational attack is presented. It allows to evaluate the results of gravitational attacks on BB84 quantitatively. It is proposed to perform state-of-the-art gravitational attacks, both for a complete security assurance of BB84 and as an unconventional search for experimental effects of quantum gravity.     

A new approach to Ermakov systems and applications in quantum physics

Milne–Pinney equation [(x)\ddot]=-w²(t)x+ k/x³\ddot x=-\omega^2(t)x+ k/{x^3} is usually studied together with the time-dependent harmonic oscillator [(y)\ddot]+w²(t) y=0\ddot y+\omega^2(t) y=0 and the system is called Ermakov system, and actually Pinney showed in a short paper that the general solution of the first equation can be written as a superposition of two solutions of the associated harmonic oscillator. A recent generalization of the concept of Lie systems for second order differential equations and the usual techniques of Lie systems will be used to study the Ermakov system. Several applications of Ermakov systems in Quantum Mechanics as the relation between Schroedinger and Milne equations or the use of Lewis–Riesenfeld invariant will be analysed from this geometric viewpoint.     

Practical error-correction procedures in quantum cryptography

Quantum cryptography (secure key distribution) systems must include procedures for correcting errors in the raw key transmitted over a quantum communication channel. Several reconciliation protocols are discussed and compared in terms of efficiency.