scholarly journals Unambiguous unitary quantum channels

2007 ◽  
Vol 7 (8) ◽  
pp. 782-798
Author(s):  
S.-J. Wu ◽  
X.-M. Chen
Keyword(s):  
Error Correction ◽  
Quantum Channel ◽  
Entangled State ◽  
Noisy Channel ◽  
Quantum Channels ◽  
Necessary And Sufficient Condition ◽  
Dense Coding ◽  
Probability Of Success ◽  
Necessary And Sufficient ◽  
Nonzero Probability

Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensures certain simple form for the measurements involved in realizing an unambiguous unitary quantum channel. Error correction and unambiguous error correction with nonzero probability are discussed in terms of unambiguous unitary quantum channels. We not only re-derive the well-known condition for a set of errors to be correctable with certainty, but also obtain a necessary and sufficient condition for the errors caused by a noisy channel to be correctable with any nonzero probability. Dense coding with a partially entangled state can also be viewed as an unambiguous unitary quantum channel when all messages are required to be transmitted with equal probability of success, the maximal achievable probability of success is derived and the optimum protocol is also obtained.

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.

scholarly journals Probabilistic Resumable Quantum Teleportation of a Two-Qubit Entangled State

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 352 ◽  
Author(s):  
Zhan-Yun Wang ◽  
Yi-Tao Gou ◽  
Jin-Xing Hou ◽  
Li-Ke Cao ◽  
Xiao-Hui Wang
Keyword(s):  
Quantum Channel ◽  
Quantum Teleportation ◽  
The State ◽  
Entangled States ◽  
Entangled State ◽  
Quantum Channels ◽  
Unknown State ◽  
Optimal Probability

We explicitly present a generalized quantum teleportation of a two-qubit entangled state protocol, which uses two pairs of partially entangled particles as quantum channel. We verify that the optimal probability of successful teleportation is determined by the smallest superposition coefficient of these partially entangled particles. However, the two-qubit entangled state to be teleported will be destroyed if teleportation fails. To solve this problem, we show a more sophisticated probabilistic resumable quantum teleportation scheme of a two-qubit entangled state, where the state to be teleported can be recovered by the sender when teleportation fails. Thus the information of the unknown state is retained during the process. Accordingly, we can repeat the teleportion process as many times as one has available quantum channels. Therefore, the quantum channels with weak entanglement can also be used to teleport unknown two-qubit entangled states successfully with a high number of repetitions, and for channels with strong entanglement only a small number of repetitions are required to guarantee successful teleportation.

scholarly journals Purification of two-qubit mixed states

2002 ◽  
Vol 2 (5) ◽  
pp. 348-354
Author(s):  
E. Jan\'e
Keyword(s):  
Qubit State ◽  
Entangled State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Mixed States ◽  
Classical Communication ◽  
Maximally Entangled State ◽  
Optimal Protocol ◽  
Necessary And Sufficient

We find the necessary and sufficient condition under which two two-qubit mixed states can be purified into a pure maximally entangled state by local operations and classical communication. The optimal protocol for such transformation is obtained. This result leads to a necessary and sufficient condition for the exact purification of $n$ copies of a two-qubit state.

scholarly journals Zero-Error Coding via Classical and Quantum Channels in Sensor Networks

Sensors ◽  
2019 ◽  
Vol 19 (23) ◽  
pp. 5071
Author(s):  
Yu ◽  
Xiong ◽  
Dong ◽  
Wang ◽  
Li ◽  
...  
Keyword(s):  
Sensor Networks ◽  
Error Correction ◽  
Channel Capacity ◽  
Quantum Channel ◽  
Critical Role ◽  
Coefficient Matrix ◽  
Quantum Channels ◽  
Classical Counterpart ◽  
Large Channel ◽  
Error Coding

Today’s sensor networks need robustness, security and efficiency with a high level of assurance. Error correction is an effective communicational technique that plays a critical role in maintaining robustness in informational transmission. The general way to tackle this problem is by using forward error correction (FEC) between two communication parties. However, by applying zero-error coding one can assure information fidelity while signals are transmitted in sensor networks. In this study, we investigate zero-error coding via both classical and quantum channels, which consist of n obfuscated symbols such as Shannon’s zero-error communication. As a contrast to the standard classical zero-error coding, which has a computational complexity of , a general approach is proposed herein to find zero-error codewords in the case of quantum channel. This method is based on a n-symbol obfuscation model and the matrix’s linear transformation, whose complexity dramatically decreases to . According to a comparison with classical zero-error coding, the quantum zero-error capacity of the proposed method has obvious advantages over its classical counterpart, as the zero-error capacity equals the rank of the quantum coefficient matrix. In particular, the channel capacity can reach n when the rank of coefficient matrix is full in the n-symbol multilateral obfuscation quantum channel, which cannot be reached in the classical case. Considering previous methods such as low density parity check code (LDPC), our work can provide a means of error-free communication through some typical channels. Especially in the quantum case, zero-error coding can reach both a high coding efficiency and large channel capacity, which can improve the robustness of communication in sensor networks.

scholarly journals The Pitfalls of Deciding Whether a Quantum Channel is (Conjugate) Degradable and How to Avoid Them

2015 ◽  
Vol 22 (04) ◽  
pp. 1550026 ◽  
Author(s):  
Kamil Brádler
Keyword(s):  
Quantum Channel ◽  
Single Letter ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Quantum Capacity ◽  
Elementary Methods ◽  
Necessary And Sufficient

To decide whether a quantum channel is degradable is relatively easy: one has to find at least one example of a degrading quantum channel. But in general, no conclusive criterion exists to show the opposite. Using elementary methods we derive a necessary and sufficient condition to decide under what circumstances the conclusion is unambiguous. The findings lead to an extension of the antidegradability region for qubit and qutrit transpose depolarizing channels. In the qubit case we reproduce the known results for the class of qubit depolarizing channels (due to their equivalence). One of the consequences is that the optimal qubit and qutrit asymmetric cloners possess a single-letter quantum capacity formula. We also investigate the ramifications of the criterion for the search of exclusively conjugate degradable channels.

scholarly journals Optimal probes and error-correction schemes in multi-parameter quantum metrology

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 288
Author(s):  
Wojciech Górecki ◽  
Sisi Zhou ◽  
Liang Jiang ◽  
Rafał Demkowicz-Dobrzański
Keyword(s):  
Parameter Estimation ◽  
Error Correction ◽  
Semidefinite Program ◽  
Sufficient Condition ◽  
Quantum Metrology ◽  
Necessary And Sufficient Condition ◽  
Estimation Precision ◽  
Pure States ◽  
Necessary And Sufficient ◽  
Quantum Error

We derive a necessary and sufficient condition for the possibility of achieving the Heisenberg scaling in general adaptive multi-parameter estimation schemes in presence of Markovian noise. In situations where the Heisenberg scaling is achievable, we provide a semidefinite program to identify the optimal quantum error correcting (QEC) protocol that yields the best estimation precision. We overcome the technical challenges associated with potential incompatibility of the measurement optimally extracting information on different parameters by utilizing the Holevo Cramér-Rao (HCR) bound for pure states. We provide examples of significant advantages offered by our joint-QEC protocols, that sense all the parameters utilizing a single error-corrected subspace, over separate-QEC protocols where each parameter is effectively sensed in a separate subspace.

scholarly journals Further Results on Weak Exogeneity in Vector Error Correction Models

2005 ◽  
Vol 25 (2) ◽  
pp. 159
Author(s):  
Christophe Rault
Keyword(s):  
Error Correction ◽  
Interesting Property ◽  
Necessary And Sufficient Condition ◽  
Error Correction Models ◽  
Vector Error Correction ◽  
Vector Error ◽  
Long Run ◽  
Weak Exogeneity ◽  
Vector Error Correction Models ◽  
Necessary And Sufficient

This paper extends the result for non-causality and strong exogeneity of Pradel and Rault and Pradel (2003) Exogeneity in VAR-ECM models with purely exogenous long-run paths, Oxford Bulletin of Economics and Statistics to weak exogeneity. More precisely, it provides a necessary and sufficient condition for weak exogeneity in vector error correction models. An interesting property is that the statistics involved in the sequential procedure for testing this condition are distributed as χ2 variables and can therefore be easily calculated with usual statistical computer packages, which makes our approach fully operational empirically

scholarly journals Necessary and sufficient conditions on measurements of quantum channels

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190832 ◽  
Author(s):  
John Burniston ◽  
Michael Grabowecky ◽  
Carlo Maria Scandolo ◽  
Giulio Chiribella ◽  
Gilad Gour
Keyword(s):  
Quantum Measurement ◽  
Quantum Channel ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Quantum Channels ◽  
Completely Positive ◽  
Principle Of Causality ◽  
Necessary And Sufficient

Quantum supermaps are a higher-order genera- lization of quantum maps, taking quantum maps to quantum maps. It is known that any completely positive and trace non-increasing (CPTNI) map can be performed as part of a quantum measurement. By providing an explicit counterexample we show that, instead, not every quantum supermap sending a quantum channel to a CPTNI map can be realized in a measurement on quantum channels. We find that the supermaps that can be implemented in this way are exactly those transforming quantum channels into CPTNI maps even when tensored with the identity supermap. We link this result to the fact that the principle of causality fails in the theory of quantum supermaps.

TELEPORTATION OF N-QUDIT STATE

2012 ◽  
Vol 10 (01) ◽  
pp. 1250013
Author(s):  
JIA-JIA SHAO ◽  
XIU-LAO TIAN ◽  
GUO-FANG SHI
Keyword(s):  
Quantum Channel ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Tensor Representation ◽  
Measurement Matrix ◽  
Parameter Matrix ◽  
Channel Parameter ◽  
Necessary And Sufficient

In this paper, we study the teleportation of arbitrary N-qudit state with the tensor representation. The necessary and sufficient condition for realizing a successful or perfect teleportation is obtained, as will be shown, which is determined by the measurement matrix Tδ and the quantum channel parameter matrix X. The general expressions of the measurement matrix Tδ are written out and the quantum channel parameter matrix X are discussed. As an example, we show the details of three-ququart state teleportation.

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