Probabilistic quantum logic operations using polarizing beam splitters
Open accessAbstract
It has previously been shown that probabilistic quantum logic operations may be performed using linear optical elements, additional photons (ancilla), and post-selection based on the output of single-photon detectors. Here we describe the operation of several quantum logic operations of an elementary nature, including a quantum parity check and a quantum encoder, and we show how they may be combined to implement a controlled-NOT (CNOT) gate. All of these gates may be constructed using polarizing beam splitters that completely transmit one state of polarization and totally reflect the orthogonal state of polarization, which allows a simple explanation of each operation. We also describe a polarizing beam splitter implementation of a CNOT gate that is closely analogous to the quantum teleportation technique previously suggested by Gottesman and Chuang [Nature 402, 390 (1999)]. Finally, our approach has the interesting feature that it makes practical use of a quantum-eraser technique.
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With probability 1/4, exactly one photon is detected in each of the modes a1_out and a2_out, heralding successful gate operation.
“With probability 1/4, exactly one photon is detected in each of the modes a 1 out and a 2 out , heralding successful gate operation.33”
From Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits (2018) · cites this paper as [33]
Section II reports that the CNOT gate succeeds 1/4 of the time when one photon is detected in each of four detectors, provided the required entangled state has been created with certainty. It does not describe detection in just the two named modes a1_out and a2_out as the heralding condition. (LLM, conf=0.87)
Experimental — accuracy not yet measuredThe ideal gate operation uses exactly four indistinguishable photons input in state |c_in,t_in>|a1_in,a2_in>, with ancilla in |Ψ−>.
“The ideal gate operation is as follows: exactly four indistinguishable photons, are input to the gate in polarization state c in ; t in j i a 1 in ; a 2 in , where c in ; t in j i is the input state of the control and target qubits, and a 1 in ; a 2 in ¼ Ψ À j i is the state of the input ancilla photons”
From Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits (2018) · cites this paper as [33]
The Nondestructive CNOT section (Eq. 3.8 and following text; page unavailable) describes two input qubits together with a two-photon entangled ancilla, supporting a four-photon input. But the Fig. 5 caption specifies the ancilla as a plus-sign Bell state proportional to |HH⟩ + |VV⟩, not |Ψ−⟩. The cited paper therefore does not support the claimed ancilla state. (LLM, conf=0.88)
Experimental — accuracy not yet measuredA CNOT operation is performed on |c_in,t_in> conditional on simultaneous detection of two output ancilla photons, exactly one at detectors D1,D2 and exactly one at detectors D3,D4, which happens with probability 1/4.
“A CNOT operation is performed on c in ; t in j i conditional on simultaneous detection of two output ancilla photons, exactly one at detectors D 1 , D 2 and exactly one at detectors D 3 , D 4 , which happens with probability 1/4.”
From Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits (2018) · cites this paper as [33]
Section D (Nondestructive CNOT; page unavailable) supports a two-photon detection condition and a 1/4 success probability. But it says the 1/4 probability requires accepting four detection outcomes and applying outcome-dependent single-qubit corrections; accepting only the passive outcome succeeds with probability 1/16. The cited paper labels its detectors differently from D1–D4. (LLM, conf=0.87)
Experimental — accuracy not yet measuredWith probability 1/4, exactly one photon is detected in each of the modes a1out and a2out, heralding successful gate operation.
“With probability 1/4, exactly one photon is detected in each of the modes a 1 out and a 2 out , heralding successful gate operation.33”
From Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits (2018) · cites this paper as [33]
Section II reports a 25% success probability for a CNOT gate when one photon is detected in each of four detectors, provided the entangled state was created with certainty. It does not identify the two modes a1out and a2out or say that detection in just those two modes heralds success. (LLM, conf=0.86)
Experimental — accuracy not yet measuredConsider a detection of a pair of photons at the output modes 3 and 4, only one photon at each output (the four mode case). Depending on the registered polarizations, up to a specific unitary transformation, a non-destructive CNOT gate operation is then performed on |χ 2 5.
“Consider a detection of a pair of photons at the output modes 3 and 4 , only one photon at each output (the four mode case).Depending on the registered polarizations, up to a specific unitary transformation, a non-destructive CNOT gate operation is then performed on |χ 2 5 .”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Pittman et al., 2001
Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measured
In this case, the output control-target state matches the desired CNOT output up to a known Pauli rotation, and one of four feed-forward unitaries must be applied depending on the ancilla measurement outcome.
“In this case, the state c out ; t out j i matches the desired CNOT output up to a known Pauli rotation: depending on the ancilla two-photon polarization measurement outcome, one of four feed-forward unitaries must be applied to the control and target photons after a successful gate operation (not shown)”
From Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits (2018) · cites this paper as [33]
To obtain the desired CNOT output state, one of four Pauli rotations must be performed on the output control-target state, depending on the polarization measurement outcome for the output ancilla state |a1_out;a2_out>.
“However, to obtain the desired CNOT output state, one of four Pauli rotations must be performed on this output control-target state, depending on the polarization measurement outcome for the output ancilla state a 1 out ; a 2 out .”
From Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits (2018) · cites this paper as [33]
Such a two-fold coincidence detection heralds successful gate operation and the presence of the two remaining photons in the output control-target state |c_out;t_out>.
“Such a two-fold coincidence detection heralds successful gate operation and the presence of the two remaining photons in the output control-target state c out ; t out j i .”
From Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits (2018) · cites this paper as [33]
The output control and target qubits need not be measured and can be used as input for subsequent logic operations.
“The output control and target qubits need not be measured and can be used as input for subsequent logic operations.”
From Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits (2018) · cites this paper as [33]
Koashi et al., 2001, and Pittman et al., 2001, showed that by using entangled pairs of photons as ancilla, the success of the gate operation can be inferred by the detection of photons in ancilla-outputs.
“In a separate development, Koashi et al., 2001, andPittman et al., 2001, showed that by using entangled pairs of photons as ancilla, the success of the gate operation can be inferred by the detection of photons in ancilla-outputs.”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Pittman et al., 2001
As suggested by Pittman et al., (2001), the success of the gate can be detected by measurement of ancilla photons and this information is classically feed-forwardable.
“As suggested by Pittman et al., (2001), the success of the gate can be detected by measurement of ancilla photons and this information is classically feed-forwardable.”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Pittman et al., 2001
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- Authors
- Pittman, T. B., Jacobs, B. C., & Franson, J. D.
- Affiliations
- Johns Hopkins University (US)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2001-11-16
- Volume
- 64
- Issue
- 6
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2069890908
- Cited by
- 434
- References
- 42
- Citations by year
- 2026: 6 · 2025: 7 · 2024: 8 · 2023: 36 · 2022: 4 · 2021: 12 · 2020: 9 · 2019: 17 · 2018: 9 · 2017: 9 · 2016: 12 · 2015: 12 · 2014: 6 · 2013: 25 · 2012: 11
- FWCI
- 26.71
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Maryland Shared Open Access Repository (USMAI Consortium) (submittedVersion)
- arXiv (Cornell University)
- Digital Repository at the University of Maryland (University of Maryland College Park)
- Funders
- Office of Naval Research
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- polarization beam splitter, CNOT gate, post-selection, single-photon detectors, quantum teleportation, quantum eraser, linear optical quantum computing
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