Poisson Quantum Information

By taking a Poisson limit for a sequence of rare quantum objects, I derive simple formulas for the Uhlmann fidelity, the quantum Chernoff quantity, the relative entropy, and the Helstrom information. I also present analogous formulas in classical information theory for a Poisson model. An operator called the intensity operator emerges as the central quantity in the formalism to describe Poisson states. It behaves like a density operator but is unnormalized. The formulas in terms of the intensity operators not only resemble the general formulas in terms of the density operators, but also coincide with some existing definitions of divergences between unnormalized positive-semidefinite matrices. Furthermore, I show that the effects of certain channels on Poisson states can be described by simple maps for the intensity operators.

Photonic quantum data locking

Quantum data locking is a quantum phenomenon that allows us to encrypt a long message with a small secret key with information-theoretic security. This is in sharp contrast with classical information theory where, according to Shannon, the secret key needs to be at least as long as the message. Here we explore photonic architectures for quantum data locking, where information is encoded in multi-photon states and processed using multi-mode linear optics and photo-detection, with the goal of extending an initial secret key into a longer one. The secret key consumption depends on the number of modes and photons employed. In the no-collision limit, where the likelihood of photon bunching is suppressed, the key consumption is shown to be logarithmic in the dimensions of the system. Our protocol can be viewed as an application of the physics of Boson Sampling to quantum cryptography. Experimental realisations are challenging but feasible with state-of-the-art technology, as techniques recently used to demonstrate Boson Sampling can be adapted to our scheme (e.g., Phys. Rev. Lett. 123, 250503, 2019).

Tri-State: From Shannon to Galois Fields in Communication Systems

Communication, compression of information, transmission of information through noisy channels, interconnecting different information systems, cryptography, gate construction –– these areas all depend on classical information theory. We show that, in classical terms, semantic aspects of communication are not at all irrelevant to the engineering problem, contrary to Shannon, and affect the message intended to be transmitted. This is revisited and captured by an analogy to trust, in that they are essential to the channel (for proper use), but cannot be transferred (under risk of flaws) through that same channel. Information is also described by, at least, a tri-state system — not by binary logic. The trust analogy semantics can be coded as the Curry-Howard relationship, connecting computer code with structural logic, by way of different categories. Two-state and Boolean logic (aka Shannon semantics) was used classically before, with Shannon theory, but without trust analogy semantics – found to be a sine qua non condition. This is now familiar in classical gate construction with physical systems with, e.g., Verilog and SystemVerilog. The applications to computation and quantum theory are further explored. The most fundamental entity in today`s theory of information is proposed to use at least three logical states, not bits, in all applications, including: cyber-physical systems, devices, in computation, and in quantum theory.

Review of The Theory of Quantum Information John Watrous

This is an extremely clear, carefully written book that covers the most important results in the sprawling field of quantum information. It is perfect for a reference, self-study, or a graduate course in quantum information. It makes no attempt to be broad or encyclopedic, but instead goes deep into the core topics. The definitions and theorems are all precisely worded, and (starting in Chapter 2) all results have complete proofs, making the book largely self-contained. The book focuses heavily on the mathematical results and nuts-and-bolts techniques underpinning current research, and as such gives the reader a thorough and flexible toolkit for proving new results. If you are just looking for a broad but cursory survey of the field, then this is probably not the book for you. If, however, you want a working knowledge of the core results and proof techniques of quantum information with an eye toward doing cutting-edge research in the field, then this book will be an indispensable addition to your library. The mathematical theory of quantum information studies the ultimate abilities and limits of transmitting and processing information using the laws of quantum mechanics. It owes much of its motivation to classical information theory, which was largely developed by Claude Shannon in the mid 20th century, and to quantum mechanics itself (of course). It addresses basic questions like: how much information can be transmitted through quantum channels, noisy or otherwise, and how entanglement helps. The theory informs, and is informed by, its sister disciplines of quantum computation and quantum communication (which overlap with physics and computer science), although in some sense it is more fundamental. Though he occasionally mentions applications to these other areas, Watrous seats his book squarely in the realm of pure mathematics.

Quantum Information: A Brief Overview and Some Mathematical Aspects

The aim of the present paper is twofold. First, to give the main ideas behind quantum computing and quantum information, a field based on quantum-mechanical phenomena. Therefore, a short review is devoted to (i) quantum bits or qubits (and more generally qudits), the analogues of the usual bits 0 and 1 of the classical information theory, and to (ii) two characteristics of quantum mechanics, namely, linearity, which manifests itself through the superposition of qubits and the action of unitary operators on qubits, and entanglement of certain multi-qubit states, a resource that is specific to quantum mechanics. A, second, focus is on some mathematical problems related to the so-called mutually unbiased bases used in quantum computing and quantum information processing. In this direction, the construction of mutually unbiased bases is presented via two distinct approaches: one based on the group SU(2) and the other on Galois fields and Galois rings.

Can bipartite classical information resources be activated?

Non-additivity is one of the distinctive traits of Quantum Information Theory: the combined use of quantum objects may be more advantageous than the sum of their individual uses. Non-additivity effects have been proven, for example, for quantum channel capacities, entanglement distillation or state estimation. In this work, we consider whether non-additivity effects can be found in Classical Information Theory. We work in the secret-key agreement scenario in which two honest parties, having access to correlated classical data that are also correlated to an eavesdropper, aim at distilling a secret key. Exploiting the analogies between the entanglement and the secret-key agreement scenario, we provide some evidence that the secret-key rate may be a non-additive quantity. In particular, we show that correlations with conjectured bound information become secret-key distillable when combined. Our results constitute a new instance of the subtle relation between the entanglement and secret-key agreement scenario.