Compound beams for direct experimental comparison of quantum operations

The gist The compound beams are suggested for simulating properties of different quantum operations used for creating highly nonclassical and entangled multi-mode states needed in quantum communication, metrology, and information protocols

Compound Beams and Operations

Compound beams are composed of simple experimental blocks that form specific quantum-correlated structures to simulate the properties of different quantum operations used for creating highly nonclassical and entangled multi-mode states. These compound beams are built from different kinds of elementary building blocks, and they naturally adopt the properties of these real beams while attaining new properties originating in the structure of the constructed beams. Because compound beams are typically composed of a greater number of elementary building blocks, they are naturally multi-mode, and their properties cannot be directly compared to both theoretical and experimental results appropriate for single-mode fields because their properties are only negligibly affected by the bosonic commutation relations. The use of temporal multiplexed measurements on weak twin beams (TWBs) in preparing compound beams provides a form of simulation of their statistical properties as the realized states do not exist in real time.

Comparison of Photon Addition and Subtraction

The paper provides a qualitative and quantitative comparison of multi-photon addition and subtraction in multi-mode thermal as well as sub-Poissonian beams and multi-mode twin beams with their intensities extending over two orders in magnitude. In general, photon addition is identified as advantageous over photon subtraction for the multi-mode thermal and sub-Poissonian beams because it induces (enhances) the nonclassicality in the former (latter) state. Contrary to this, photon subtraction outperforms photon addition in the multi-mode twin beams. Furthermore, exploiting temporal photon-pair correlations in compound twin beams when post-selecting nearly ideal experimental photon(s) addition is demonstrated.

Experimental Setup and Data Processing

The experimental setup involved generating compound TWBs with varying intensity by concatenating different and increasing numbers of identical weak photon-pair fields, which originated in a nonlinear (LiIO3) crystal pumped by the third harmonic of an Nd-YAG laser. The signal and idler photons were spatially filtered by coupling into multi-mode fibers using lenses L3. Data processing involved careful processing of detection data in two synchronized channels, where the marginal histogram fth then characterizes a TS, i.e., fth(cs; Mw) = ∑∞ ci=0 f(cs, ci; Mw). Similarly, the histogram fsP belonging to an SPS obtained from the TWB by post-selecting ci idler photocounts is obtained as fsP(cs; ci, Mw) = f(cs, ci; Mw)/∑∞ cs=0 f(cs, ci; Mw).

Analysis of State Properties

The analysis systematically denotes nine groups of potentially nonclassical states available under the same experimental conditions: TWB, PATWB, PSTWB, TS, PATS, PSTS, SPS, PASPS, and PSSPS. The application of PA and PS on three prepared states TWBs (thermal states (TS), sub-Poissonian states (SPS), and twin beams) leaves 9 groups of potentially nonclassical states that are systematically denoted as TWB, PATWB, PSTWB, TS, PATS, PSTS, SPS, PASPS, and PSSPS. The noise-reduction parameter R is a simple quantity used to assess the nonclassicality of the beams.

Nonclassicality Quantification

Nonclassicality is identified by definition by negative values of the Glauber-Sudarshan P-function or its existence as a generalized function. The nonclassicality criteria IF and IR defined in Eqs. (6) and (7) in the main text belong to the most efficient because they are based on second-order intensity moments, and it usually holds that with the increasing order of intensity moments the efficiency of the nonclassicality criteria drops down. The nonclassicality depth τ is defined in terms of the threshold value sth of the ordering parameter s at which the nonclassicality present in the state is concealed by the detection noise, where τ ≡ (1 − sth)/2.

Conclusion

Compound beams with their versatile structures have been suggested for direct experimental comparison of different quantum operations used in the generation of highly nonclassical and entangled multi-mode states occurring in various quantum-information protocols. Both quantum operations were found as efficient tools for inducing or enhancing the state nonclassicality. The technique of compound beams has been shown to be able to study side-by-side the beams with intensities differing in orders of magnitude as well as to mimic post-selection by an ideal photon-number-resolving detector. The structures of the analyzed compound beams can directly be embedded into the more complex schemes implementing suitable quantum information protocols realized in the same way as the compound beams. The schemes based on the temporal compound beams can alternatively be mapped onto real experimental setups using naturally multi-mode beams being detected by spatially resolved photon-number-resolving detectors.

How it works

1. Compound beams are constructed from different kinds of elementary building blocks that form specific quantum-correlated structures to simulate the properties of different quantum operations used for creating highly nonclassical and entangled multi-mode states needed in quantum communication, metrology, and information protocols.

2. Photon addition (PA) is generally advantageous over photon subtraction (PS) for the multi-mode thermal and sub-Poissonian beams because it induces (enhances) the nonclassicality in the former (latter) state.

3. In contrast, photon subtraction outperforms photon addition in the multi-mode twin beams.

4. Exploiting temporal photon-pair correlations in compound twin beams when post-selecting nearly ideal experimental photon(s) addition is demonstrated.

5. Photon addition increases the mean photon numbers ⟨n⟩a th and simultaneously generates the nonclassicality, with the greater number of added photons leading to a stronger and more nonclassical beam.

6. Photon subtraction decreases the beam intensity, although it lowers the values of the Fano factor Fs, but cannot provide a nonclassical state.

7. Ideal addition of photons naturally results in greater nonclassicality of the ideally PA states compared to their real PA states.

8. The technique allows for direct comparison of PS and PA by subtracting the same number of photocounts from the signal beam and analyzing the nonclassicality induced in the idler beam.

9. The technique can mimic the operation of an ideal photon-number-resolving detector in post-selection once temporal correlations of photons in weak TWBs—the building blocks of compound beams—are exploited, allowing for ideal PA.

Model for Photon States

The photon-number distributions of the analyzed groups of states are derived from the photon-number distributions pTWBp and pTWBa of the twin beams TWBp and TWBa, respectively. A multi-mode thermal state (TS) is obtained as a marginal state of TWBp, where pth(ns) = ∑∞ ni=0 pTWBp(ns, ni). A sub-Poissonian state (SPS) with photon-number distribution psP [pa] arises in conditional photon-number resolving detection on the idler beam of TWBp.

Experimental Reconstruction

The experimental reconstruction of frequency histograms for the states discussed involves concatenating neighbor Mw detection windows in two synchronized (signal and idler) channels whose individual signal (c˜s) and idler (c˜i) photocount numbers characterize detections of weak TWBs.

1. Better quantum state simulation for quantum communication and metrology protocols by using compound beams to simulate their statistical properties as realized states do not exist in real time. This allows AI systems to develop more accurate simulators for continuous variable quantum information protocols, overcoming limitations of single-mode theoretical results when dealing with multi-mode fields.

2. Enhanced nonclassicality quantification for quantum state characterization by using the nonclassicality depth τ introduced by Lee [63] as the most natural and also convenient nonclassicality quantifier. AI systems can then use this depth to estimate from below the actual nonclassicality, providing a more physically meaningful measure of the state's quantum features than just Fano factor or noise-reduction parameter.

3. Superior experimental design optimization for generating nonclassical states by using the comparison between photon addition and subtraction: photon addition is identified as advantageous over photon subtraction for the multi-mode thermal and sub-Poissonian beams. This allows AI to automatically select the optimal quantum operation (PA vs PS) based on whether it seeks to induce (enhances) the nonclassicality in the former (latter) state or exploit correlations in twin beams.

4. Development of noise-resilient quantum amplification methods by leveraging specific experimental findings: nearly ideal experimental photon(s) addition is demonstrated when exploiting temporal photon-pair correlations in compound twin beams post-selection, enabling AI to design noiseless amplification circuits for coherent states.

5. Direct implementation of quantum information protocols by embedding beam structures: The structures of the analyzed compound beams can directly be embedded into the more complex schemes implementing suitable quantum information protocols realized in the same way as the compound beams. This enables AI to generate optimized, experimentally realizable architectures for quantum communication and metrology rather than relying solely on idealized theoretical models.

Compound beams composed of simple experimental blocks (detected in simultaneous detection windows) that form specific quantum-correlated structures are suggested for simulating the properties of different quantum operations used for creating highly nonclassical and entangled multi-mode states needed in quantum communication, metrology, and information protocols. Qualitative and quantitative comparison of multi-photon addition and subtraction in compound multi-mode thermal as well as sub-Poissonian beams and multi-mode twin beams with their intensities extending over two orders in magnitude is provided. Adding and subtracting up to twenty photocounts, optimal conditions for the generation of experimental nonclassical states are identified. In general, photon addition is identified as advantageous over photon subtraction for the multi-mode thermal and sub-Poissonian beams: It induces (enhances) the nonclassicality in the former (latter) state. Contrary to this, photon subtraction outperforms photon addition in the multi-mode twin beams. Moreover, exploiting temporal photon-pair correlations in compound twin beams when post-selecting, nearly ideal experimental photon(s) addition is demonstrated. The results apply for the beams with mean photon number per mode much less than one.