Optimal Discrimination of Quantum States and the Trade-off Between Coherence and Distinguishability

Keskeiset käsitteet

There is an inherent trade-off between the quantum coherence that can be preserved and the classical distinguishability that can be extracted when optimally discriminating a set of mutually orthogonal pure quantum states.

Tiivistelmä

The paper explores the manipulation of quantum coherence within the task of quantum state discrimination (QSD). It proposes a general QSD paradigm via quantum operations, treating coherence and distinguishability as two complementary resources.
The key findings are:

Optimal discrimination of a quantum state ensemble can be achieved without consuming additional coherence, as the optimal discrimination probability can be realized through free operations within the quantum resource theory of coherence.

The paper unveils a novel coherence-distinguishability duality relation. For a mutually orthogonal pure-state ensemble, the sum of the maximum 'co-bits' (coherence preserved after discrimination) and the 'c-bits' (classical distinguishability extracted) is bounded by the logarithm of the Hilbert space dimension.

This duality relation reveals that the more classical information one extracts from the ensemble, the less coherence can be preserved. Two boundary cases are explored:

When the ensemble contains a complete orthonormal basis, no coherence can be preserved after perfect discrimination.
When the ensemble consists of mutually orthogonal maximally coherent states, the duality relation is tight, achieving the upper bound.

The work establishes a profound connection between coherence and distinguishability as fundamental resources, generalizing the wave-particle duality relation into a new scenario within the realm of quantum resource theory.

Tilastot

The sum of the maximum 'co-bits' (coherence preserved after discrimination) and the 'c-bits' (classical distinguishability extracted) is bounded by the logarithm of the Hilbert space dimension.

Lainaukset

"The more one extracts classical information by discriminating states in the ensemble, the less one can preserve the coherence, and vice versa."
"When the ensemble contains a complete orthonormal basis, no coherence can be preserved after perfect discrimination."
"When the ensemble consists of mutually orthogonal maximally coherent states, the duality relation is tight, achieving the upper bound."

Tärkeimmät oivallukset

Quantum Coherence and Distinguishability: A Resource-Theoretic Perspective on Wave-Particle Duality

by Zhiping Liu,... klo arxiv.org 04-23-2024

https://arxiv.org/pdf/2404.14323.pdf

Syvällisempiä Kysymyksiä

How can the coherence-distinguishability duality relation be extended to more general quantum state ensembles beyond mutually orthogonal pure states

The coherence-distinguishability duality relation can be extended to more general quantum state ensembles beyond mutually orthogonal pure states by considering non-uniform distributions within the ensemble. In the context of quantum information theory, this extension involves characterizing the distinguishability of states using the min-entropy of the ensemble. By incorporating the min-entropy into the coherence-distinguishability duality relation, a bound can be established for the sum of post-discrimination coherence and the min-entropy of the ensemble. This extension allows for a broader application of the duality relation to a wider range of quantum state ensembles, providing insights into the interplay between coherence and distinguishability in various quantum scenarios.

Can the inherent trade-off between coherence and distinguishability be formulated as an uncertainty relation, similar to the connection between the wave-particle duality and the Heisenberg uncertainty principle

The inherent trade-off between coherence and distinguishability can indeed be formulated as an uncertainty relation, analogous to the connection between the wave-particle duality and the Heisenberg uncertainty principle. By quantifying the coherence resource preserved after discrimination and the classical distinguishability extracted through perfect discrimination, a trade-off relation is established. This trade-off relation reveals that the more classical information is extracted, the less coherence can be preserved, and vice versa. This duality relation can be expressed in a form similar to an uncertainty relation, highlighting the fundamental trade-off between quantum coherence and classical distinguishability resources in quantum systems.

What are the implications of the coherence-distinguishability duality for the practical applications of quantum information processing, such as quantum communication, computation, and metrology

The coherence-distinguishability duality has significant implications for the practical applications of quantum information processing, such as quantum communication, computation, and metrology. Understanding the trade-off between coherence and distinguishability is crucial for optimizing quantum protocols and algorithms. In quantum communication, the duality relation can guide the design of communication schemes that balance the extraction of classical information with the preservation of coherence. In quantum computation, the duality relation can inform the development of algorithms that leverage coherence while maintaining distinguishability for efficient computation. In quantum metrology, the trade-off between coherence and distinguishability can impact the precision and accuracy of quantum measurements, leading to improved sensing and measurement technologies. By incorporating the coherence-distinguishability duality into practical applications, researchers and engineers can enhance the performance and reliability of quantum information processing systems.