Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · quant-ph/0107143

Remote operations and interactions for systems of arbitrary dimensional Hilbert space: a state-operator approach

Benni Reznik·Yakir Aharonov·Berry Groisman
View original source ↗Read source document ↗Export metadata ↓

Abstract

We present a systematic simple method for constructing deterministic remote operations on single and multiple systems of arbitrary discrete dimensionality. These operations include remote rotations, remote interactions and measurements. The resources needed for an operation on a two-level system are one ebit and a bidirectional communication of two cbits, and for an n-level system, a pair of entangled n-level particles and two classical ``nits''. In the latter case, there are $n-1$ possible distinct operations per one n-level entangled pair. Similar results apply for generating interaction between a pair of remote systems and for remote measurements. We further consider remote operations on $N$ spatially distributed systems, and show that the number of possible distinct operations increases here exponentially, with the available number of entangled pairs that are initial distributed between the systems. Our results follow from the properties of a hybrid state-operator object (``stator''), which describes quantum correlations between states and operations.

Explore related subjects

quant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Benni Reznik, Yakir Aharonov, Berry Groisman. 2001-08-03. Remote operations and interactions for systems of arbitrary dimensional Hilbert space: a state-operator approach. https://doi.org/10.1103/physreva.65.032312

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Everlasting secure key agreement from a quantum computational hybrid security model

We introduce the Quantum Computational Timelock (QCT) model, combining time-lock encryption with a quantitative noisy-quantum-storage assumption. Time-lock encryption gives Bob immediate access to the encoding seed and gives Eve the same final information as access to that seed only after a protected interval. Eve may then process her retained information without computational restriction. We state this delayed-access encryption assumption explicitly and construct MUB-QCT from a complete set of mutually unbiased bases in dimension $d$ and an affine pair-wise independent permutation family. For single-copy encoding, every seed-independent immediate measurement has trace-distance advantage at most $1/(2\sqrt{d+1})$ and mutual information at most $1/(d+1)$. Effective residual storage at diamond distance at most $δ$ from replacement adds at most $δ$ to the individual-attack distinguishing bound. Under i.i.d. individual attacks and entropy-preserving acceptance, we obtain an asymptotic key-rate bound and formulate final-key secrecy in composable trace distance. For $m$ independently randomized signals sharing one bit and seed, the optimal leakage under non-adaptive product measurements is $\min\{1,m/(d+1)\}$, allowing a linear-in-$d$ detection enhancement in that attack model. We also construct a seed-independent joint measurement that recovers the bit after disclosure with error at most $\varepsilon$ from $O(\log d+\log(1/\varepsilon))$ signals, retaining only classical information after measurement. This gives a quantitative separation between product and joint measurements. Bob uses two logical detection outcomes independently of $d$.

quant-ph↗
arXiv2026

Linear optics and the problem of Bell-like state discrimination

A linear optics-based scheme to implement various quantum information processing tasks is of paramount importance due to its ease of implementation and low noise. Many information-theoretic tasks depend on the successful discrimination of Bell states. A no-go theorem states that it is not possible to perfectly discriminate among the four Bell states when the measurement apparatus is restricted to linear optical elements. The success probability is only $50\%$. Using extra resources such as hyperentanglement, ancillary entanglement, and even a minimum amount of non-linearity, complete Bell-state discrimination can be achieved. The success probability for Bell-like state discrimination is only $25\%$. Bell-like states are non-maximally entangled two-qubit states that resemble Bell states in structure but have unequal Schmidt coefficients. We find that this can be boosted to $50\%$ using hyperentanglement, where extra ancillary degrees of freedom (DOF) of photons, such as polarization, momentum, or OAM, are also entangled along with the system DOF. This contrasts with Bell-state discrimination, where $100\%$ can be achieved. Furthermore, we find that using correlations in the photons' arrival times, all four Bell states can be distinguished with $100\%$ success probability, while for Bell-like state discrimination, it increases only to $37.5\%$ from $25\%$. We observe a similar contrast when using ancillary entangled photons. While the success probability for discriminating all four Bell states increases as $1-\frac{1}{2^N}$, where $N$ is the number of ancillary photon pairs, for Bell-like states, it depends on the state parameters and can be less than $25\%$ in some cases. Also, adding further ancillary photons decreases the success probability. We then show that using non-linear gadgets, namely SFG, $100\%$ success probability can be achieved even for Bell-like state discrimination.

quant-ph↗
arXiv2026

Memory-Augmented Hybrid Quantum Reservoir Computing

Reservoir computing (RC) is an effective method for predicting chaotic systems by using a high-dimensional dynamic reservoir with fixed internal weights, while keeping the learning phase linear, which simplifies training and reduces computational complexity compared to fully trained recurrent neural networks (RNNs). Quantum reservoir computing (QRC) uses the exponential growth of Hilbert spaces in quantum systems, allowing for greater information processing, memory capacity, and computational power. However, the original QRC proposal requires coherent injection of inputs multiple times, complicating practical implementation. We present a hybrid quantum-classical approach that implements memory through classical post-processing of quantum measurements. This approach avoids the need for multiple coherent input injections and is evaluated on benchmark tasks, including the chaotic Mackey-Glass time series prediction. We tested our model on two physical platforms: a fully connected Ising model and a Rydberg atom array. The optimized model demonstrates promising predictive capabilities, achieving a higher number of steps compared to previously reported approaches.

quant-ph↗