Unspeakable Coherence Concentration Enables Increased Coherence in Subsystems Via Non-Increasing Unitaries

The fundamental distinction between classical and quantum physics lies in the phenomenon of coherence, and recent research focuses on a particularly subtle form known as ‘unspeakable coherence’. Benjamin Stratton, Chung-Yun Hsieh, and Paul Skrzypczyk, all from the University of Bristol, investigate whether low-coherence states can be transformed into more coherent ones using operations that do not themselves increase coherence. Their work fully resolves this question for qubits, revealing the possibility of ‘bound coherence’ and developing a practical method to enhance coherence across multiple qubits, unexpectedly demonstrating states where coherence amplification is limitless. Extending beyond qubits, the team establishes fundamental limits on coherence enhancement and proves that certain correlations resist conversion into local coherence, representing a significant advance in understanding and manipulating quantum states.

Quantifying Unspeakable Coherence in Quantum Systems

Unspeakable coherence represents a fundamental difference between quantum and classical physics, characterized by asymmetry in distinguishing quantum states. This work investigates how unspeakable coherence concentrates under various quantum operations and in different physical scenarios. Researchers developed a rigorous mathematical framework to quantify this concentration, enabling precise comparisons between quantum systems and operations. The study demonstrates that certain operations, such as depolarizing channels, rapidly diminish unspeakable coherence, while unitary transformations perfectly preserve it. These findings deepen our understanding of quantum mechanics and have implications for developing robust quantum technologies.

Considering transformations generated by physically relevant observables, unspeakable coherence proves essential for achieving quantum advantages in tasks like metrology, reference frame alignment, and work extraction. A key question is whether low-coherence states can be transformed into more coherent ones using coherence non-increasing operations. This research addresses this question by examining the limiting case of two uncorrelated copies of a coherent state, investigating whether coherence can be increased via globally coherence non-increasing unitaries.

Maximizing Coherence in Bipartite Qutrit Systems

This research focuses on maximizing coherence in a bipartite system, concentrating quantum information into a particular mode of two qutrits. The team developed a method for manipulating these modes to increase coherence, crucial for quantum communication, computation, and other quantum information processing tasks. The methodology involves decomposing the system’s state into modes and manipulating them to achieve maximum coherence.

The researchers decompose the system’s state into local modes, related to individual qutrits, and global modes, representing combinations of states of both qutrits. They restricted allowed transformations to preserve certain properties of the system, then decomposed the global mode into subspaces that evolve independently. This decomposition is crucial for achieving tighter bounds on coherence. By initially relaxing the problem to consider any unitary transformation, they found an upper bound on achievable coherence, then refined this bound by considering the restrictions on allowed transformations.

Coherence Amplification and Bound Coherence Discovery

This research significantly advances our understanding of coherence by investigating whether low-coherence states can be transformed into more coherent ones through permitted operations. Researchers fully solved this problem for two qubits, identifying optimal strategies for coherence concentration and discovering ‘bound coherence’, states that cannot be made more coherent through allowed transformations. They also developed a practical, multi-qubit protocol that effectively amplifies coherence, demonstrating that, for certain initial states, the ratio of output to input coherence can be increased without limit.

The findings demonstrate that global entanglement does not guarantee the ability to create local coherence, even when permitted operations are employed, and establish fundamental limits on how much local coherence can be increased. Researchers identified specific states where coherence concentration is impossible, revealing a nuanced relationship between entanglement and coherence. Future work will focus on assessing the trade-offs between practicality and coherence concentration, exploring the impact of introducing incoherent states into the protocol, and investigating whether bound-coherence states exist in higher-dimensional systems.