Unambiguous discrimination among oracle operators

Abstract

We address the problem of unambiguous discrimination among oracle operators. The general theory of unambiguous discrimination among unitary operators is extended with this application in mind. We prove that entanglement with an ancilla cannot assist any discrimination strategy for commuting unitary operators. We also obtain a simple, practical test for the unambiguous distinguishability of an arbitrary set of unitary operators on a given system. Using this result, we prove that the unambiguous distinguishability criterion is the same for both standard and minimal oracle operators. We then show that, except in certain trivial cases, unambiguous discrimination among all standard oracle operators corresponding to integer functions with fixed domain and range is impossible. However, we find that it is possible to unambiguously discriminate among the Grover oracle operators corresponding to an arbitrarily large unsorted database. The unambiguous distinguishability of standard oracle operators corresponding to totally indistinguishable functions, which possess a strong form of classical indistinguishability, is analysed. We prove that these operators are not unambiguously distinguishable for any finite set of totally indistinguishable functions on a Boolean domain and with arbitrary fixed range. Sets of such functions on a larger domain can have unambiguously distinguishable standard oracle operators and we provide a complete analysis of the simplest case, that of four functions. We also examine the possibility of unambiguous oracle operator discrimination with multiple parallel calls and investigate an intriguing unitary superoperator transformation between standard and entanglement-assisted minimal oracle operators.

35 pages. Final version. To appear in J. Phys. A: Math. & Theor

References in corpus (24)

• Secure Direct Communication with a Quantum One-Time-Pad
• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Unknown Quantum States and Operations, a Bayesian View
• Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulses implementations
• Probabilistic cloning and identification of linearly independent quantum states
• Unambiguous Discrimination Between Linearly-Independent Quantum States
• Unambiguous state discrimination in quantum cryptography with weak coherent states
• Quantum stream cipher by Yuen 2000 protocol: Design and experiment by intensity modulation scheme
• Optical realization of optimal unambiguous discrimination for pure and mixed quantum states
• Unambiguous discrimination among quantum operations
• Distinguishability of States and von Neumann Entropy
• Condition for unambiguous state discrimination with local operations and classical communication
• Optimum unambiguous discrimination among linearly-independent non-orthogonal quantum states and its optical realization
• Quantum state filtering and discrimination between sets of Boolean functions
• Unambiguous Discrimination Between Linearly Dependent States with Multiple Copies
• Entanglement is not very useful for estimating multiple phases
• A Comparison of Quantum Oracles
• Unambiguous comparison of the states of multiple quantum systems
• Retrodiction of Generalised Measurement Outcomes
• How many functions can be distinguished with k quantum queries?
• A general approach to physical realization of unambiguous quantum-state discrimination
• Robust Quantum Algorithms for Oracle Identification
• Quantum-state filtering applied to the discrimination of Boolean functions
• Comparative Computational Strength of Quantum Oracles

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• Optimal Perfect Distinguishability between Unitaries and Quantum Operations
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• Quantum Approximation of Normalized Schatten Norms and Applications to Learning
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