© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:quant-ph/0603174 · Physical Review A

Optical implementation of the encoding of two qubits to a single qutrit

Lucie Bartůšková, Antonín Černoch, Radim Filip, Jaromı́r Fiurášek, Jan Soubusta, Miloslav Dušek

Published Aug 28, 2006• 26 citations

Abstract

We have devised an optical scheme for the recently proposed protocol for encoding two qubits into one qutrit. In this protocol, Alice encodes an arbitrary pure product state of two qubits into a state of one qutrit. Bob can then restore either of the two encoded qubit states error-free but not both of them simultaneously. We have successfully realized this scheme experimentally using spatial-mode encoding. Each qubit (qutrit) was represented by a single photon that could propagate through two (three) separate fibers. We theoretically propose two generalizations of the original protocol. We have found a probabilistic operation that enables us to retrieve both qubits simultaneously with average fidelity above 90% and we have proposed an extension of the original encoding transformation to encode $N$ qubits into one $(N+1)$-dimensional system.

DOI: 10.1103/physreva.74.022325

Related papers

Probabilistic coding of quantum states

Andrzej Grudka, Antoni Wójcik, Mikołaj Czechlewski

We discuss the properties of probabilistic coding of two qubits to one qutrit and generalize the scheme to higher dimensions. We show that the protocol preserves the entanglement between the qubits to be encoded and the environment and can also be applied to mixed states. We present a protocol that enables encoding of $n$ qudits to one qudit of dimension smaller than the Hilbert space of the original system and then allows probabilistic but error-free decoding of any subset of $k$ qudits. We give a formula for the probability of successful decoding.

arXiv:quant-ph/0603244•Physical Review A•Jul 6, 2006•2 citations

Arbitrary unitary operations of the biphoton qutrits

Qing Lin

Qutrits, the triple level quantum systems in various forms, have been proposed for quantum information processing recently. By the methods presented in this paper a bi-photonic qutrit, which is encoded with the polarizations of two photons in the same spatial-temporal mode, can be mapped to a single photon qutrit in spatial modes. It will make arbitrary unitary operation on such bi-photonic qutrit possible if we can also realize the inverse map to polarization space. Among the two schemes proposed in this paper, the one based only on linear optics realizes an arbitrary U(3) operation with a very small success probability. However, if added with weak nonlinearity, the success probability can be greatly improved. These schemes are feasible with the current experimental technology.

•May 20, 2009•0 citations

Bi-directional mapping between polarization and spatially encoded photonic qutrits

Qing Lin, Bing He

Qutrits, the triple level quantum systems in various forms, have been proposed for quantum information processing recently. By the methods presented in this paper, a biphotonic qutrit, which is encoded with the polarizations of two photons in the same spatial-temporal mode, can be mapped to a single-photon qutrit in spatial modes. It will make arbitrary unitary operation on such biphotonic qutrit possible if we can also realize the inverse map to polarization space. Among the two schemes proposed in this paper, the one based only on linear optics realizes an arbitrary U(3) operation with a very small success probability. However, if added with weak nonlinearity, the success probability can be greatly improved. These schemes are feasible with the current experimental technology.

arXiv:0905.3214•Physical Review A•Dec 7, 2009•23 citations

Linear Optical Quantum Computing in a Single Spatial Mode

Peter C. Humphreys, Benjamin J. Metcalf, Justin B. Spring +5 more

We present a scheme for linear optical quantum computing using time-bin-encoded qubits in a single spatial mode. We show methods for single-qubit operations and heralded controlled-phase (cphase) gates, providing a sufficient set of operations for universal quantum computing with the Knill-Laflamme-Milburn [Nature (London) 409, 46 (2001)] scheme. Our protocol is suited to currently available photonic devices and ideally allows arbitrary numbers of qubits to be encoded in the same spatial mode, demonstrating the potential for time-frequency modes to dramatically increase the quantum information capacity of fixed spatial resources. As a test of our scheme, we demonstrate the first entirely single spatial mode implementation of a two-qubit quantum gate and show its operation with an average fidelity of 0.84±0.07.

arXiv:1305.3592•Physical Review Letters•Oct 9, 2013•159 citations

Quantum Key Distribution with Qubits Encoded in Qutrit

Rupesh Kumar, Rafał Demkowicz-Dobrzański, Konrad Banaszek

We present a novel one-way quantum key distribution protocol based on 3-dimensional quantum state, a qutrit, that encodes two qubits in its 2-dimensional subspaces. The qubits hold the classical bit information that has to be shared between the legitimate users. Alice sends such a qutrit to Bob where he decodes one of the qubit and measures it along the random Pauli basis. This scheme has higher secure key rate at longer transmission distance than the standard BB84 protocol.

arXiv:1202.0456•Feb 2, 2012•0 citations

High-fidelity Z -measurement error encoding of optical qubits

Jeremy L. O’Brien, Geoff J. Pryde, Andrew G. White +1 more

We demonstrate a quantum error correction scheme that protects against accidental measurement, using a parity encoding where the logical state of a single qubit is encoded into two physical qubits using a nondeterministic photonic controlled-NOT gate. For the single qubit input states $\ensuremath{\mid}0⟩$, $\ensuremath{\mid}1⟩$, $\ensuremath{\mid}0⟩\ifmmode\pm\else\textpm\fi{}\ensuremath{\mid}1⟩$, and $\ensuremath{\mid}0⟩\ifmmode\pm\else\textpm\fi{}i\ensuremath{\mid}1⟩$ our encoder produces the appropriate two-qubit encoded state with an average fidelity of $0.88\ifmmode\pm\else\textpm\fi{}0.03$ and the single qubit decoded states have an average fidelity of $0.93\ifmmode\pm\else\textpm\fi{}0.05$ with the original state. We are able to decode the two-qubit state (up to a bit flip) by performing a measurement on one of the qubits in the logical basis; we find that the 64 one-qubit decoded states arising from 16 real and imaginary single-qubit superposition inputs have an average fidelity of $0.96\ifmmode\pm\else\textpm\fi{}0.03$.

arXiv:quant-ph/0408064•Physical Review A•Jun 9, 2005•25 citations

We have devised an optical scheme for the recently proposed protocol for encoding two qubits into one qutrit. In this protocol, Alice encodes an arbitrary pure product state of two qubits into a state of one qutrit. Bob can then restore either of the two encoded qubit states error-free but not both of them simultaneously. We have successfully realized this scheme experimentally using spatial-mode encoding. Each qubit (qutrit) was represented by a single photon that could propagate through two (three) separate fibers. We theoretically propose two generalizations of the original protocol. We have found a probabilistic operation that enables us to retrieve both qubits simultaneously with average fidelity above 90% and we have proposed an extension of the original encoding transformation to encode

N

qubits into one

(N+1)

-dimensional system.

We discuss the properties of probabilistic coding of two qubits to one qutrit and generalize the scheme to higher dimensions. We show that the protocol preserves the entanglement between the qubits to be encoded and the environment and can also be applied to mixed states. We present a protocol that enables encoding of

n

qudits to one qudit of dimension smaller than the Hilbert space of the original system and then allows probabilistic but error-free decoding of any subset of

k

qudits. We give a formula for the probability of successful decoding.

Qutrits, the triple level quantum systems in various forms, have been proposed for quantum information processing recently. By the methods presented in this paper a bi-photonic qutrit, which is encoded with the polarizations of two photons in the same spatial-temporal mode, can be mapped to a single photon qutrit in spatial modes. It will make arbitrary unitary operation on such bi-photonic qutrit possible if we can also realize the inverse map to polarization space. Among the two schemes proposed in this paper, the one based only on linear optics realizes an arbitrary U(3) operation with a very small success probability. However, if added with weak nonlinearity, the success probability can be greatly improved. These schemes are feasible with the current experimental technology.

Qutrits, the triple level quantum systems in various forms, have been proposed for quantum information processing recently. By the methods presented in this paper, a biphotonic qutrit, which is encoded with the polarizations of two photons in the same spatial-temporal mode, can be mapped to a single-photon qutrit in spatial modes. It will make arbitrary unitary operation on such biphotonic qutrit possible if we can also realize the inverse map to polarization space. Among the two schemes proposed in this paper, the one based only on linear optics realizes an arbitrary U(3) operation with a very small success probability. However, if added with weak nonlinearity, the success probability can be greatly improved. These schemes are feasible with the current experimental technology.

We present a scheme for linear optical quantum computing using time-bin-encoded qubits in a single spatial mode. We show methods for single-qubit operations and heralded controlled-phase (cphase) gates, providing a sufficient set of operations for universal quantum computing with the Knill-Laflamme-Milburn [Nature (London) 409, 46 (2001)] scheme. Our protocol is suited to currently available photonic devices and ideally allows arbitrary numbers of qubits to be encoded in the same spatial mode, demonstrating the potential for time-frequency modes to dramatically increase the quantum information capacity of fixed spatial resources. As a test of our scheme, we demonstrate the first entirely single spatial mode implementation of a two-qubit quantum gate and show its operation with an average fidelity of 0.84±0.07.

We demonstrate a quantum error correction scheme that protects against accidental measurement, using a parity encoding where the logical state of a single qubit is encoded into two physical qubits using a nondeterministic photonic controlled-NOT gate. For the single qubit input states $\ensuremath{\mid}0⟩$, $\ensuremath{\mid}1⟩$, $\ensuremath{\mid}0⟩\ifmmode\pm\else\textpm\fi{}\ensuremath{\mid}1⟩$, and $\ensuremath{\mid}0⟩\ifmmode\pm\else\textpm\fi{}i\ensuremath{\mid}1⟩$ our encoder produces the appropriate two-qubit encoded state with an average fidelity of $0.88\ifmmode\pm\else\textpm\fi{}0.03$ and the single qubit decoded states have an average fidelity of $0.93\ifmmode\pm\else\textpm\fi{}0.05$ with the original state. We are able to decode the two-qubit state (up to a bit flip) by performing a measurement on one of the qubits in the logical basis; we find that the 64 one-qubit decoded states arising from 16 real and imaginary single-qubit superposition inputs have an average fidelity of $0.96\ifmmode\pm\else\textpm\fi{}0.03$.