Suppose that Alice and Bob are located in distant laboratories, which are connected by an ideal quantum channel. Suppose further that they share many copies of a quantum state ρ_{ABE}, such that Alice possesses the A systems and Bob the BE systems. In our model, there is an identifiable part of Bob's laboratory that is insecure: a third party named Eve has infiltrated Bob's laboratory and gained control of the E systems. Alice, knowing this, would like use their shared state and the ideal quantum channel to communicate a message in such a way that Bob, who has access to the whole of his laboratory (BE systems), can decode it, while Eve, who has access only to a sector of Bob's laboratory (E systems) and the ideal quantum channel connecting Alice to Bob, cannot learn anything about Alice's transmitted message. We call this task the conditional one-time pad, and in this Letter, we prove that the optimal rate of secret communication for this task is equal to the conditional quantum mutual information I(A;B|E) of their shared state. We thus give the conditional quantum mutual information an operational meaning that is different from those given in prior works, via state redistribution, conditional erasure, or state deconstruction. We also generalize the model and method in several ways, one of which is a secret-sharing task, i.e., the case in which Alice's message should be secure from someone possessing only the AB or AE systems, but should be decodable by someone possessing all systems A, B, and E.
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http://dx.doi.org/10.1103/PhysRevLett.124.050503 | DOI Listing |
Nat Phys
May 2024
Department of Physics, University of Basel, Basel, Switzerland.
Semiconductor spin qubits offer the potential to employ industrial transistor technology to produce large-scale quantum computers. Silicon hole spin qubits benefit from fast all-electrical qubit control and sweet spots to counteract charge and nuclear spin noise. However, the demonstration of a two-qubit interaction has remained an open challenge.
View Article and Find Full Text PDFPhys Rev Lett
November 2024
Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA.
We study the evolution of conditional mutual information (CMI) in generic open quantum systems, focusing on one-dimensional random circuits with interspersed local noise. Unlike in noiseless circuits, where CMI spreads linearly while being bounded by the light cone, we find that noisy random circuits with an error rate p exhibit superlinear propagation of CMI, which diverges far beyond the light cone at a critical circuit depth t_{c}∝p^{-1}. We demonstrate that the underlying mechanism for such rapid spreading is the combined effect of local noise and a scrambling unitary, which selectively removes short-range correlations while preserving long-range correlations.
View Article and Find Full Text PDFNat Comput Sci
November 2024
IBM Quantum, IBM Research Europe-Zurich, Rueschlikon, Switzerland.
Entropy (Basel)
September 2024
Hunter College and Graduate Center, City University of New York, New York, NY 10065, USA.
We consider the local value of an operator for a given position or momentum and, more generally on the value of another arbitrary observable. We develop a general approach that is based on breaking up Aψ(x) as Aψ(x)ψ(x)=Aψ(x)ψ(x)R+iAψ(x)ψ(x)I where A is the operator whose local value we seek and ψ(x) is the position wave function. We show that the real part is related to the conditional value for a given position and the imaginary part is related to the standard deviation of the conditional value.
View Article and Find Full Text PDFNature
October 2024
California Institute of Technology, Pasadena, CA, USA.
Enhancing the precision of measurements by harnessing entanglement is a long-sought goal in quantum metrology. Yet attaining the best sensitivity allowed by quantum theory in the presence of noise is an outstanding challenge, requiring optimal probe-state generation and read-out strategies. Neutral-atom optical clocks, which are the leading systems for measuring time, have shown recent progress in terms of entanglement generation but at present lack the control capabilities for realizing such schemes.
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