scholarly journals Explicit Construction of Optimal Witnesses for Input-Output Correlations Attainable by Quantum Channels

2020 ◽  
Vol 27 (04) ◽  
pp. 2050017
Author(s):  
Michele Dall’Arno ◽  
Sarah Brandsen ◽  
Francesco Buscemi
Keyword(s):  
Quantum Channel ◽  
Explicit Construction ◽  
Quantum Channels ◽  
Input Output ◽  
Noisy Channels ◽  
Completely Positive ◽  
Communication Games ◽  
Single Use ◽  
Classical Quantum ◽  
Communication Resource

Given a quantum channel — that is, a completely positive trace-preserving linear map — as the only communication resource available between two parties, we consider the problem of characterizing the set of classical noisy channels that can be obtained from it by means of suitable classical-quantum encodings and quantum-classical decodings, respectively, on the sender’s and the receiver’s side. We consider various classes of linear witnesses and compute their optimum values in closed form for several classes of quantum channels. The witnesses that we consider here are formulated as communication games, in which Alice’s aim is to exploit a single use of a given quantum channel to help Bob guess some information she has received from an external referee.

scholarly journals On the one-shot zero-error classical capacity of classical-quantum channels assisted by quantum non-signalling correlations

2017 ◽  
Vol 17 (5&6) ◽  
pp. 380-398
Author(s):  
Ching-Yi Lai ◽  
Runyao Duan
Keyword(s):  
Quantum Channel ◽  
Quantum Communication ◽  
Semidefinite Program ◽  
Circulant Graph ◽  
Quantum Channels ◽  
Kraus Operator ◽  
Cyclotomic Cosets ◽  
Classical Capacity ◽  
Classical Quantum ◽  
The One

Duan and Winter studied the one-shot zero-error classical capacity of a quantum channel assisted by quantum non-signalling correlations, and formulated this problem as a semidefinite program depending only on the Kraus operator space of the channel. For the class of classical-quantum channels, they showed that the asymptotic zero-error classical capacity assisted by quantum non-signalling correlations, minimized over all classicalquantum channels with a confusability graph G, is exactly log ϑ(G), where ϑ(G) is the celebrated Lov´asz theta function. In this paper, we show that the one-shot capacity for a classical-quantum channel, induced from a circulant graph G defined by equal-sized cyclotomic cosets, is logbϑ(G)c, which further implies that its asymptotic capacity is log ϑ(G). This type of graphs include the cycle graphs of odd length, the Paley graphs of prime vertices, and the cubit residue graphs of prime vertices. Examples of other graphs are also discussed. This gives Lov´asz ϑ function another operational meaning in zero-error classical-quantum communication.

scholarly journals Device-independent tests of quantum channels

2017 ◽  
Vol 473 (2199) ◽  
pp. 20160721 ◽  
Author(s):  
Michele Dall’Arno ◽  
Sarah Brandsen ◽  
Francesco Buscemi
Keyword(s):  
Closed Form ◽  
Quantum Channel ◽  
Arbitrary Dimension ◽  
Quantum Channels ◽  
Input Output ◽  
Amplitude Damping ◽  
Universal Cloning

We develop a device-independent framework for testing quantum channels. That is, we falsify a hypothesis about a quantum channel based only on an observed set of input–output correlations. Formally, the problem consists of characterizing the set of input–output correlations compatible with any arbitrary given quantum channel. For binary (i.e. two input symbols, two output symbols) correlations, we show that extremal correlations are always achieved by orthogonal encodings and measurements, irrespective of whether or not the channel preserves commutativity. We further provide a full, closed-form characterization of the sets of binary correlations in the case of: (i) any dihedrally covariant qubit channel (such as any Pauli and amplitude-damping channels) and (ii) any universally-covariant commutativity-preserving channel in an arbitrary dimension (such as any erasure, depolarizing, universal cloning and universal transposition channels).

scholarly journals Convex decomposition of dimension-altering quantum channels

2016 ◽  
Vol 14 (08) ◽  
pp. 1650045 ◽  
Author(s):  
Dong-Sheng Wang
Keyword(s):  
Quantum Channel ◽  
Convex Set ◽  
Quantum Circuit ◽  
Quantum Channels ◽  
Completely Positive ◽  
Decomposition Problem ◽  
Convex Decomposition ◽  
Decomposition Scheme ◽  
Low Dimensional ◽  
Channel Decomposition

Quantum channels, which are completely positive and trace preserving mappings, can alter the dimension of a system, e.g. a quantum channel from a qubit to a qutrit. We study the convex set properties of dimension-altering quantum channels, and particularly the channel decomposition problem in terms of convex sum of extreme channels. We provide various quantum circuit representations of extreme and generalized extreme channels, which can be employed in an optimization to approximately decompose an arbitrary channel. Numerical simulations of low-dimensional channels are performed to demonstrate our channel decomposition scheme.

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.

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 Polar Codes for Classical-Quantum Channels

2013 ◽  
Vol 59 (2) ◽  
pp. 1175-1187 ◽  
Author(s):  
Mark M. Wilde ◽  
Saikat Guha
Keyword(s):  
Polar Codes ◽  
Quantum Channels ◽  
Classical Quantum

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.

Performance characterization of Pauli channels assisted by indefinite causal order and post-measurement

2020 ◽  
Vol 20 (15&16) ◽  
pp. 1261-1280
Author(s):  
Francisco Delgado ◽  
Carlos Cardoso-Isidoro
Keyword(s):  
Quantum Channel ◽  
Communication Channel ◽  
Quantum Communication ◽  
Quantum Channels ◽  
Causal Order ◽  
Combined Process ◽  
Performance Characterization ◽  
Output State ◽  
Transmission Of Information

Indefinite causal order has introduced disruptive procedures to improve the fidelity of quantum communication by introducing the superposition of { orders} on a set of quantum channels. It has been applied to several well characterized quantum channels as depolarizing, dephasing and teleportation. This work analyses the behavior of a parametric quantum channel for single qubits expressed in the form of Pauli channels. Combinatorics lets to obtain affordable formulas for the analysis of the output state of the channel when it goes through a certain imperfect quantum communication channel when it is deployed as a redundant application of it under indefinite causal order. In addition, the process exploits post-measurement on the associated control to select certain components of transmission. Then, the fidelity of such outputs is analysed to characterize the generic channel in terms of its parameters. As a result, we get notable enhancement in the transmission of information for well characterized channels due to the combined process: indefinite causal order plus post-measurement.

Sign in / Sign up

Export Citation Format

Share Document