Unambiguous quantum state elimination for qubit sequences

Crickmore, Jonathan; Puthoor, Ittoop Vergheese; Ricketti, Berke; Croke, Sarah; Hillery, Mark; Andersson, Erika

doi:10.1103/physrevresearch.2.013256

Cited by 12 publications

(17 citation statements)

References 24 publications

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“…Note that this expression holds only for θ ≤ π/8, and P f = 0 for θ ≥ π/8. Again, we have not proven that this is the optimal success probability, but it turns out that it is [9]. Finally, if one goes from Z 2 × Z 2 to Z N × Z N using the same representation as in the previous section, the expressions for the failure operator and the failure probability remain the same.…”

Section: Addition Of a Failure Operatormentioning

confidence: 87%

“…As we will see below, for θ < π/8 it is possible to sometimes eliminate one two-qubit state. Crickmore et al [9] give an alternative construction for the measurement in the whole range 0 < θ ≤ π/4, and also prove optimality. Now suppose we want to consider more states.…”

Section: Single-state Elimination For Two Qubitsmentioning

confidence: 99%

“…This will require a failure operator, that is a POVM element that will give us the probability of the measurement failing. This case was studied in [9], but here we would like to consider it from the point of view of group theory.…”

Section: Addition Of a Failure Operatormentioning

confidence: 99%

“…This means that there is a POVM each of whose results corresponds to eliminating one element of the set. Measurements for eliminating pairs of two qubit states, which generalize some of the results in [2], were presented in [9].…”

Section: Introductionmentioning

confidence: 97%

See 3 more Smart Citations

A group-theoretic approach to elimination measurements of qubit sequences

Hillery¹,

Andersson²,

Vergheese³

2020

Preprint

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Most measurements are designed to tell you which of several alternatives have occurred, but it is also possible to make measurements that eliminate possibilities and tell you an alternative that did not occur. Measurements of this type have proven useful in quantum foundations and in quantum cryptography. Here we show how group theory can be used to design such measurements. After some general considerations, we focus on the case of measurements on two-qubit and three-qubit states. Initially we find measurements that eliminate one state, and then proceed to look at a measurement that eliminates pairs of three-qubit states. Finally, in an appendix, we briefly consider the case of elimination measurements on n-qubit states.

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Section: Addition Of a Failure Operatormentioning

confidence: 87%

Section: Single-state Elimination For Two Qubitsmentioning

confidence: 99%

Section: Addition Of a Failure Operatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

See 2 more Smart Citations

A group-theoretic approach to elimination measurements of qubit sequences

Hillery¹,

Andersson²,

Vergheese³

2020

Preprint

Self Cite

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“…USE measurements [35][36][37][38][39][40][41][42][43] on the other hand can more often be successful with probability 1, but only guarantee that x / ∈ Y ⊂ X , i.e. the measurement rules out states rather than definitively identifying the state.…”

Section: A Unambiguous Measurementsmentioning

confidence: 99%

Imperfect 1-out-of-2 quantum oblivious transfer: bounds, a protocol, and its experimental implementation

Amiri,

Stárek,

Reichmuth

et al. 2020

Preprint

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Demonstration of optimal non-projective measurement of binary coherent states with photon counting

DiMario

Becerra

2022

npj Quantum Inf

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Quantum state discrimination is a central problem in quantum measurement theory, with applications spanning from quantum communication to computation. Typical measurement paradigms for state discrimination involve a minimum probability of error or unambiguous discrimination with a minimum probability of inconclusive results. Alternatively, an optimal inconclusive measurement, a non-projective measurement, achieves minimal error for a given inconclusive probability. This more general measurement encompasses the standard measurement paradigms for state discrimination and provides a much more powerful tool for quantum information and communication. Here, we experimentally demonstrate the optimal inconclusive measurement for the discrimination of binary coherent states using linear optics and single-photon detection. Our demonstration uses coherent displacement operations based on interference, single-photon detection, and fast feedback to prepare the optimal feedback policy for the optimal non-projective quantum measurement with high fidelity. This generalized measurement allows us to transition among standard measurement paradigms in an optimal way from minimum error to unambiguous measurements for binary coherent states. As a particular case, we use this general measurement to implement the optimal minimum error measurement for phase-coherent states, which is the optimal modulation for communications under the average power constraint. Moreover, we propose a hybrid measurement that leverages the binary optimal inconclusive measurement in conjunction with sequential, unambiguous state elimination to realize higher dimensional inconclusive measurements of coherent states.

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Unambiguous quantum state elimination for qubit sequences

Cited by 12 publications

References 24 publications

A group-theoretic approach to elimination measurements of qubit sequences

A group-theoretic approach to elimination measurements of qubit sequences

Imperfect 1-out-of-2 quantum oblivious transfer: bounds, a protocol, and its experimental implementation

Demonstration of optimal non-projective measurement of binary coherent states with photon counting

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