Fidelity deviation in quantum teleportation with a two-qubit state

Abstract

Quantum teleportation with an arbitrary two-qubit state can be appropriately characterized in terms of maximal fidelity and fidelity deviation. The former quantifies optimality of the process and is defined as the maximal average fidelity achievable within the standard protocol and local unitary strategies, whereas the latter, defined as the standard deviation of fidelity over all input states, is a measure of fidelity fluctuations. The maximal fidelity for a two-qubit state is known and is given by a simple formula that can be exactly computed, but no such formula is known for the fidelity deviation. In this paper, we derive an exact computable formula for the fidelity deviation in optimal quantum teleportation with an arbitrary state of two qubits. From this formula, we obtain the dispersion-free condition, also known as the universality condition: the condition that all input states are teleported equally well and provide a necessary and sufficient condition for a state to be both useful (maximal fidelity larger than the classical bound) and universal (zero fidelity deviation). We also show that for any given maximal fidelity, larger than the classical bound, there always exist dispersion-free or universal states and argue that such states are the most desirable ones within the set of useful states. We illustrate these results with well-known families of two-qubit states: pure entangled states, Bell-diagonal states, and subsets of $X$ states.

arXiv comment21 pages; minor revisions, references added; accepted for publication in Journal of Physics A; minor typos corrected, published version

References in corpus (15)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolski-Rosen Channels
• Quantum teleportation using active feed-forward between two Canary Islands
• Information-theoretic aspects of quantum inseparability of mixed states
• Teleportation, Bell's Inequalities and Inseparability
• Efficient Teleportation between Remote Single-Atom Quantum Memories
• Local environment can enhance fidelity of quantum teleportation
• Optimal teleportation with a mixed state of two qubits
• Entanglement universality of two-qubit X-states
• On the origin of noisy states whose teleportation fidelity can be enhanced through dissipation
• Dynamics of entanglement in Two-Qubit Open System Interacting with a Squeezed Thermal Bath via Dissipative interaction
• Fidelity deviation in quantum teleportation
• Entanglement Dynamics in Two-Qubit Open System Interacting with a Squeezed Thermal Bath via Quantum Nondemolition interaction
• Procedures for realizing an approximate universal NOT gate

Cited by in corpus (9)

• Optimal two-qubit states for quantum teleportation vis-à-vis state properties
• Characterizing qubit channels in the context of quantum teleportation
• Rating the performance of noisy teleportation using fluctuations in fidelity
• Towards realization of universal quantum teleportation using weak measurements
• Gain in Performance of Teleportation with Uniformity-breaking Distributions
• Significance of Fidelity Deviation in Continuous Variable Teleportation
• Optimal teleportation fidelity and its deviation in noisy scenarios
• Dynamics of Quantum Coherence and Non-Classical Correlations in Open Quantum System Coupled to a Squeezed Thermal Bath
• Quality assessment of quantum teleportation through the distribution of fidelity