scholarly journals Zero-Error Communication via Quantum Channels, Noncommutative Graphs, and a Quantum Lovász Number

2013 ◽  
Vol 59 (2) ◽  
pp. 1164-1174 ◽  
Author(s):  
Runyao Duan ◽  
Simone Severini ◽  
Andreas Winter
Keyword(s):  
Quantum Channels ◽  
Lovász Number

scholarly journals Quantum Graphs as Quantum Relations

2021 ◽  
Author(s):  
Nik Weaver
Keyword(s):  
Error Correction ◽  
Channel Coding ◽  
Error Correcting Codes ◽  
Quantum Channels ◽  
Information Encoding ◽  
Graph Theoretic ◽  
Graph Homomorphisms ◽  
Special Cases ◽  
Quantum Error ◽  
Lovász Number

AbstractThe “noncommutative graphs” which arise in quantum error correction are a special case of the quantum relations introduced in Weaver (Quantum relations. Mem Am Math Soc 215(v–vi):81–140, 2012). We use this perspective to interpret the Knill–Laflamme error-correction conditions (Knill and Laflamme in Theory of quantum error-correcting codes. Phys Rev A 55:900-911, 1997) in terms of graph-theoretic independence, to give intrinsic characterizations of Stahlke’s noncommutative graph homomorphisms (Stahlke in Quantum zero-error source-channel coding and non-commutative graph theory. IEEE Trans Inf Theory 62:554–577, 2016) and Duan, Severini, and Winter’s noncommutative bipartite graphs (Duan et al., op. cit. in Zero-error communication via quantum channels, noncommutative graphs, and a quantum Lovász number. IEEE Trans Inf Theory 59:1164–1174, 2013), and to realize the noncommutative confusability graph associated to a quantum channel (Duan et al., op. cit. in Zero-error communication via quantum channels, noncommutative graphs, and a quantum Lovász number. IEEE Trans Inf Theory 59:1164–1174, 2013) as the pullback of a diagonal relation. Our framework includes as special cases not only purely classical and purely quantum information theory, but also the “mixed” setting which arises in quantum systems obeying superselection rules. Thus we are able to define noncommutative confusability graphs, give error correction conditions, and so on, for such systems. This could have practical value, as superselection constraints on information encoding can be physically realistic.

scholarly journals Jordan products of quantum channels and their compatibility

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Mark Girard ◽  
Martin Plávala ◽  
Jamie Sikora
Keyword(s):  
Quantum State ◽  
Sufficient Conditions ◽  
The Other ◽  
Independent Interest ◽  
Quantum Channels ◽  
Semidefinite Programs ◽  
Jordan Product ◽  
Marginal Problem ◽  
Jordan Products ◽  
Product Of Matrices

AbstractGiven two quantum channels, we examine the task of determining whether they are compatible—meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting the output of the other channel). Here, we present several results concerning this task. First, we show it is equivalent to the quantum state marginal problem, i.e., every quantum state marginal problem can be recast as the compatibility of two channels, and vice versa. Second, we show that compatible measure-and-prepare channels (i.e., entanglement-breaking channels) do not necessarily have a measure-and-prepare compatibilizing channel. Third, we extend the notion of the Jordan product of matrices to quantum channels and present sufficient conditions for channel compatibility. These Jordan products and their generalizations might be of independent interest. Last, we formulate the different notions of compatibility as semidefinite programs and numerically test when families of partially dephasing-depolarizing channels are compatible.

scholarly journals Maximum relative entropy of coherence for quantum channels

2021 ◽  
Vol 64 (8) ◽  
Author(s):  
Zhi-Xiang Jin ◽  
Long-Mei Yang ◽  
Shao-Ming Fei ◽  
Xianqing Li-Jost ◽  
Zhi-Xi Wang ◽  
...  
Keyword(s):  
Relative Entropy ◽  
Quantum Channels ◽  
Relative Entropy Of Coherence

scholarly journals Polarization of Quantum Channels using Clifford-based Channel Combining

2021 ◽  
pp. 1-1
Author(s):  
Frederic Dupuis ◽  
Ashutosh Goswami ◽  
Mehdi Mhalla ◽  
Valentin Savin
Keyword(s):  
Quantum Channels

scholarly journals Absorption in Invariant Domains for Semigroups of Quantum Channels

2021 ◽  
Author(s):  
Raffaella Carbone ◽  
Federico Girotti
Keyword(s):  
Hilbert Space ◽  
Ergodic Theory ◽  
Markov Processes ◽  
Separable Hilbert Space ◽  
Quantum Channels ◽  
Quantum Markov Processes ◽  
Positive Recurrent ◽  
Markov Evolution ◽  
Absorption Probabilities ◽  
Invariant Domains

AbstractWe introduce a notion of absorption operators in the context of quantum Markov processes. The absorption problem in invariant domains (enclosures) is treated for a quantum Markov evolution on a separable Hilbert space, both in discrete and continuous times: We define a well-behaving set of positive operators which can correspond to classical absorption probabilities, and we study their basic properties, in general, and with respect to accessibility structure of channels, transience and recurrence. In particular, we can prove that no accessibility is allowed between the null and positive recurrent subspaces. In the case, when the positive recurrent subspace is attractive, ergodic theory will allow us to get additional results, in particular about the description of fixed points.

scholarly journals Optimal teleportation via noisy quantum channels without additional qubit resources

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Dong-Gil Im ◽  
Chung-Hyun Lee ◽  
Yosep Kim ◽  
Hyunchul Nha ◽  
M. S. Kim ◽  
...  
Keyword(s):  
Quantum Computing ◽  
Quantum Teleportation ◽  
Quantum Communication ◽  
Quantum Noise ◽  
Single Copy ◽  
Entangled State ◽  
Quantum Network ◽  
Quantum Channels ◽  
Maximally Entangled State ◽  
Near Term

AbstractQuantum teleportation exemplifies how the transmission of quantum information starkly differs from that of classical information and serves as a key protocol for quantum communication and quantum computing. While an ideal teleportation protocol requires noiseless quantum channels to share a pure maximally entangled state, the reality is that shared entanglement is often severely degraded due to various decoherence mechanisms. Although the quantum noise induced by the decoherence is indeed a major obstacle to realizing a near-term quantum network or processor with a limited number of qubits, the methodologies considered thus far to address this issue are resource-intensive. Here, we demonstrate a protocol that allows optimal quantum teleportation via noisy quantum channels without additional qubit resources. By analyzing teleportation in the framework of generalized quantum measurement, we optimize the teleportation protocol for noisy quantum channels. In particular, we experimentally demonstrate that our protocol enables to teleport an unknown qubit even via a single copy of an entangled state under strong decoherence that would otherwise preclude any quantum operation. Our work provides a useful methodology for practically coping with decoherence with a limited number of qubits and paves the way for realizing noisy intermediate-scale quantum computing and quantum communication.

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