scholarly journals Quantum complementarity and operator structures

2019 ◽  
Vol 19 (1&2) ◽  
pp. 67-83
Author(s):  
David W. Kribs ◽  
Jeremy Livick ◽  
Mike I. Nelson ◽  
Rajesh Perira ◽  
Mizanur Rahaman
Keyword(s):  
Operator Algebras ◽  
Quantum States ◽  
Quantum Channels ◽  
Operator Spaces ◽  
Trade Off ◽  
Operator Structure ◽  
Private Operator

We establish operator structure identities for quantum channels and their error-correcting and private codes, emphasizing the complementarity relationship between the two perspectives. Relevant structures include correctable and private operator algebras, and operator spaces such as multiplicative domains and nullspaces of quantum channels and their complementary maps. For the case of privatizing to quantum states, we also derive dimension inequalities on the associated operator algebras that further quantify the trade-off between correction and privacy.

scholarly journals Superadditivity in Trade-Off Capacities of Quantum Channels

2018 ◽  
Author(s):  
Elton Yechao Zhu ◽  
Quntao Zhuang ◽  
Min-Hsiu Hsieh ◽  
Peter W. Shor
Keyword(s):  
Quantum Channels ◽  
Trade Off

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.

scholarly journals Experimental study of quantum coherence decomposition and trade-off relations in a tripartite system

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Zhe Ding ◽  
Ran Liu ◽  
Chandrashekar Radhakrishnan ◽  
Wenchao Ma ◽  
Xinhua Peng ◽  
...  
Keyword(s):  
Experimental Study ◽  
Nuclear Spin ◽  
Quantum Coherence ◽  
Quantum Systems ◽  
Spin Systems ◽  
Quantum States ◽  
Product State ◽  
Trade Off ◽  
Global Coherence ◽  
Multipartite System

AbstractQuantum coherence is the most fundamental of all quantum quantifiers, underlying other well-known quantities such as entanglement. It can be distributed in a multipartite system in various ways—for example, in a bipartite system it can exist within subsystems (local coherence) or collectively between the subsystems (global coherence), and exhibits a trade-off relation. In this paper, we experimentally verify these coherence trade-off relations in adiabatically evolved nuclear spin systems using an NMR spectrometer. We study the full set of coherence trade-off relations between the original state, the bipartite product state, the tripartite product state, and the decohered product state. We also experimentally verify the monogamy inequality and show that both the quantum systems are polygamous during the evolution. We find that the properties of the state in terms of coherence and monogamy are equivalent. This illustrates the utility of using coherence as a characterization tool for quantum states.

scholarly journals Superadditivity in Trade-Off Capacities of Quantum Channels

2019 ◽  
Vol 65 (6) ◽  
pp. 3973-3989 ◽  
Author(s):  
Elton Yechao Zhu ◽  
Quntao Zhuang ◽  
Min-Hsiu Hsieh ◽  
Peter W. Shor
Keyword(s):  
Quantum Channels ◽  
Trade Off

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.

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