ENCRYPTION OF QUANTUM INFORMATION

2003 ◽  
Vol 14 (05) ◽  
pp. 741-755 ◽  
Author(s):  
JAN BOUDA ◽  
VLADIMÍ R. BUŽEK
Keyword(s):  
Quantum Information ◽  
Quantum Channel ◽  
Composite System ◽  
Quantum Systems ◽  
Noisy Channel ◽  
Classical Description ◽  
Quantum Analogue ◽  
Known Plaintext Attack

We study in detail the problem of encryption of quantum information. We present an attack on a private quantum channel (PQC) which applies when partial classical description of a ciphertext is known (the so-called known-ciphertext attack) and we show how this situation can be avoided. The quantum analogue of the known plaintext attack is also discussed. We determine how correlations between quantum systems can be encrypted and we conclude that two PQCs on the subsystems form a PQC on the whole composite system. Finally, some applications of the PQC are suggested and a security of a noisy channel is discussed.

scholarly journals Fundamental limitations on distillation of quantum channel resources

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Bartosz Regula ◽  
Ryuji Takagi
Keyword(s):  
Lower Bounds ◽  
Quantum Channel ◽  
Quantum Communication ◽  
Fault Tolerant ◽  
State Of The Art ◽  
Quantum Systems ◽  
Noisy Channels ◽  
General Transformation ◽  
Fundamental Limitations ◽  
Strong Converse

AbstractQuantum channels underlie the dynamics of quantum systems, but in many practical settings it is the channels themselves that require processing. We establish universal limitations on the processing of both quantum states and channels, expressed in the form of no-go theorems and quantitative bounds for the manipulation of general quantum channel resources under the most general transformation protocols. Focusing on the class of distillation tasks — which can be understood either as the purification of noisy channels into unitary ones, or the extraction of state-based resources from channels — we develop fundamental restrictions on the error incurred in such transformations, and comprehensive lower bounds for the overhead of any distillation protocol. In the asymptotic setting, our results yield broadly applicable bounds for rates of distillation. We demonstrate our results through applications to fault-tolerant quantum computation, where we obtain state-of-the-art lower bounds for the overhead cost of magic state distillation, as well as to quantum communication, where we recover a number of strong converse bounds for quantum channel capacity.

scholarly journals Topological protection of biphoton states

Science ◽  
2018 ◽  
Vol 362 (6414) ◽  
pp. 568-571 ◽  
Author(s):  
Andrea Blanco-Redondo ◽  
Bryn Bell ◽  
Dikla Oren ◽  
Benjamin J. Eggleton ◽  
Mordechai Segev
Keyword(s):  
Quantum Information ◽  
Thermal Environment ◽  
Propagation Constant ◽  
Quantum Systems ◽  
Quantum Gates ◽  
Scattering Loss ◽  
Spatial Features ◽  
Quantum Optical ◽  
Nontrivial Topology ◽  
Large Quantum

The robust generation and propagation of multiphoton quantum states are crucial for applications in quantum information, computing, and communications. Although photons are intrinsically well isolated from the thermal environment, scaling to large quantum optical devices is still limited by scattering loss and other errors arising from random fabrication imperfections. The recent discoveries regarding topological phases have introduced avenues to construct quantum systems that are protected against scattering and imperfections. We experimentally demonstrate topological protection of biphoton states, the building block for quantum information systems. We provide clear evidence of the robustness of the spatial features and the propagation constant of biphoton states generated within a nanophotonics lattice with nontrivial topology and propose a concrete path to build robust entangled states for quantum gates.

scholarly journals Characterization of linear maps onMnwhose multiplicity maps have maximal norm, with an application in quantum information

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 51
Author(s):  
Daniel Puzzuoli
Keyword(s):  
Quantum Information ◽  
Quantum Channel ◽  
Operator Algebras ◽  
Optimal Performance ◽  
Single Shot ◽  
Trace Norm ◽  
Linear Maps ◽  
The Family ◽  
Matrix Transposition

Given a linear mapΦ:Mn→Mm, its multiplicity maps are defined as the family of linear mapsΦ⊗idk:Mn⊗Mk→Mm⊗Mk, whereidkdenotes the identity onMk. Let‖⋅‖1denote the trace-norm on matrices, as well as the induced trace-norm on linear maps of matrices, i.e.‖Φ‖1=max{‖Φ(X)‖1:X∈Mn,‖X‖1=1}. A fact of fundamental importance in both operator algebras and quantum information is that‖Φ⊗idk‖1can grow withk. In general, the rate of growth is bounded by‖Φ⊗idk‖1≤k‖Φ‖1, and matrix transposition is the canonical example of a map achieving this bound. We prove that, up to an equivalence, the transpose is the unique map achieving this bound. The equivalence is given in terms of complete trace-norm isometries, and the proof relies on a particular characterization of complete trace-norm isometries regarding preservation of certain multiplication relations.We use this result to characterize the set of single-shot quantum channel discrimination games satisfying a norm relation that, operationally, implies that the game can be won with certainty using entanglement, but is hard to win without entanglement. Specifically, we show that the well-known example of such a game, involving the Werner-Holevo channels, is essentially the unique game satisfying this norm relation. This constitutes a step towards a characterization of single-shot quantum channel discrimination games with maximal gap between optimal performance of entangled and unentangled strategies.

Probabilistic secret sharing through noise quantum channe

2012 ◽  
Vol 12 (3&4) ◽  
pp. 253-261
Author(s):  
Satyabrata Adhikari ◽  
Indranil Chakrabarty ◽  
Pankaj Agrawal
Keyword(s):  
Quantum Information ◽  
Secret Sharing ◽  
Mixed State ◽  
Pure State ◽  
Noisy Channel ◽  
Noisy Channels ◽  
Superdense Coding ◽  
Classical Information ◽  
Phase Damping ◽  
Realistic Situation

In a realistic situation, the secret sharing of classical or quantum information will involve the transmission of this information through noisy channels. We consider a three qubit pure state. This state becomes a mixed-state when the qubits are distributed over noisy channels. We focus on a specific noisy channel, the phase-damping channel. We propose a protocol for secret sharing of classical information with this and related noisy channels. This protocol can also be thought of as cooperative superdense coding. We also discuss other noisy channels to examine the possibility of secret sharing of classical information.

scholarly journals Quantum state space dimension as a quantum resource

2015 ◽  
Vol 13 (06) ◽  
pp. 1550039 ◽  
Author(s):  
A. Plastino ◽  
G. Bellomo ◽  
A. R. Plastino
Keyword(s):  
Quantum Information ◽  
State Space ◽  
Quantum State ◽  
Space Dimension ◽  
Quantum Systems ◽  
Quantum States ◽  
Information Tasks

We argue that the dimensionality of the space of quantum systems’ states should be considered as a legitimate resource for quantum information tasks. The assertion is supported by the fact that quantum states with discord-like capacities can be obtained from classically-correlated states in spaces of dimension large enough. We illustrate things with some simple examples that justify our claim.

Support projection of state and a quantum Lévy–Austin–Ornstein theorem

2014 ◽  
Vol 17 (03) ◽  
pp. 1450020 ◽  
Author(s):  
Skander Hachicha
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Markov Semigroup ◽  
Open Quantum ◽  
Quantum Analogue ◽  
Quantum Markov Semigroup ◽  
Support Projection

We prove two characterizations of the support projection of a state evolving under the action of a quantum Markov semigroup and a quantum analogue of the Lévy–Austin–Ornstein theorem. We discuss applications to open quantum systems.

TOWARDS A THEORY OF DECOHERENCE

2004 ◽  
Vol 18 (04n05) ◽  
pp. 643-654 ◽  
Author(s):  
GIANFAUSTO DELL'ANTONIO
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Particle ◽  
Small Mass ◽  
Quantum Systems ◽  
Classical Description ◽  
Large Quantum

Consider a quantum particle of mass M in R3, described at time 0 by a wave function ϕ(x) with dispersion Δ, interacting independently with a collection of N particles of mass m. Using only Schroedinger's Quantum Mechanics we prove that when N becomes large and m/M becomes small, and if the information at time t>0 about the N particles of small mass in negleted, the system admits a "classical" description, i.e. a description in which the coherence of the wave function over distances of the order of mM-1N-1Δ have disappeared. We consider this a first step towards proving that most "sufficiently large" quantum systems interacting with an uncontrolled environment admit a classical description at least for position measurements.

QUANTUM CHANNELS OF THE QUTRIT STATE TELEPORTATION

2011 ◽  
Vol 09 (03) ◽  
pp. 893-901 ◽  
Author(s):  
XIU-LAO TIAN ◽  
GUO-FANG SHI ◽  
Yong ZHAO
Keyword(s):  
Quantum Information ◽  
Quantum System ◽  
Quantum Channel ◽  
Sufficient Condition ◽  
Quantum Channels ◽  
Necessary And Sufficient Condition ◽  
Measurement Matrix ◽  
Parameter Matrix ◽  
Channel Parameter ◽  
Necessary And Sufficient

Qudit quantum system can carry more information than that of qubit, the teleportation of qudit state has significance in quantum information task. We propose a method to teleport a general qutrit state (three-level state) and discuss the necessary and sufficient condition for realizing a successful and perfect teleportation, which is determined by the measurement matrix Tα and the quantum channel parameter matrix (CPM) X. By using this method, we study the channels of two-qutrit state and three-qutrit state teleportation.

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