Online identification of symmetric pure states

Sentís, Gael; Martínez-Vargas, Esteban; Muñoz-Tapia, R.

doi:10.22331/q-2022-02-21-658

Cited by 4 publications

(1 citation statement)

References 51 publications

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“…The objective is that the verifier passes the test with a worst-case probability of δ. They consider independent sequential measurements [11].…”

Section: Introductionmentioning

confidence: 99%

Stability verification of quantum non-i.i.d. sources

Martínez Vargas

2024

Phys. Scr.

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We introduce the problem of stability verification of quantum sources which are non-i.i.d.. The problem consists in ascertaining whether a given quantum source is stable or not, in the sense that it produces always a desired quantum state or if it suffers deviations. Stability is a statistical notion related to the sparsity of errors. This problem is closely related to the problem of quantum verification first proposed by Pallister et. al. [1], however, it extends the notion of the original problem. We introduce a family of states that come from these non-i.i.d. sources which we call a Markov state. These sources are more versatile than the i.i.d. ones as they allow statistical deviations from the norm instead of the more coarse previous approach. We prove in theorem 1 that the Markov states are not well described with tensor products over a changing source. In theorem 2 we further provide a lower bound on the trace distance between two Markov states, or conversely, an upper bound on the fidelity between these states. This is a bound on the capacity of determining the stability property of the source, which shows that it is exponentially easier to ascertain this with respect to n, the number of outcomes from the source.

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“…The objective is that the verifier passes the test with a worst-case probability of δ. They consider independent sequential measurements [11].…”

Section: Introductionmentioning

confidence: 99%

Stability verification of quantum non-i.i.d. sources

Martínez Vargas

2024

Phys. Scr.

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Multipartite subspaces containing no locally inaccessible information

Croke

2022

Phys. Rev. A

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One notion of non-locality in quantum theory is the fact that information may be encoded in a composite system in such a way that it is not accessible through local measurements, even with the assistance of classical communication. Thus, contrary to the classical case, there exists information in quantum many body systems which cannot be accessed locally. We show however that, remarkably, two-dimensional subspaces do not have this property: any physically allowed measurement on information encoded in any two-dimensional subspace, regardless of entanglement or multi-partite structure, may be performed locally. Further, this requires only local measurement and feed-forward of classical information, readily achievable in many experimental platforms. As an application to quantum secret sharing we suggest a twist on a well known quantum information splitting protocol, which ensures that no receiving party ever has access to the full state sent, but parties must work together to perform measurements on the state. These results may have practical applications to the measurement of encoded qubits in e.g. quantum secret sharing, quantum error correction, and reveal a fundamental property unique to two-dimensional subspaces.

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Quantum advantage in learning from experiments

Huang

Broughton

Cotler

et al. 2022

Science

249

122

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Quantum technology promises to revolutionize how we learn about the physical world. An experiment that processes quantum data with a quantum computer could have substantial advantages over conventional experiments in which quantum states are measured and outcomes are processed with a classical computer. We proved that quantum machines could learn from exponentially fewer experiments than the number required by conventional experiments. This exponential advantage is shown for predicting properties of physical systems, performing quantum principal component analysis, and learning about physical dynamics. Furthermore, the quantum resources needed for achieving an exponential advantage are quite modest in some cases. Conducting experiments with 40 superconducting qubits and 1300 quantum gates, we demonstrated that a substantial quantum advantage is possible with today’s quantum processors.

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Online identification of symmetric pure states

Cited by 4 publications

References 51 publications

Stability verification of quantum non-i.i.d. sources

Stability verification of quantum non-i.i.d. sources

Multipartite subspaces containing no locally inaccessible information

Quantum advantage in learning from experiments

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