Operator valued frames and applications to quantum channels

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.

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Maximum relative entropy of coherence for quantum channels

Science China Physics Mechanics and Astronomy ◽

10.1007/s11433-021-1709-9 ◽

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

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Quantum Optimal Transport with Quantum Channels

Annales Henri Poincaré ◽

10.1007/s00023-021-01042-3 ◽

2021 ◽

Author(s):

Giacomo De Palma ◽

Dario Trevisan

Keyword(s):

Optimal Transport ◽

Quantum Channels

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Polarization of Quantum Channels using Clifford-based Channel Combining

IEEE Transactions on Information Theory ◽

10.1109/tit.2021.3063093 ◽

2021 ◽

pp. 1-1

Author(s):

Frederic Dupuis ◽

Ashutosh Goswami ◽

Mehdi Mhalla ◽

Valentin Savin

Keyword(s):

Quantum Channels

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Absorption in Invariant Domains for Semigroups of Quantum Channels

Annales Henri Poincaré ◽

10.1007/s00023-021-01016-5 ◽

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.

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Optimal teleportation via noisy quantum channels without additional qubit resources

npj Quantum Information ◽

10.1038/s41534-021-00426-x ◽

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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