Design and Experimental Realization of Various Protocols for Secure Quantum Computation and Communication

Satish Kumar

REVIEW 2 major objections 6 minor 235 references

Design and Experimental Realization of Various Protocols for Secure Quantum Computation and Communication

T0 review · 2 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Two Bell states suffice for multi-output quantum teleportation, and known-state broadcasting is remote state preparation.

desk verdict A thesis with a solid MQT/QB core and a seriously flawed remote-operator chapter; the θ=π degeneracy invalidates the headline success probabilities. read the letter →

arxiv 2507.09532 v1 pith:VPYFKA7U submitted 2025-07-13 quant-ph

Satish Kumar This is my paper · ORCID

classification quant-ph MSC 81P6881P94 PACS 03.67.-a03.67.Dd03.67.Hk03.67.Lx03.67.Mn

keywords Multi-outputquantumteleportationbroadcastingRemotestatepreparationimplementationofoperatorsCross-KerrinteractionanonymousvetokeydistributionOptimalresources

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This thesis attempts to show that a handful of quantum communication tasks, previously demonstrated with large multipartite entangled states, can be performed with the smallest possible Bell-state resources. Its central theoretical claim is that multi-output quantum teleportation of GHZ-like states requires only two copies of the Bell state rather than a five-qubit cluster state, because each such state reduces by CNOT gates to a single logical qubit. A second claim is that schemes advertised as quantum broadcasting of a known state are actually multiparty remote state preparation, so one Bell state per receiver is enough and no no-go theorem is violated. The thesis supports these claims with logical circuits, noise analysis, and proof-of-principle runs on a cloud-accessible superconducting quantum processor, and extends the minimal-resource pattern to remote implementation of hidden and partially unknown operators and to secure multiparty tasks.

What carries the argument

The carrying object is the generalized Bell-type state $\alpha|x\rangle + \beta|\bar{x}\rangle$ with $\bar{x}$ the bitwise complement of $x$, together with the CNOT-based reduction that concentrates its unknown coefficients into one qubit. This reduction converts multi-output teleportation into parallel single-qubit teleportations, so two Bell states do the work of the five-qubit cluster state. For the operator variants, the controlling mechanism is the cross-Kerr interaction between a photonic spatial path and an auxiliary coherent state $|z\rangle$; an $X$-quadrature measurement on the coherent state selects the feed-forward unitary, and the separation condition $z\theta^2 \gg 1$ determines the discrimination error. The CJRIO protocol additionally uses a hyper-entangled state in both spatial and polarization degrees of freedom.

What would settle it

Execute the two-Bell-state and five-qubit-cluster versions of the same multi-output teleportation circuit on the same calibrated device with equal shots and noise models, and compare output fidelity; if the cluster version systematically matches or beats the Bell version at equal total error budget, the practical superiority of the claimed optimal resource would be undercut. For the operator protocols, directly test whether a real cross-Kerr medium can resolve $|z\rangle$ from $|ze^{\pm i\theta}\rangle$ with error at or below $P_{\text{error}} = \frac{1}{2}\mathrm{erfc}[z(1-\cos\theta)/\sqrt{2}]$ at the claimed values of $z$ and $\theta$; if the required discrimination is not physically achievable, the RIHO and RIPUO success probabilities are not experimentally established.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is a resource accounting: unknown states of the form $\alpha|x\rangle + \beta|\bar{x}\rangle$ carry their whole informational content in one logical qubit, so an $m$-qubit GHZ-like state can be disentangled into a single qubit plus ancillas by CNOT gates. That makes one Bell state per output sufficient and makes the five-qubit cluster state of the earlier MQT protocol non-minimal; the thesis demonstrates the $m=1$ case on a cloud device. The same accounting shows that broadcasting a known state is not cloning but remote state preparation, realizable with two Bell states for two receivers and with improved noise resilience compared with the four-qubit cluster-state version. For operators, the thesis constructs a controlled joint remote implementation of operators (CJRIO) on a four-qubit spatial-polarization hyperentangled state and derives remote implementation of hidden operators (RIHO) and partially unknown operators (RIPUO) from a single Bell state, with success probabilities that include errors from coherent-state dissipation.

Load-bearing premise

The RIHO and RIPUO protocols stand on the assumption that a cross-Kerr medium can produce a phase shift large enough to distinguish overlapping coherent states at the required error rate while leaving the photonic qubits intact; if real media cannot deliver that discrimination, the claimed success probabilities are not supported.

Editorial extensions

If this is right

Two-copy Bell-state circuits can replace five-qubit cluster-state circuits for multi-output teleportation, lowering the hardware size required and reducing sensitivity to amplitude-damping, phase-damping, bit-flip, and depolarizing noise.
Known-state quantum broadcasting is reclassified as multiparty remote state preparation, so existing claims of broadcasting do not conflict with the no-broadcasting theorem.
Remote implementation of hidden and partially unknown operators, previously associated with GHZ or larger channels, is claimed to be possible with a single Bell state, with direct applications to blind and distributed quantum computing.
The CJRIO protocol gives a deterministic controlled joint remote operation on an unknown qubit with efficiency $\eta = M/(5M + 3N + 2)$ for $M$ joint parties and $N$ controllers.
Anonymous veto can be run on a cloud quantum processor, and DPS and COW key rates can be quantitatively modeled as functions of disclose rate, compression ratio, detector dead time, and distance.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The CNOT dissolution argument suggests a general criterion: any family of states that is unitarily equivalent to a single logical qubit can be teleported with one Bell state per unknown coefficient pair; testing it on W states or Dicke states would delineate its scope.
The coherent-state discrimination assumption implies that the RIHO and RIPUO protocols stand or fall on the achievable cross-Kerr phase shift; atomic or circuit-QED platforms, rather than all-optical Kerr media, may be the first place to realize them.
The broadcasting-as-RSP equivalence predicts that any future 'quantum broadcasting' protocol for a known state can be rewritten with only bipartite entanglement and classical communication, a claim one could verify by re-examining existing protocols.
The QKD analysis singles out detector dead time and disclose rate as knobs whose joint optimization could raise secure key rate without hardware changes; a direct experimental scan over those parameters would test that prediction.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Best to read this as a PhD thesis compilation, not a fresh research paper. The two main results that hold up are the MQT experiment and the QB-as-RSP framing. The MQT scheme is exactly the ⌈log2 m⌉ Bell-state bound from Ref. [91] applied to Yan-Yu's task, and the m=1 IBM implementation with ~80% fidelity is a reasonable proof of principle. The QB chapter makes the correct conceptual point that existing 'quantum broadcasting' schemes for known states are really multiparty RSP, and the reduction to two Bell states is clean.

The soft spots are real. First, the QB experiment contradicts its own conclusion: the cluster-state circuit gave 86.47% average fidelity, the two-Bell-state circuit gave 58.27%, yet the text claims the Bell-state version 'outperforms' the cluster state. That is simply wrong as written and needs an explanation or a corrected comparison. Second, and more serious, the RIHO/RIPUO (and by extension CJRIO) success-probability analysis collapses at θ=π. The four 'outcomes' pq=00,01,10,11 are assigned to |z>, |ze^{iθ}>, |ze^{i2θ}>, |ze^{i3θ}>. For θ=π these are only two distinct states, so the measurement cannot distinguish 00 from 10 or 01 from 11. The correction rules treat those pairs differently, which is impossible; no fixed unitary can repair both branches after the measurement. The success probability formulas (4.58), (4.62) and Fig. 4.8, which plot near-1 values at θ=π, are artifacts of labeling identical coherent states as distinct. This is load-bearing for Chapter 4.

The thesis also republishes the author's prior papers without much disclaimer, but that is normal thesis practice; the arXiv posting should be upfront about provenance. The QKD and QAV experimental chapters are more routine and appear sound, though I haven't dug into the detector-dead-time modeling.

Who gets value: anyone wanting a concise demonstration that MQT and known-state broadcasting need only Bell states, and the explicit circuits. The remote-operator protocols need substantial revision before they can be taken seriously, and the θ=π case should be either excluded or re-analyzed with two-outcome measurements.

I'd send it to a referee because the MQT/QB parts are worth capturing, but the referee should focus on the fidelity reversal and the coherent-state degeneracy.

Referee Report

2 major / 6 minor

Summary. This PhD-thesis manuscript, posted as arXiv:2507.09532, reports a set of quantum communication and computation protocols. Chapter 2 proposes a multi-output quantum teleportation (MQT) scheme using two copies of a Bell state instead of a five-qubit cluster state and demonstrates the m=1 case on an IBM quantum computer. Chapter 3 argues that existing quantum broadcasting (QB) schemes are actually multiparty remote state preparation of known states, proposes a two-Bell-state resource, and reports an IBM implementation. Chapter 4 proposes controlled-joint remote implementation of operators (CJRIO) using a hyper-entangled photonic state, and remote implementation of hidden and partially unknown operators (RIHO and RIPUO) using Bell states plus coherent-state cross-Kerr measurements, with success probabilities analyzed under dissipation. Chapter 5 reports an IBM implementation of quantum anonymous veto protocols, and Chapter 6 reports experimental demonstrations of COW and DPS QKD with key-rate analyses. The central resource-counting arguments for MQT and QB are straightforward and appear correct, but two load-bearing points in the manuscript are internally inconsistent or technically invalid, as detailed below.

Significance. If the claims were fully established, the resource reductions would be practically useful: MQT and QB with two Bell states are simpler than cluster-state resources, and the reduction of QB to multiparty RSP clarifies the reach of the no-broadcasting theorem. The RIHO/RIPUO protocols would also be a notable step toward blind and distributed quantum computing if the coherent-state discrimination step were sound. The thesis also provides a useful set of proof-of-principle experimental demonstrations, including noise studies and QKD key-rate analyses. However, the QB experimental data contradict the stated conclusion, and the RIHO/RIPUO success-probability analysis is invalid for the plotted parameter θ=π. These issues must be resolved before the claimed results can be accepted.

major comments (2)

[§3.5, p. 58; §3.6] The manuscript reports that the cluster-state circuit (Figure 3.4(a)) has average fidelity 86.47% and the two-Bell-state circuit (Figure 3.4(b)) has average fidelity 58.27%, but then concludes that 'the technique which is used for broadcasting known quantum information using two Bell states outperforms that using the cluster state.' These numbers directly contradict the conclusion: the cluster-state circuit performed substantially better. This is an internal inconsistency in a load-bearing experimental claim of Chapter 3. The authors should either correct the data, clarify which circuit corresponds to which fidelity, or revise the conclusion to match the reported results.
[§4.7.1, Step 4; §4.7.2, Step 3; Eqs. (4.58), (4.62); Fig. 4.8] For θ=π, the four coherent states |z e^{inθ}>, n=0,1,2,3, used for the X-quadrature measurement in Step 4 of RIHO (and the analogous step in RIPUO) collapse to only two distinct states: |z e^{i0}>=|z e^{i2π}>=|z> and |z e^{iπ}>=|z e^{i3π}>=|-z>. The purported four-outcome discrimination is therefore only two-outcome, and the outcomes 00 vs. 10 (and 01 vs. 11) cannot be distinguished. Since the correction rules assign different operations to 00 (no action) and 10 (phase flip), the post-measurement state is a mixture of branches requiring different corrections; for equal-weight coefficients the success probability is at most 1/2. This invalidates the near-unity success probabilities plotted in Fig. 4.8 for θ=π, z=1. The error formula in Eq. (4.58)/(4.62) itself signals the problem: P32 = 1/2 erfc[z(cosθ - cos2θ)/√2] tends to about 1 at θ=π, so the four-state discrimination fails exactly in the regime plotted. The RIHO/RIPUO success-probability analysis is therefore not established for the reported parameters.

minor comments (6)

[Abstract] The abstract says Alice teleports states 'to a receiver (Bob),' but the MQT scheme has two receivers (Bob1 and Bob2); this should be corrected for accuracy.
[Table 3.2 caption] The caption says the calibration data are for ibmq_casablanca, but Section 3.5 states that the QB experiment was run on ibmq_manila; the device name should be corrected.
[§3.5, Figure 3.5] In light of the fidelity values reported in the text, the figure captions or the text should be clarified so that the reader can unambiguously associate each fidelity value with the cluster-state and Bell-state circuits.
[§4.5 title] The section title 'Existing variants of RIO as a sunset of CJRIO' contains a typo; 'sunset' should be 'subset.'
[§4.7.1, Step 1] The notation 'ˆX = a† + a' for the quadrature measurement is unconventional; the authors should define the X-quadrature observable explicitly, including normalization, to avoid ambiguity in the error-probability formulas.
[§4.8.2] The claim that a controller can maintain control 'even without keeping a qubit' is an interesting observation, but the discussion would benefit from a precise security model specifying what 'semi-honest' means and what adversarial actions are excluded; otherwise the claim is hard to evaluate.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: central claims are derived from stated resources and measurement rules; self-citations are historical and non-load-bearing.

full rationale

The thesis's central claims do not reduce to their inputs. In Chapter 2, the multi-output teleportation scheme is derived by explicitly compressing GHZ-like states of the form alpha|x>+beta|x-bar> via CNOT gates to single-qubit states and teleporting each with one Bell state, citing the external result [60] and providing circuits; the Bell-state resource is not fitted to the five-qubit-cluster output. In Chapter 3, the reduction of quantum broadcasting to multiparty remote state preparation is an argument from the known-state assumption and is supported by explicit RSP circuits and Table 3.1; it is not a restatement of the conclusion. In Chapter 4, the CJRIO, RIHO and RIPUO protocols are constructed step-by-step from the chosen hyperentangled or Bell channels and cross-Kerr measurement rules, and the success probabilities are computed from stated misidentification error probabilities rather than fitted to target values. The efficiency formula eta=c/(b+e) is introduced as a definition, not derived as a prediction. The extensive self-citations (e.g., [81,82,85,86,78,84]) are historical markers of the author's prior publications; the thesis itself contains the derivations, so the citations are not load-bearing. The theta=pi degeneracy of the four coherent states noted in the skeptical review is a validity/correctness concern about the measurement analysis, not a circularity, and is therefore outside this pass.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central claims rest on standard quantum-information axioms plus two domain assumptions about cross-Kerr interactions and coherent-state discrimination that are taken from prior photonics literature without fresh experimental support. No fitted free parameters are introduced; scanned variables (z, theta, D, DR, CR, DT) are physical or post-processing parameters. No new physical entities are postulated.

assumptions (5)

domain assumption X-quadrature measurement on a coherent state can reliably distinguish |z> from |ze^{±iθ}> provided zθ^2 >> 1.
Invoked in Chapter 4, Step 1 of RIHO (Section 4.7.1) as the basis for entanglement generation and for the success probability expressions. No experimental validation is provided in the thesis.
domain assumption Cross-Kerr nonlinearity enables controllable photon-photon interaction with negligible signal-mode phase disturbance.
Used throughout Chapter 4 to mediate interactions between photonic qubits; relies on prior experimental results cited in Section 4.3, not on measurements in this thesis.
domain assumption IBM cloud quantum computers' measurement statistics can be interpreted as the ideal circuit plus calibration-reported errors.
The experimental claims in Chapters 2, 3, and 5 use IBM devices without independent verification; no raw counts or circuit executables are provided.
standard math No-broadcasting theorem prohibits broadcasting unknown states, so only known states can be broadcast.
Section 3.1 uses this to reframe all existing 'quantum broadcasting' schemes as multiparty RSP; this is standard quantum information.
standard math Quantum state tomography reconstructs the output density matrix from repeated measurements.
Used in Section 2.3.1 to compute fidelity; standard assumption.

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Cite this review

Pith. "Pith review of Design and Experimental Realization of Various Protocols for Secure Quantum Computation and Communication." pith.science (2026). https://pith.science/paper/VPYFKA7U

@misc{pith2026250709532,
  author       = {Pith},
  title        = {Pith review of: Design and Experimental Realization of Various Protocols for Secure Quantum Computation and Communication},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VPYFKA7U}},
  note         = {Machine review of arXiv:2507.09532}
}

read the original abstract

A set of new schemes for quantum computation and communication have been either designed or experimentally realized using optimal quantum resources. A multi-output quantum teleportation scheme, where a sender (Alice) teleports an m and m+1-qubit GHZ-like unknown state to a receiver (Bob), has been demonstrated using two copies of the Bell state instead of a five-qubit cluster state and implemented on IBM's quantum computer for the m=1 case. Another scheme, known as quantum broadcasting where a known state is sent to two spatially separated parties (Bob and Charlie) has also been realized using two Bell states. It is shown that existing quantum broadcasting schemes can be reduced to multiparty remote state preparation. After achieving teleportation of unknown and known states, sending a quantum operator becomes the next step. A scheme for remote implementation of operators (RIO), specifically a controlled joint-RIO (CJRIO), has been proposed using a four-qubit hyper-entangled state involving spatial and polarization degrees of freedom. In this direction, two more variants, remote implementation of hidden and partially unknown operators (RIHO and RIPUO) have also been proposed. Their success probabilities are analyzed considering dissipation of an auxiliary coherent state interacting with the environment. For secure multiparty tasks like quantum voting or auction, secure multiparty quantum computation (SMQC) becomes essential. A quantum anonymous voting (QAV) scheme has been experimentally implemented on IBM's quantum computer. Finally, two quantum key distribution (QKD) protocols, coherent one-way (COW) and differential phase shift (DPS), are experimentally demonstrated and the key rates are analyzed as functions of post-processing parameters and detector dead times across various distances.

Figures

Figures reproduced from arXiv: 2507.09532 by the authors.

**Figure 1.1.** A brief structure of the thesis 3 [PITH_FULL_IMAGE:figures/full_fig_p032_1_1.png] view at source ↗

**Figure 1.2.** An example of quantum communication schemes that does not require security. Traditional computers typically provide a definite answer, whereas quantum computers provides a range of possible solutions. This might seem less precision in quantum computers. However, the unique problem solving approach of a quantum computers could dramatically accelerate its capability to solve highly complex problems which potentially r… view at source ↗

Figures from the paper (46 more)

**Figure 1.3.** Figure 1.3: One-dimensional system which has six sites. Particle can only exist in one of the six sites. ||ψ||2 = Z |ψ(x,t)| 2 dx = 1. (1.2) In any such discretized system, the state of the system is represented by a vector. The popular notations used to represent a quantum stat…

**Figure 1.4.** Figure 1.4: Representation of a qubit on Bloch sphere 1.2.3 MEASUREMENT BASIS A measurement basis is required to measure a qubit. A qubit can be measured using different bases. Each basis gives different measurement outcomes. A set of vectors {v1, v2, v3,..., vn} can form a meas…

**Figure 1.5.** Figure 1.5: Single qubit quantum gates with their representation and corresponding matrices. operators given as follows: Rx(θ) ≡ e −i θ 2 X = cos θ 2 I −isin θ 2 X =   cos θ 2 −isin θ 2 −isin θ 2 cos θ 2  , (1.18) Ry(θ) ≡ e −i θ 2 Y = cos θ 2 I −isin θ 2 Y =   cos θ 2 −sin…

**Figure 1.6.** Figure 1.6: Symbolic representation of CNOT and SWAP gates. qubit gates discussed in this thesis are shown in [PITH_FULL_IMAGE:figures/full_fig_p041_1_6.png]

**Figure 1.7.** Figure 1.7: Snap of few platforms where one can access quantum computers on cloud. few of them are listed below IBM Quantum IBM provides an online platform called IBM Quantum Platform where one can access quantum computers on the cloud. Qiskit is a python library that is used to…

**Figure 1.8.** Figure 1.8: Quantum teleportation circuit. various schemes where secure communication is required. A few of them are QT, RSP, SDC, quantum cryptography, etc. Here, three such schemes will be studied. 1.4.1 QUANTUM TELEPORTATION QT is a process to teleport an unknown quantum stat…

**Figure 1.9.** Figure 1.9: Circuit illustrating the RSP process. 1.4.2 REMOTE STATE PREPARATION Similar to the Quantum Teleportation (QT) scheme, where an unknown qubit is teleported, here in Remote State Preparation (RSP), a known state is remotely prepared. The concept of RSP was first intro…

**Figure 1.10.** Figure 1.10: Pictorial representation for modeling of (a) close and (b) open quantum system. sum representation. Let {|ek⟩} be an orthonormal basis of a finite-dimensional environment and |e0⟩⟨e0| be the initial state of the environment then Equation (1.33) can be rewritten as ρ…

**Figure 2.1.** Figure 2.1: A sketch to visualize the MQT scheme of Yan Yu et al. understand this point with an example, suppose sender wants to teleport an unknown quantum state |ψ⟩ = α|0⟩ ⊗n +β|1⟩ ⊗n : |α| 2 +|β| 2 then the application of the CNOT gates in a manner ⊗n i=2CNOT1→i |ψ⟩ will tran…

**Figure 2.2.** Figure 2.2: A quantum circuit illustrating the generalized MQT scheme of Yan Yu et al. 37 [PITH_FULL_IMAGE:figures/full_fig_p066_2_2.png]

**Figure 2.3.** Figure 2.3: A quantum circuit illustrating the MQT scheme using optimal resources. 2.3 EXPERIMENTAL REALIZATION OF THE MQT SCHEME ON IBM QUANTUM COMPUTER Here, a simple quantum circuit has been built, as shown in [PITH_FULL_IMAGE:figures/full_fig_p068_2_3.png]

**Figure 2.4.** Figure 2.4: A quantum circuit illustrating the MQT scheme for m = 1 case using optimal resources. resources for the MQT scheme, are prepared at qubit Q0 & Q2 and Q4 & Q6. After the preparation of Bell states, the qubits are distributed such that Q1, Q5, Q0 and Q4 are with Alice…

**Figure 2.5.** Figure 2.5: (a) A quantum circuit to teleport |+⟩ = √ 1 2 (|0⟩+|1⟩) to two distinct receivers at qubit Q2 and Q6 using two copies of a Bell states |φ +⟩ ⊗2 (b) Topology of the quantum computer used (ibmq_casablanca). 41 [PITH_FULL_IMAGE:figures/full_fig_p070_2_5.png]

**Figure 2.6.** Figure 2.6: Experimentally obtained result after executing the quantum circuit depicted in [PITH_FULL_IMAGE:figures/full_fig_p071_2_6.png]

**Figure 2.7.** Figure 2.7: Experimental quantum state tomography result with (a) real and (b) imaginary parts for the circuit shown in [PITH_FULL_IMAGE:figures/full_fig_p072_2_7.png]

**Figure 2.8.** Figure 2.8: Plot for success probability of the MQT scheme under various noisy environment having variable noise percentage. modified MQT scheme is resilient to several noises in an increasing order as phase damping, amplitude damping, depolarizing and bit-flip noise. It is hope…

**Figure 3.1.** Figure 3.1: A sketch to visualize the QB scheme of Yan Yu et al. leading to a large number of variants of it. 3.3 POSSIBLE GENERALIZATIONS AND POTENTIAL APPLICATIONS Recent work has proposed a potential generalization to teleport a n−qubit quantum information having m−unknown c…

**Figure 3.2.** Figure 3.2: A quantum circuit for the generation of (a) Bell state and (b) cluster state. then to build special cases of those scenarios. Until now, the possible variations of the QB scheme and the methods to execute them with the best available resources, or just the necessary …

**Figure 3.3.** Figure 3.3: Impact of (a) amplitude damping, (b) phase damping, (c) bit-flip and (d) depolarizing noise on a pair of Bell states and cluster states. 55 [PITH_FULL_IMAGE:figures/full_fig_p084_3_3.png]

**Figure 3.4.** Figure 3.4: A quantum circuit for broadcasting the state α|0⟩+β|1⟩ with |α| 2 = |β| 2 = 1 2 to two distinct receivers using (a) the four-qubit cluster state and (b) two copies of the Bell state. Here, c.c. stands for classical communication. 3.5 IMPLEMENTATION OF THE PROPOSED SC…

**Figure 3.5.** Figure 3.5: The obtained results after executing the quantum circuit depicted in (a) [PITH_FULL_IMAGE:figures/full_fig_p088_3_5.png]

**Figure 4.1.** Figure 4.1: A sketch to visualize (a) the CJRIO task and (b) the quantum resources used. required an additional quantum resource. Finally, Section 4.9 concludes this chapter. 4.2 THE CJRIO TASK The goal of CJRIO is to controllably and cooperatively apply an unknown quantum opera…

**Figure 4.2.** Figure 4.2: A schematic illustrating the first two steps of the CJRIO protocol is provided. A circle labeled V,H represents a photon simultaneously in vertical and horizontal polarization, while a circle labeled V only represents a photon in vertical polarization. Circles with t…

**Figure 4.3.** Figure 4.3: A schematic illustrating Step 3 and Step 4 of the CJRIO protocol. Here, Charlie as a controller, first blends paths of her photon using BBS and enables the interaction Kck (θ)|z⟩|ck⟩ and perform X-quadrature measures the CS, yielding the outcome s, which destroys the…

**Figure 4.4.** Figure 4.4: A schematic illustrating Step 5 and Step 6 of the CJRIO protocol is provided. Here, Bob1 first initiates a new photon path using a BBS and enables the non-linear interaction Kb 1 k⊕l⊕1 (θ)|z⟩|b 1 k⊕l⊕1 ⟩ and forwards it to Bob2 which enables the interaction Kb 2 0 (−…

**Figure 4.5.** Figure 4.5: A schematic illustrating Step 7 to Step 9 of the CJRIO protocol is presented. Here, the joint parties Bob1 and Bob2 and the controller Charlie measure their respective photons in suitable basis. The measurement leads the collapse of photons B1 , B2 , and C and we are…

**Figure 4.6.** Figure 4.6: This figure illustrates the steps involved in the protocol for remote implementation of hidden operators. An unpolarized photon is represented by a circle. Notably, Alice obtained Um|ψ⟩X (m = 0,1) despite Bob applying the operation UB. Alice is now certain that she h…

**Figure 4.7.** Figure 4.7: This figure illustrates the steps involved in the protocol for remote implementation of a partially unknown operator. 4.7.3 DISSIPATION OF AUXILIARY COHERENT STATE In real physical scenario, the environment is associated with the CS |z⟩. Some photons may be lost to t…

**Figure 4.8.** Figure 4.8: The modified success probabilities is shown in (a) and (b) as functions of dissipative parameter D and initial amplitude z of coherent state, with θ = π radians phase shift for both the RIHO (P1Suc) and the RIPUO (P2Suc) protocols. In (c), the behavior of the same pr…

**Figure 5.1.** Figure 5.1: Topology of the IBMQ Manila [PITH_FULL_IMAGE:figures/full_fig_p132_5_1.png]

**Figure 5.2.** Figure 5.2: A quantum circuit designed for the experimental realization of Protocol A. conclusive result. There are total five different possibilities of voting patterns in this scenario: no voter has vetoed, one voter among four has vetoed, two voters among four have vetoed, th…

**Figure 5.3.** Figure 5.3: Results obtained from the real device and simulator for Protocol A using Bell state for the (a) conclusive and (b) inconclusive outcomes. 107 [PITH_FULL_IMAGE:figures/full_fig_p136_5_3.png]

**Figure 5.4.** Figure 5.4: A quantum circuit for implementing Protocol B using (a) the cluster state and (b) the GHZ state. tional basis measurement outcome (see the rightmost part of [PITH_FULL_IMAGE:figures/full_fig_p137_5_4.png]

**Figure 5.5.** Figure 5.5: Result obtained from the real device and simulator for Protocol B using cluster state and GHZ state, showing the (a,c) inconclusive and (b,d) conclusive outcomes. 112 [PITH_FULL_IMAGE:figures/full_fig_p141_5_5.png]

**Figure 5.6.** Figure 5.6: Impact of phase damping, amplitude damping, depolarization, and bit flip noise on: (a) Protocol A with the Bell state (b) Protocol B with the GHZ state (c) Protocol B with the cluster state. An approach different from the noise modeling technique available on qiskit …

**Figure 5.7.** Figure 5.7: Impact of (a) phase damping (b) amplitude damping (c) bit flip and (d) depolarizing noise on Protocol A and Protocol B. 115 [PITH_FULL_IMAGE:figures/full_fig_p144_5_7.png]

**Figure 6.1.** Figure 6.1: Classification of QKD where P & M refers to prepare-and-measure-based and EB refers to entanglement based QKD protocol [210]. Although the DPR QKD systems have been successfully implemented in various locations, several issues remain unaddressed, as the focus has pri…

**Figure 6.2.** Figure 6.2: A block diagram illustrating the DPS protocol. PM: phase modulator, BS1, BS2 are beam splitters and M1, M2 are mirrors. 1. Alice generates a sequence of empty and non-empty pulses in different orders |0⟩|α⟩ and |α⟩|0⟩ corresponds to classical bit 1, 0 with each proba…

**Figure 6.3.** Figure 6.3: A block diagram illustrating the COW protocol. IM: intensity modulator, BS1: beamsplitter. shifted key produce a private secret key for both encryption and decryption. 6.2.3 POST-PROCESSING The procedure described above for both COW and DPS QKD helps in obtaining the…

**Figure 6.4.** Figure 6.4: A snapshot of the experimental set-up used for the DPR QKD implementation. nication distance [83], but without monitoring arm. However, the COW QKD realization with monitoring arm is also reported in this chapter. The components along with its specification used for …

**Figure 6.5.** Figure 6.5: Plots for the obtained KR of the DPS protocol as a function of CR for various DR (a) at 80 km (b) at 100 km, (c) at 120, with detector’s DT = 50µs. The KR decreases with increasing distance and increases with higher DR. 130 [PITH_FULL_IMAGE:figures/full_fig_p159_6_5.png]

**Figure 6.6.** Figure 6.6: Plots for the obtained KR of the DPS protocol as a function of DR (CR) for various CR (DR) at detector’s DT = 40µs, = 30µs and = 20µs for 80 km communication distance. 132 [PITH_FULL_IMAGE:figures/full_fig_p161_6_6.png]

**Figure 6.7.** Figure 6.7: Plots for the obtained KR of the COW QKD protocol as a function of (a) DR for various CR and (b) CR for various DR, for 100 km distance with detector’s DT = 50µs. 133 [PITH_FULL_IMAGE:figures/full_fig_p162_6_7.png]

**Figure 6.8.** Figure 6.8: Plots for obtained KR as a function of DR for various CR for both DPS (Purple dashed and Red solid line) and COW (Blue and Green line with plot markers) QKD protocol. It is obvious that KR for DPS is higher than COW. ♣ ♣ ♣ ♣ ♣ ★ ★ ★ ★ ★ ♣ DPS ★ COW 16 17 18 19 20 500…

**Figure 6.9.** Figure 6.9: Plots for obtained KR as function of channel losses for both COW and DPS QKD protocol. 6.4.4 A COMPARATIVE ANALYSIS OF KEY RATE OF DPS AND COW QKD Both COW and DPS QKD scheme belongs to the same DPR category QKD, making it relevant to compare their performance under …

**Figure 6.10.** Figure 6.10: The stability plot for (a) KR and (b) QBER for both COW and DPS QKD protocol with fixed value of DS to 3.125 %, CR to 90 % and DT to = 50µs for 80 km communication distance. 6.4.5 KEY RATE AND QBER STABILITY To check the stability of KR and QBER value which is obtai…

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