[Paper Review] Gate Fidelities, Quantum Broadcasting, and Assessing Experimental Realization

Hyang‐Tag Lim, Young-Sik Ra+3 more|arXiv (Cornell University)|Jun 29, 2011

Quantum Information and Cryptography1 references3 citations

TL;DR

This paper establishes a direct link between gate fidelities in experimental quantum operations and the broadcasting capability of ideal quantum operations. It shows that higher broadcasting capacity (i.e., ability to distribute quantum information to more parties) implies a higher lower bound on gate fidelities, meaning that even noisy realizations of highly broadcastable operations can achieve high fidelities, necessitating worst-case benchmarks for accurate assessment.

ABSTRACT

We relate gate fidelities of experimentally realized quantum operations to the broadcasting property of their ideal operations, and show that the more parties a given quantum operation can broadcast to, the higher gate fidelities of its experimental realization are in general. This is shown by establishing the correspondence between two operational quantities, quantum state shareability and quantum broadcasting. This suggests that, to assess an experimental realization using gate fidelities, the worst case of realization such as noisy operations should be taken into account and then compared to obtained gate fidelities. In addition, based on the correspondence, we also translate results in quantum state shareability to their counterparts in quantum operations.

Motivation & Objective

• To address the ambiguity in interpreting high gate fidelity values as indicators of successful experimental quantum operation realization.
• To identify fundamental limits on experimental assessment of quantum operations based on quantum theory's constraints.
• To establish a quantitative link between the broadcasting property of ideal quantum operations and the achievable gate fidelities in their experimental realizations.
• To provide a framework for assessing experimental quantum operations by comparing to worst-case noise models, particularly depolarizing channels.
• To translate results from quantum state shareability into properties of quantum operations via the Choi-Jamiołkowski isomorphism.

Proposed method

• Using the Choi-Jamiołkowski isomorphism to map quantum operations to quantum states, enabling the translation of state shareability properties to operation broadcasting properties.
• Defining gate fidelities as either average or minimum fidelity between ideal and experimental operation outputs on pure input states.
• Deriving a general lower bound on gate fidelities using the shareability of the Choi-Jamiołkowski state and the distance between entanglement-breaking and noise channels.
• Applying trace distance and fidelity inequalities to bound gate fidelities in terms of the operation's broadcasting capability and noise channel distance.
• Analyzing a specific example: a depolarizing-noise realization of an entanglement-breaking operation with varying p, showing fidelity increases with p (broadcasting capacity).
• Using the correspondence between state shareability and operation broadcasting to derive a hierarchy of lower bounds on gate fidelities based on the number of parties an operation can broadcast to.

Experimental results

Research questions

• RQ1 Can high gate fidelity values in experimental quantum operations be misleading if not compared to a worst-case benchmark?
• RQ2 How does the broadcasting capability of an ideal quantum operation influence the minimum achievable gate fidelity in its experimental realization?
• RQ3 What is the fundamental lower bound on gate fidelity for a given quantum operation, independent of the quality of its experimental implementation?
• RQ4 How can results from quantum state shareability be systematically translated into properties of quantum operations?
• RQ5 To what extent does the structure of the ideal operation—specifically its ability to broadcast—determine the gate fidelity of its noisy realization?

Key findings

• Gate fidelities of experimental quantum operations are fundamentally bounded from below by the broadcasting capability of the ideal operation, regardless of the actual noise level in the realization.
• Operations that can broadcast to more parties (higher k-broadcasting) have higher minimum gate fidelities, even when the experimental realization is noisy.
• For the optimal transpose operation (p=2/3), gate fidelity exceeds 0.98 regardless of noise, due to its high broadcasting capacity.
• The lowest achievable gate fidelity for a given operation is bounded below by 1 - dε(k), where ε(k) quantifies the shareability of the Choi-Jamiołkowski state for k-party broadcasting.
• A gate fidelity of 0.99 does not guarantee successful implementation if the ideal operation has high broadcasting capacity, as even depolarizing noise can achieve similar fidelities.
• The study establishes that gate fidelity alone is insufficient for assessing experimental quantum operations; the worst-case noise model must be considered to interpret fidelity values meaningfully.