Quantifying the difference between many-body quantum states

Abstract

The quantum state overlap is the textbook measure of the difference between two quantum states. Yet, it is inadequate to compare the complex configurations of many-body systems. The problem is inherited by the widely employed quantum state fidelity and related distances. We introduce the weighted distances, a new class of information-theoretic measures that overcome these limitations. They quantify how hard it is to discriminate between two quantum states of many particles, factoring in the structure of the required measurement apparatus. Therefore, they can be used to evaluate both the theoretical and the experimental performances of complex quantum devices. We also show that the newly defined "weighted Bures length" between the input and output states of a quantum process is a lower bound to the experimental cost of the transformation. The result uncovers an exact quantum limit to our ability to convert physical resources into computational ones.

arXiv comment4+2 pages, change from previous version: the contractivity of weighted distances holds only for single site operations

References in corpus (22)

• Quantum Computing in the NISQ era and beyond
• Advances in Quantum Metrology
• Predicting Many Properties of a Quantum System from Very Few Measurements
• 14-qubit entanglement: creation and coherence
• Quantum algorithms: an overview
• Randomized Benchmarking of Quantum Gates
• Quantum metrology from a quantum information science perspective
• Quantum optimization using variational algorithms on near-term quantum devices
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Quantum Computation as Geometry
• Direct Fidelity Estimation from Few Pauli Measurements
• Generalized Limits for Single-Parameter Quantum Estimation
• The Second Law of Quantum Complexity
• Generalized Geometric Quantum Speed Limits
• Learning the quantum algorithm for state overlap
• Characterizing the entanglement of symmetric many-particle spin-1/2 systems
• Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems
• Quantum fidelity measures for mixed states
• Introduction to quantum Fisher information
• Certifying the building blocks of quantum computers from Bell's theorem
• Detecting metrologically useful asymmetry and entanglement by a few local measurements
• How difficult is it to prepare a quantum state?

Cited by in corpus (9)

• Resource theory of quantum uncomplexity
• Quantum Genetic Algorithm with Individuals in Multiple Registers
• Geometric properties of evolutionary graph states and their detection on a quantum computer
• Weighted Bures Length Uncovers Quantum State Sensitivity
• Wasserstein Complexity of Quantum Circuits
• Coherent Quantum Speed Limits
• Quantum Wasserstein distance between unitary operations
• Attention to Quantum Complexity
• Evaluating Pauli errors on cluster states by weighted distances