QUANTUM COMPLEXITY THEORY GOALS AND CHALLENGES

2005 ◽  
Vol 03 (01) ◽  
pp. 31-39 ◽  
Author(s):  
JOZEF GRUSKA
Keyword(s):  
Quantum Mechanics ◽  
Information Processing ◽  
Quantum Information ◽  
Complexity Theory ◽  
Quantum Information Processing ◽  
Short Review ◽  
Quantum Complexity ◽  
Quantum Complexity Theory

Quantum complexity theory is a powerful tool that provides deep insights into Quantum Information Processing (QIP) and aims to do that also for Quantum Mechanics (QM), in general. This paper is a short review of the main and new motivations, goals, tools, results and challenges of quantum complexity, oriented mainly for pedestrians.

On measures of quantum entanglement — A brief review

2016 ◽  
Vol 14 (06) ◽  
pp. 1640024 ◽  
Author(s):  
Debasis Sarkar
Keyword(s):  
Quantum Mechanics ◽  
Information Processing ◽  
Quantum Information ◽  
Quantum Entanglement ◽  
Quantum Correlation ◽  
Composite System ◽  
Quantum Information Processing ◽  
Bipartite Entanglement

Entanglement is one of the most useful resources in quantum information processing. It is effectively the quantum correlation between different subsystems of a composite system. Mathematically, one of the most hard tasks in quantum mechanics is to quantify entanglement. However, progress in this field is remarkable but not complete yet. There are many things to do with quantification of entanglement. In this review, we will discuss some of the important measures of bipartite entanglement.

scholarly journals Quantum Information: A Brief Overview and Some Mathematical Aspects

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 273
Author(s):  
Maurice Kibler
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Short Review ◽  
Mutually Unbiased Bases ◽  
Quantum Bits ◽  
Mathematical Problems ◽  
Classical Information Theory ◽  
Main Ideas

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.

scholarly journals Environmental Effects on Nonlocal Correlations

Quanta ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 57-67
Author(s):  
Tamal Guha ◽  
Bihalan Bhattacharya ◽  
Debarshi Das ◽  
Some Sankar Bhattacharya ◽  
Amit Mukherjee ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Information Processing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Classical Mechanics ◽  
Complete Loss ◽  
Quantum Channels ◽  
Output State ◽  
Environmental Interactions ◽  
Nonlocal Correlations

Environmental interactions are ubiquitous in practical instances of any quantum information processing protocol. The interaction results in depletion of various quantum resources and even complete loss in numerous situations. Nonlocality, which is one particular quantum resource marking a significant departure of quantum mechanics from classical mechanics, meets the same fate. In the present work we study the decay in nonlocality to the extent of the output state admitting a local hidden state model. Using some fundamental quantum channels we also demonstrate the complete decay in the resources in the purview of the Bell–Clauser–Horne–Shimony–Holt inequality and a three-settings steering inequality. We also obtain bounds on the parameter of the depolarizing map for which it becomes steerability breaking pertaining to a general class of two qubit states.Quanta 2019; 8: 57–67.

scholarly journals Quantum Mechanics and the Origin of Life

2004 ◽  
Vol 213 ◽  
pp. 237-244
Author(s):  
Paul Davies
Keyword(s):  
Quantum Mechanics ◽  
Information Processing ◽  
Quantum Information ◽  
Quantum Computation ◽  
Origin Of Life ◽  
Quantum Information Processing ◽  
Quantum Computer ◽  
The Origin Of Life ◽  
Concept Of Information

The race to build a quantum computer has led to a radical re-evaluation of the concept of information. In this paper I conjecture that life, defined as an information processing and replicating system, may be exploiting the considerable efficiency advantages offered by quantum computation, and that quantum information processing may dramatically shorten the odds for life originating from a random chemical soup. The plausibility of this conjecture rests, however, on life somehow circumventing the decoherence effects of the environment. I offer some speculations on ways in which this might happen.

scholarly journals THE PHYSICS OF QUANTUM INFORMATION: COMPLEMENTARITY, UNCERTAINTY, AND ENTANGLEMENT

2013 ◽  
Vol 11 (08) ◽  
pp. 1330002 ◽  
Author(s):  
JOSEPH M. RENES
Keyword(s):  
Information Theory ◽  
Quantum Mechanics ◽  
Information Processing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Quantum Information Theory ◽  
Wave Particle Duality ◽  
Double Slit Experiment ◽  
Slit Experiment ◽  
Double Slit

Complementarity is one of the central mysteries of quantum mechanics, dramatically illustrated by the wave-particle duality in Young's double-slit experiment, and famously regarded by Feynman as "impossible, absolutely impossible to describe classically, [and] which has in it the heart of quantum mechanics" (emphasis original).1 The overarching goal of this thesis is to demonstrate that complementarity is also at the heart of quantum information theory, that it allows us to make (some) sense of just what information "quantum information" refers to, and that it is useful in understanding and constructing quantum information processing protocols.

scholarly journals CAN QUANTUM MECHANICS HELP DISTRIBUTED COMPUTING?

2010 ◽  
Vol 08 (01n02) ◽  
pp. 259-269
Author(s):  
ANNE BROADBENT ◽  
ALAIN TAPP
Keyword(s):  
Quantum Mechanics ◽  
Information Processing ◽  
Quantum Information ◽  
Distributed Computing ◽  
Communication Complexity ◽  
Quantum Information Processing ◽  
Distributed Computation ◽  
Distributed Tasks

We present a brief survey of results where quantum information processing is useful for performing distributed computation tasks. We describe problems that are impossible to solve using classical resources but that become feasible with the help of quantum mechanics. We also give examples where the use of quantum information significantly reduces the need for communication. The main focus of the survey is on communication complexity but we also address other distributed tasks.

scholarly journals Entanglement enhanced distinguishability of coherence-breaking channels

2019 ◽  
Vol 17 (04) ◽  
pp. 1950036
Author(s):  
Long-Mei Yang ◽  
Tao Li ◽  
Shao-Ming Fei ◽  
Zhi-Xi Wang
Keyword(s):  
Quantum Mechanics ◽  
Information Processing ◽  
Quantum Information ◽  
Quantum Entanglement ◽  
Error Probability ◽  
Quantum Information Processing ◽  
Superposition Principle ◽  
Important Resource ◽  
Minimal Error ◽  
Different Types

Originating from the superposition principle in quantum mechanics, coherence has been extensively studied as a kind of important resource in quantum information processing. We investigate the distinguishability of coherence-breaking channels with the help of quantum entanglement. By explicitly computing the minimal error probability of channel discrimination, it is shown that entanglement can enhance the capacity of coherence-breaking channel distinguishability with same types for some cases while it cannot be enhanced for some other cases. For coherence-breaking channels with different types, the channel distinguishability cannot be enhanced via entanglement.

scholarly journals Union bound for quantum information processing

2019 ◽  
Vol 475 (2221) ◽  
pp. 20180612 ◽  
Author(s):  
Samad Khabbazi Oskouei ◽  
Stefano Mancini ◽  
Mark M. Wilde
Keyword(s):  
Quantum Information ◽  
Communication Theory ◽  
Quantum Information Processing ◽  
Quantum Algorithms ◽  
Schwarz Inequality ◽  
Classical Communication ◽  
Root Measurement ◽  
Union Bound ◽  
Quantum Complexity ◽  
Quantum Complexity Theory

In this paper, we prove a quantum union bound that is relevant when performing a sequence of binary-outcome quantum measurements on a quantum state. The quantum union bound proved here involves a tunable parameter that can be optimized, and this tunable parameter plays a similar role to a parameter involved in the Hayashi–Nagaoka inequality (Hayashi & Nagaoka 2003 IEEE Trans. Inf. Theory 49 , 1753–1768. ( doi:10.1109/TIT.2003.813556 )), used often in quantum information theory when analysing the error probability of a square-root measurement. An advantage of the proof delivered here is that it is elementary, relying only on basic properties of projectors, Pythagoras' theorem, and the Cauchy–Schwarz inequality. As a non-trivial application of our quantum union bound, we prove that a sequential decoding strategy for classical communication over a quantum channel achieves a lower bound on the channel's second-order coding rate. This demonstrates the advantage of our quantum union bound in the non-asymptotic regime, in which a communication channel is called a finite number of times. We expect that the bound will find a range of applications in quantum communication theory, quantum algorithms and quantum complexity theory.

scholarly journals “Quantumness” versus “classicality” of quantum states and quantum protocols

2018 ◽  
Vol 16 (02) ◽  
pp. 1850014
Author(s):  
Aharon Brodutch ◽  
Berry Groisman ◽  
Dan Kenigsberg ◽  
Tal Mor
Keyword(s):  
Quantum Mechanics ◽  
Information Processing ◽  
Quantum Information ◽  
Quantum State ◽  
Quantum Information Processing ◽  
Quantum States ◽  
Separable States ◽  
Quantum Properties ◽  
Quantum Protocols

Entanglement is one of the pillars of quantum mechanics and quantum information processing, and as a result, the quantumness of nonentangled states has typically been overlooked and unrecognized until the last decade. We give a robust definition for the classicality versus quantumness of a single multipartite quantum state, a set of states, and a protocol using quantum states. We show a variety of nonentangled (separable) states that exhibit interesting quantum properties, and we explore the “zoo” of separable states; several interesting subclasses are defined based on the diagonalizing bases of the states, and their nonclassical behavior is investigated.

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