Limitation of maximally entangled probes for single-shot distinguishability of unitaries

Abstract

There have been many instances where the maximally entangled state as a probe acts better than the product and the non-maximally entangled states in the task of distinguishing quantum channels. We provide a proof that for single-shot discrimination of two unitary channels, entangled and product states are operationally equivalent. But we identify pairs of unitaries that are perfectly distinguishable using a non-maximally entangled state, but not with a maximally entangled one. This contrast becomes more pronounced when the number of unitaries exceeds two. In every dimension $⩾3$, we show that there exists a class of unitaries that are indistinguishable under maximally entangled probes, yet perfectly distinguishable using product or non-maximally entangled inputs. Another interesting set of unitaries in every dimension $⩾3$ has been presented where only non-maximally entangled state acts as the successful probe, while product states and maximally entangled states cannot.

References in corpus (32)

• Separability of Mixed States: Necessary and Sufficient Conditions
• Quantum Teleportation with a Complete Bell State Measurement
• Distance measures to compare real and ideal quantum processes
• Statistical distinguishability between unitary operations
• Teleportation, Bell's Inequalities and Inseparability
• Optimal discrimination of quantum operations
• All entangled states are useful for channel discrimination
• Entanglement can enhance the distinguishability of entanglement-breaking channels
• The Perfect Distinguishability of Quantum Operations
• No $\psi$-epistemic model can fully explain the indistinguishability of quantum states
• Fundamental limits to quantum channel discrimination
• Adaptive versus non-adaptive strategies for quantum channel discrimination
• Entanglement assisted random access codes
• Optimal estimation of quantum dynamics
• How ψ-epistemic models fail at explaining the indistinguishability of quantum states
• Distinguishing mixed quantum states: Minimum-error discrimination versus optimum unambiguous discrimination
• $\psi$-epistemic models are exponentially bad at explaining the distinguishability of quantum states
• Distinguishability of generic quantum states
• Quantum circuits for maximally entangled states
• Entanglement and coherence in Bernstein-Vazirani algorithm
• Strategies for optimal single-shot discrimination of quantum measurements
• Communication tasks with infinite quantum-classical separation
• Quantum error correction codes and absolutely maximally entangled states
• Entanglement in channel discrimination with restricted measurements
• Improved discrimination of unitaries by entangled probes
• Tight bounds on the distinguishability of quantum states under separable measurements
• Quantum prescriptions are more ontologically distinct than they are operationally distinguishable
• Single-shot discrimination of quantum unitary processes
• Perfect discrimination of quantum measurements using entangled systems
• Unbounded quantum advantage in communication complexity measured by distinguishability
• Query complexity of unitary operation discrimination
• Single-shot Distinguishability and Anti-distinguishability of Quantum Measurements

Cited by in corpus (2)

• Single-shot antidistinguishability of unitary operations
• Global versus Local Discrimination of Locally Implementable Multipartite Unitaries