Causal Limit on Quantum Communication

Pisarczyk, Robert; Zhao, Zhikuan; Ouyang, Yingkai; Vedral, Vlatko; Fitzsimons, Joseph F.

doi:10.1103/physrevlett.123.150502

Cited by 29 publications

(29 citation statements)

References 52 publications

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“…Evaluating the quantum capacity of an arbitrary quantum channel is difficult, and simple upper bounds for it are not necessarily tight [28]. Evaluating the quantum capacity simplifies when the quantum channel is degradable [29].…”

Section: Achievability Bounds On Multimode G-gapped Codesmentioning

confidence: 99%

Trade-Offs on Number and Phase Shift Resilience in Bosonic Quantum Codes

Ouyang

Campbell

2021

IEEE Trans. Inform. Theory

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Quantum codes typically rely on large numbers of degrees of freedom to achieve low error rates. However each additional degree of freedom introduces a new set of error mechanisms. Hence minimizing the degrees of freedom that a quantum code utilizes is helpful. One quantum error correction solution is to encode quantum information into one or more bosonic modes. We revisit rotation-invariant bosonic codes, which are supported on Fock states that are gapped by an integer g apart, and the gap g imparts number shift resilience to these codes. Intuitively, since phase operators and number shift operators do not commute, one expects a trade-off between resilience to number-shift and rotation errors. Here, we obtain results pertaining to the non-existence of approximate quantum error correcting g-gapped single-mode bosonic codes with respect to Gaussian dephasing errors. We show that by using arbitrarily many modes, g-gapped multi-mode codes can yield good approximate quantum error correction codes for any finite magnitude of Gaussian dephasing and amplitude damping errors.

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Section: Achievability Bounds On Multimode G-gapped Codesmentioning

confidence: 99%

Trade-Offs on Number and Phase Shift Resilience in Bosonic Quantum Codes

Ouyang

Campbell

2021

IEEE Trans. Inform. Theory

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“…[18] in order to establish a formalism which treats space and time indiscriminately. This proposition of state over time was further studied in [30][31][32][33].Analogously to n qubits in space, let us consider n events in space-time, where at each event a measurement of a single Pauli operator can be performed. A density matrix describing system composed of n qubits can be written as…”

Section: A States Over Time and Temporal Entanglementmentioning

confidence: 99%

Hierarchy and robustness of multilevel two-time temporal quantum correlations

Maskalaniec,

Bartkiewicz

2021

Preprint

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Quantum steering refers to correlations that can be classified as intermediate between entanglement and Bell nonlocality. Every state exhibiting Bell nonlocality exhibits also quantum steering and every state exhibiting quantum steering is also entangled. In low dimensional cases similar hierarchical relations have been observed between the temporal counterparts of these correlations.Here, we study the hierarchy of such temporal correlations for a general multilevel quantum system. We demonstrate that the same hierarchy holds for two definitions of state over time. In order to compare different types of temporal correlations, we show that temporal counterparts of Bell nonlocality and entanglement can be quantified with a temporal nonlocality robustness and temporal entanglement robustness. Our numerical result reveal that in contrast to temporal steering, for temporal nonlocality to manifest itself we require the initial state not to be in a completely mixed state.

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“…In what follows, we only consider a "two"-event PDO with the maximally mixed input. The information of a qubit channel is contained in the PDO, namely [64]…”

Section: A Certifying Non-eb Channel With Temporal Quantum Correlationsmentioning

confidence: 99%

Quantifying Quantumness of Channels Without Entanglement

Ku,

Kadlec,

Černoch

et al. 2021

Preprint

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Quantum channels which break entanglement, incompatibility, or nonlocality are not useful for entanglementbased, one-sided device-independent, or device-independent quantum information processing, respectively. Here, we show that such breaking channels are related to certain temporal quantum correlations: temporal separability, channel unsteerability, temporal unsteerability, and macrorealism. More specifically, we first define the steerability-breaking channel, which is conceptually similar to the entanglement and nonlocality-breaking channels and prove that it is identical to the incompatibility-breaking channel. Similar to the hierarchy relations of the temporal and spatial quantum correlations, the hierarchy of non-breaking channels is discussed. We then introduce the concept of the channels which break temporal correlations, explain how they are related to the standard breaking channels, and prove the following results: (1) A certain measure of temporal nonseparability can be used to quantify a non-entanglement-breaking channel in the sense that the measure is a restricted memory monotone under the framework of the resource theory of the quantum memory. (2) A non-steerabilitybreaking channel can be certified with channel steering because the steerability-breaking channel is equivalent to the incompatibility-breaking channel. (3) The temporal steerability and non-macrorealism can respectively distinguish the steerability-breaking and the nonlocality-breaking unital channel with their corresponding nonbreaking channels. Finally, a two-dimensional depolarizing channel is experimentally implemented as a proofof-principle example to compare the temporal quantum correlations with non-breaking channels.

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Causal Limit on Quantum Communication

Cited by 29 publications

References 52 publications

Trade-Offs on Number and Phase Shift Resilience in Bosonic Quantum Codes

Trade-Offs on Number and Phase Shift Resilience in Bosonic Quantum Codes

Hierarchy and robustness of multilevel two-time temporal quantum correlations

Quantifying Quantumness of Channels Without Entanglement

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