scholarly journals Conditions for uniqueness of product representations for separable quantum channels and separable quantum states

2014 ◽  
Vol 55 (6) ◽  
pp. 062202 ◽  
Author(s):  
Scott M. Cohen
Keyword(s):  
Quantum States ◽  
Quantum Channels

scholarly journals Operational applications of the diamond norm and related measures in quantifying the non-physicality of quantum maps

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 522
Author(s):  
Bartosz Regula ◽  
Ryuji Takagi ◽  
Mile Gu
Keyword(s):  
Quantum Dynamics ◽  
Distance Measure ◽  
Quantum States ◽  
Quantum Channels ◽  
Linear Combinations ◽  
Operational Approach ◽  
Completely Positive ◽  
Error Mitigation ◽  
Linear Maps ◽  
The Cost

Although quantum channels underlie the dynamics of quantum states, maps which are not physical channels — that is, not completely positive — can often be encountered in settings such as entanglement detection, non-Markovian quantum dynamics, or error mitigation. We introduce an operational approach to the quantitative study of the non-physicality of linear maps based on different ways to approximate a given linear map with quantum channels. Our first measure directly quantifies the cost of simulating a given map using physically implementable quantum channels, shifting the difficulty in simulating unphysical dynamics onto the task of simulating linear combinations of quantum states. Our second measure benchmarks the quantitative advantages that a non-completely-positive map can provide in discrimination-based quantum games. Notably, we show that for any trace-preserving map, the quantities both reduce to a fundamental distance measure: the diamond norm, thus endowing this norm with new operational meanings in the characterisation of linear maps. We discuss applications of our results to structural physical approximations of positive maps, quantification of non-Markovianity, and bounding the cost of error mitigation.

SHARING OF D-DIMENSIONAL QUANTUM STATES

2012 ◽  
Vol 10 (02) ◽  
pp. 1250003 ◽  
Author(s):  
OMAR JIMÉNEZ ◽  
CARLOS MUÑOZ ◽  
ANDREI B. KLIMOV ◽  
ALDO DELGADO
Keyword(s):  
Quantum State ◽  
Success Probability ◽  
Quantum States ◽  
Quantum State Sharing ◽  
Quantum Channels ◽  
Quantum State Discrimination ◽  
State Discrimination ◽  
Ideal Quantum

We propose a scheme for the deterministic sharing arbitrary qudit states among three distant parties and characterize the set of ideal quantum channels. We also show that the use of non-ideal quantum channels for quantum state sharing can be related to the problem of quantum state discrimination. This allows us to formulate a protocol which leads to perfect quantum state sharing with a finite success probability.

PERFECT TELEPORTATION OF UNKNOWN QUDIT BY A d-LEVEL GHZ CHANNEL

2009 ◽  
Vol 07 (04) ◽  
pp. 755-770 ◽  
Author(s):  
YINXIANG LONG ◽  
DAOWEN QIU ◽  
DONGYANG LONG
Keyword(s):  
General Scheme ◽  
Bell State ◽  
Ghz State ◽  
Quantum States ◽  
Entangled State ◽  
Input State ◽  
Quantum Channels ◽  
Maximally Entangled State ◽  
Ghz States ◽  
Measurement Basis

In the past decades, various schemes of teleportation of quantum states through different types of quantum channels (a prior shared entangled state between the sender and the receiver), e.g. EPR pairs, generalized Bell states, qubit GHZ states, standard W states and its variations, genuine multiqubit entanglement states, etc., have been developed. Recently, three-qutrit quantum states and two-qudit quantum states have also been considered as quantum channels for teleportation. In this paper, we investigate the teleportation of an unknown qudit using a d level GHZ state, i.e. a three-qudit maximally entangled state, as quantum channel. We design a general scheme of faithful teleportation of an unknown qudit using a d-level GHZ state shared between the sender and the receiver, or among the sender, the receiver and the controller; an unknown two-qudit of Schmidt form using a d level GHZ state shared between the sender and the receiver; as well as an unknown arbitrary two-qudit using two shared d level GHZ states between the sender, the receiver and the controller, or using one shared d level GHZ state and one shared generalized Bell state. We obtain the general formulas of Alice's measurement basis, Charlie's measurement basis and Bob's unitary operations to recover the input state of Alice. It is intuitionistic to generalize the protocols of teleporting an arbitrary two-qudit state to teleporting an arbitrary n-qudit state.

scholarly journals Optimal bounds on functions of quantum states under quantum channels

2016 ◽  
Vol 16 (9&10) ◽  
pp. 845-861
Author(s):  
Chi-Kwong Li ◽  
Diane Christine Pelejo ◽  
Kuo-Zhong Wang
Keyword(s):  
Relative Entropy ◽  
Scalar Function ◽  
Quantum States ◽  
Quantum Channels ◽  
Trace Distance ◽  
Optimal Bounds ◽  
Class Of Functions

Let ρ1, ρ2 be quantum states and (ρ1, ρ2) 7→ D(ρ1, ρ2) be a scalar function such as the trace distance, the fidelity, and the relative entropy, etc. We determine optimal bounds for D(ρ1, Φ(ρ2)) for Φ blongs to S for different class of functions D(·, ·), where S is the set of unitary quantum channels, the set of mixed unitary channels, the set of unital quantum channels, and the set of all quantum channels.

Cohering power and decohering power of Gaussian unitary operations

2019 ◽  
Vol 19 (7&8) ◽  
pp. 575-586
Author(s):  
Yangyang Wang ◽  
Xiaofei Qi ◽  
Jinchuan Hou ◽  
Rufen Ma
Keyword(s):  
Relative Entropy ◽  
Continuous Variable ◽  
Quantum States ◽  
Entropy Measure ◽  
Quantum Channels ◽  
Gaussian States ◽  
Basic Properties ◽  
Suitable Measure

Having a suitable measure to quantify the coherence of quantum states, a natural task is to evaluate the power of quantum channels for creating or destroying the coherence of input quantum states. In the present paper, by introducing the maximal coherent Gaussian states based on the relative entropy measure of coherence, we propose the (generalized) cohering power and the (generalized) decohering power of Gaussian unitary operations for continuous-variable systems. Some basic properties are obtained and the cohering power and decohering power of two special kinds of Gaussian unitary operations are calculated.

Multi-party quantum key agreement with teleportation

2017 ◽  
Vol 31 (10) ◽  
pp. 1750102 ◽  
Author(s):  
Binbin Cai ◽  
Gongde Guo ◽  
Song Lin
Keyword(s):  
Quantum Teleportation ◽  
Key Agreement ◽  
Security Analysis ◽  
Quantum States ◽  
Quantum Key Agreement ◽  
Quantum Channels ◽  
Secret Key ◽  
Key Agreement Protocol ◽  
Shared Key ◽  
Quantum Key Agreement Protocol

Based on the technique of quantum teleportation, a new multi-party quantum key agreement protocol is proposed. In this protocol, all users first share EPR pairs via public quantum channels. Afterwards, the states of signal particles can be transferred between two adjacent users by quantum teleportation. With the help of four unitary encoding operations, all users can encode their separate secret key into the traveling quantum states. In the end, all users can derive the final shared key synchronously. The security analysis shows that the presented protocol is secure against some common attacks and completely loss tolerant.

scholarly journals SINGULAR VALUE DECOMPOSITION AND MATRIX REORDERINGS IN QUANTUM INFORMATION THEORY

2011 ◽  
Vol 22 (09) ◽  
pp. 897-918 ◽  
Author(s):  
JAROSŁAW ADAM MISZCZAK
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Singular Value Decomposition ◽  
Computing System ◽  
Quantum Information Theory ◽  
Singular Value ◽  
Quantum States ◽  
Quantum Channels ◽  
Basic Functions ◽  
Value Decomposition

We review Schmidt and Kraus decompositions in the form of singular value decomposition using operations of reshaping, vectorization and reshuffling. We use the introduced notation to analyze the correspondence between quantum states and operations with the help of Jamiołkowski isomorphism. The presented matrix reorderings allow us to obtain simple formulae for the composition of quantum channels and partial operations used in quantum information theory. To provide examples of the discussed operations, we utilize a package for the Mathematica computing system implementing basic functions used in the calculations related to quantum information theory.

scholarly journals On Partially Trace Distance Preserving Maps and Reversible Quantum Channels

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Long Jian ◽  
Kan He ◽  
Qing Yuan ◽  
Fei Wang
Keyword(s):  
Quantum States ◽  
Quantum Channels ◽  
Trace Distance ◽  
Linear Maps ◽  
Unitary Transformations ◽  
Pure States ◽  
Positive Linear Maps

We give a characterization of trace-preserving and positive linear maps preserving trace distance partially, that is, preservers of trace distance of quantum states or pure states rather than all matrices. Applying such results, we give a characterization of quantum channels leaving Helstrom's measure of distinguishability of quantum states or pure states invariant and show that such quantum channels are fully reversible, which are unitary transformations.

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