International Journal of Modern Physics: Conference Series

The paper is motivated by the discussion of feasibility of large scale quantum computations which should incorporate both unitarity of quantum dynamics for information bearing degrees of freedom and stability with respect to environmental noise. The minimal thermodynamic cost of a single CNOT gate, which is equivalent to the minimal cost of a quantum measurement of a binary observable is analyzed using a generic quantum model of one bit memory. For this model stability of memory with respect to thermal and quantum noise and the error of readout can be quantified. One obtains the relations between the minimal work which is invested in a measurement or CNOT gate, the error and the stability factor. The basic formula differs from the standard Landauer one and seems to be much more realistic. The results show the fundamental conflict between stability and irreversibility of information processing. This explains the feasibility of classical stable and scalable information processing performed by irreversible gates and suggests impossibility of large scale quantum computations based on unitary gates.

Landauer's Principle (LP) associates an entropy increase with the irreversible loss of information from a physical system. Clear statement, unambiguous interpretation, and proper application of LP requires precise, mutually consistent, and sufficiently general definitions for a set of interlocking fundamental notions and quantities (entropy, information, irreversibility, erasure). In this work, we critically assess some common definitions and quantities used or implied in statements of LP, and reconsider their definition within an alternative “referential” approach to physical information theory that embodies an overtly relational conception of physical information. We prove an inequality on the entropic cost of irreversible information loss within this context, as well as “referential analogs” of LP and its more general restatement by Bennett. Advantages of the referential approach for establishing fundamental limits on the physical costs of irreversible information loss in communication and computing systems are discussed throughout.

The idealized Kish-Sethuraman (KS) cipher is theoretically known to offer perfect security through a classical information channel. However, realization of the protocol is hitherto an open problem, as the required mathematical operators have not been identified in the previous literature. A mechanical analogy of this protocol can be seen as sending a message in a box using two padlocks; one locked by the Sender and the other locked by the Receiver, so that theoretically the message remains secure at all times. We seek a mathematical representation of this process, considering that it would be very unusual if there was a physical process with no mathematical description. We select Clifford's geometric algebra for this task as it is a natural formalism to handle rotations in spaces of various dimension. The significance of finding a mathematical description that describes the protocol, is that it is a possible step toward a physical realization having benefits in increased security with reduced complexity.

We study the aperiodic signal transmission in a static nonlinearity in the context of aperiodic stochastic resonance. The performance of a nonlinearity over that of the linear system is defined as the transmission efficacy. The theoretical and numerical results demonstrate that the noise-enhanced transmission efficacy effects occur for different signal strengths in various noise scenarios.

The quantum computer is supposed to process information by applying unitary transformations to 2^N complex amplitudes defining the state of N qubits. A useful machine needing N~10³ or more, the number of continuous parameters describing the state of a quantum computer at any given moment is at least 2¹⁰⁰⁰ ~10³⁰⁰ which is much greater than the number of protons in the Universe. However, the theorists believe that the feasibility of large-scale quantum computing has been proved via the “threshold theorem”. Like for any theorem, the proof is based on a number of assumptions considered as axioms. However, in the physical world none of these assumptions can be fulfilled exactly. Any assumption can be only approached with some limited precision. So, the rather meaningless “error per qubit per gate” threshold must be supplemented by a list of the precisions with which all assumptions behind the threshold theorem should hold. Such a list still does not exist. The theory also seems to ignore the undesired free evolution of the quantum computer caused by the energy differences of quantum states entering any given superposition. Another important point is that the hypothetical quantum computer will be a system of 10³ –10⁶ qubits PLUS an extremely complex and monstrously sophisticated classical apparatus. This huge and strongly nonlinear system will generally exhibit instabilities and chaotic behavior.

Generally, one thinks of a “quantum jump” as the process in which an electron “jumps” between a pair of quantum states, even as the process is treated within perturbation theory. This jump of an electron has remained a key point of conservative (i.e., traditional) quantum mechanics. But, the question of the time dependence of such a transition, e.g. the time for an atom to be ionized by radiation, is somewhat different than this view. A detailed approach in which an incoming wave first polarizes the quantum states and then completes the transition has allowed for a detailed discussion of the smooth transition of the electron from one state to the next. Here, we will discuss the history of the process, and illustrate the approach with the question of “how long does it take for an electron to emit a phonon?” The entire process arises from the proper application of wave mechanics and obviates the need to even consider a discussion of quantum jumps.

A possible mechanism of nonlinear quantum evolution is introduced and its implications for quantum communication are investigated. First, it is argued that an appropriate combination of wavefunction collapse and the consciousness of observer may permit the observer to distinguish nonorthogonal quantum states in principle, and thus consciousness will introduce certain nonlinearity into quantum dynamics. Next, it is shown that the distinguishability of nonorthogonal states can be used to achieve quantum superluminal communication, by which information can be transmitted nonlocally and faster than the speed of light. Finally, the issue of apparent incompatibility between superluminal communication and special relativity is briefly addressed.

Parrondo's paradox is a well-known situation where losing strategies can be combined to win, and is based on a thermodynamic Brownian ratchet principle. We demonstrate a new extension of Parrondo's paradox called the Allison mixture where it is possible to paradoxically generate random sequences with nonzero autocovariance, out of sub-sequences of zero autocovariance. We explain the effect with a ratchet analogy and show the behavior of random digits follows a thermodynamic analogy. As Kish-based cipher techniques rely on the Second Law for their security, this raises the tantalizing open question of whether the Allison mixture can be exploited for new Kish-inspired digital security schemes.

While information-theoretic security is often associated with the one-time pad and quantum key distribution, noisy transport media leave room for classical techniques and even covert operation. Transit times across the public internet exhibit a degree of randomness, and cannot be determined noiselessly by an eavesdropper. We demonstrate the use of these measurements for information-theoretically secure communication over the public internet.

This paper deals with the Kirchhoff-law–Johnson-noise (KLJN) classical statistical physical key exchange method and surveys criticism—often stemming from a lack of understanding of its underlying premises or from other errors—and our related responses against these, often unphysical, claims. Some of the attacks are valid, however, an extended KLJN system remains protected against all of them, implying that its unconditional security is not impacted.

Noise-based logic is a practically deterministic logic scheme inspired by the randomness of neural spikes and uses a system of uncorrelated stochastic processes and their superposition to represent the logic state. We briefly discuss various questions such as (i) What does practical determinism mean? (ii) Is noise-based logic a Turing machine? (iii) Is there hope to beat (the dreams of) quantum computation by a classical physical noise-based processor, and what are the minimum hardware requirements for that? Finally, (iv) we address the problem of random number generators and show that the common belief that quantum number generators are superior to classical (thermal) noise-based generators is nothing but a myth.

This talk addressed the following questions in the public debate at HoTPI: (i) energy dissipation limits of switches, memories and control; (ii) whether reversible computers are possible, or does their concept violate thermodynamics; (iii) Szilard's engine, Maxwell's demon and Landauer's principle: corrections to their exposition in the literature; (iv) whether Landauer's erasure–dissipation principle is valid, if the same energy dissipation holds for writing information, or if it is invalid; and (v) whether (non-secure) erasure of memories, or the writing of the same amount of information, dissipates most heat.

The Kirchhoff-Law-Johnson-Noise (KLJN) secure key distribution system provides a way of exchanging secure keys by using classical physics (electricity and thermodynamics). Several theoretical studies have addressed the performance and applicability of the communication protocol, and they have indicated that it is protected against all known types of attacks. However, until now, there have been very few real physical implementations and experimental tests of the protocol. With our work, we continue filling this gap. Details of implementing a KLJN based system are presented using a dedicated hardware and an off-the-shelf solution as well. Furthermore, the results of experimental tests and analysis of the performance will be presented.

Brownian computation, as presently characterized in the literature, is thermodynamically irreversible, the analog of an uncontrolled expansion of a one-molecule gas. I propose a modification to the protocol that brings the process as close to thermodynamic reversibility as the overcoming of thermal fluctuations allows.

We classify and analyze bit errors in the voltage and current measurement modes of the Kirchhoff-law–Johnson-noise (KLJN) secure key distribution system. In both measurement modes, the error probability decays exponentially with increasing duration of the bit sharing period (BSP) at fixed bandwidth. We also present an error mitigation strategy based on the combination of voltage-based and current-based schemes. The combination method has superior fidelity, with drastically reduced error probability compared to the former schemes, and it also shows an exponential dependence on the duration of the BSP.

The Kirchhoff-Law-Johnson-Noise (KLJN) secure key distribution system provides a way of exchanging information theoretic secure keys by measuring the random voltage and current through the wire connecting two different resistors at Alice's and Bob's ends. Recently new advanced protocols for the KLJN method have been proposed with enhanced performance. In this paper we analyze the KLJN system and compare with “intelligent” KLJN (iKLJN) scheme. This task requires the determination of the applied resistors and the identification of the various superpositions of known and unknown noise components. Some statistical tools to determine how the duration of the bit exchange window (averaging time) influences the performance of secure bit exchange will be explored.

Using the correlation of the GHZ triplet states, a broadcasting multiple blind signature scheme is proposed. Different from classical multiple signature and current quantum signature schemes, which could only deliver either multiple signature or unconditional security, our scheme guarantees both by adopting quantum key preparation, quantum encryption algorithm and quantum entanglement. Our proposed scheme has the properties of multiple signature, blindness, non-disavowal, non-forgery and traceability. To the best of our knowledge, we are the first to propose the broadcasting multiple blind signature of quantum cryptography.

In the realistic quantum key distribution (QKD), Alice and Bob respectively get a quantum state from an unknown channel, whose dimension may be unknown. However, while discussing the security, sometime we need to know exact dimension, since current exponential de Finetti theorem, crucial to the information-theoretical security proof, is deeply related with the dimension and can only be applied to finite dimensional case. Here we address this problem in detail. We show that if POVM elements corresponding to Alice and Bob's measured results can be well described in a finite dimensional subspace with sufficiently small error, then dimensions of Alice and Bob's states can be almost regarded as finite. Since the security is well defined by the smooth entropy, which is continuous with the density matrix, the small error of state actually means small change of security. Then the security of unknown-dimensional system can be solved. Finally we prove that for heterodyne detection continuous variable QKD and differential phase shift QKD, the collective attack is optimal under the infinite key size case.