Modern Physics Letters B

OPTIMAL ANTI-CLONING FOR REAL STATE

LI-HUA ZHANG, Bing Shi, Zhuo‐Liang Cao

Published Mar 30, 2008• 0 citations

Abstract

We present two optimal quantum anti-cloning machines for real state in two dimensions, i.e., input state lying in the x–z equator. The first anti-cloning machine produces two outputs which are orthogonal to the input, and the second one produces two anti-parallel outputs for a single input state. The optimal fidelities are also derived.

DOI: 10.1142/s0217984908015061

Related papers

Quantum Anti-Cloning

Song, David D., Lucién Hardy

We derive the transformation for the optimal universal quantum anti-cloner which produces two anti-parallel outputs for a single input state. The fidelity is shown to be 2/3 which is same as the measurement fidelity. We consider a probabilistic quantum anti-cloner and show quantum states can be anti-cloned exactly with non-zero probability and its efficiency is higher than the efficiency of distinguishing between the two states.

arXiv:quant-ph/0001105Jan 28, 20002 citations

OPTIMAL CLONING AND NO SIGNALING

Sibasish Ghosh A, Guruprasad Kar, Anirban Roy Physics

It is shown that no signaling constraint generates the whole class of 1 → 2 optimal quantum cloning machines of single qubits

Jan 1, 199925 citations

Optimal universal and state-dependent quantum cloning

Dagmar Bruß, David Peter Divincenzo, ARTUR K. EKERT +3 more

arXiv:quant-ph/9705038Physical Review AApr 1, 1998554 citations

Cloning of qubits with both the cloned state and the state orthogonal to it as inputs

Go Kato

Physical Review AMar 13, 20093 citations

Extremal asymmetric universal cloning machines

Mingming Jiang, Sixia Yu

arXiv:1202.1633Journal of Mathematical PhysicsMay 1, 20108 citations

Asymmetric quantum cloning machines

Nicolas J. Cerf

Acta Physica Slovaca Reviews and TutorialsJan 1, 19985 citations

Modern Physics Letters B

OPTIMAL ANTI-CLONING FOR REAL STATE

LI-HUA ZHANG, Bing Shi, Zhuo‐Liang Cao

Published Mar 30, 2008• 0 citations

Publisher

Abstract

DOI: 10.1142/s0217984908015061

Related papers

Quantum Anti-Cloning

Song, David D., Lucién Hardy

arXiv:quant-ph/0001105Jan 28, 20002 citations

OPTIMAL CLONING AND NO SIGNALING

Sibasish Ghosh A, Guruprasad Kar, Anirban Roy Physics

It is shown that no signaling constraint generates the whole class of 1 → 2 optimal quantum cloning machines of single qubits

Jan 1, 199925 citations

Optimal universal and state-dependent quantum cloning

Dagmar Bruß, David Peter Divincenzo, ARTUR K. EKERT +3 more

We establish the best possible approximation to a perfect quantum cloning machine that produces two clones out of a single input. We analyze both universal and state-dependent cloners. The maximal fidelity of cloning is shown to be 5/6 for universal cloners. It can be achieved either by a special unitary evolution or by a teleportation scheme. We construct the optimal state-dependent cloners operating on any prescribed two nonorthogonal states and discuss their fidelities and the use of auxiliary physical resources in the process of cloning. The optimal universal cloners permit us to derive an upper bound on the quantum capacity of the depolarizing quantum channel.We establish the best possible approximation to a perfect quantum cloning machine that produces two clones out of a single input. We analyze both universal and state-dependent cloners. The maximal fidelity of cloning is shown to be 5/6 for universal cloners. It can be achieved either by a special unitary evolution or by a teleportation scheme. We construct the optimal state-dependent cloners operating on any prescribed two nonorthogonal states and discuss their fidelities and the use of auxiliary physical resources in the process of cloning. The optimal universal cloners permit us to derive an upper bound on the quantum capacity of the depolarizing quantum channel.

arXiv:quant-ph/9705038Physical Review AApr 1, 1998554 citations

Cloning of qubits with both the cloned state and the state orthogonal to it as inputs

Go Kato

A universal cloning machine is derived. The machine produces $c$ clones of an unknown qubit from $s$ identical replicas of qubit and $k$ identical replicas of its orthogonal qubit. For the standard cloning machine, i.e., $k=0$ , the universal-not machine, $s=0$ , and some other cases, the optimum machine is well known. The universal cloning machine derived in this paper gives clones whose fidelity is the same value as that for the optimum machine. In the case of sufficiently large $c$ , we show that the clone fidelity generated by the cloning machine from $s\ensuremath{\ne}0$ replicas and $k\ensuremath{\ne}0$ orthogonal replicas is higher than that generated by the optimal cloning machine from $s+k$ replicas in case $s+k\ensuremath{\le}300$.A universal cloning machine is derived. The machine produces $c$ clones of an unknown qubit from $s$ identical replicas of qubit and $k$ identical replicas of its orthogonal qubit. For the standard cloning machine, i.e., $k=0$, the universal-not machine, $s=0$, and some other cases, the optimum machine is well known. The universal cloning machine derived in this paper gives clones whose fidelity is the same value as that for the optimum machine. In the case of sufficiently large $c$, we show that the clone fidelity generated by the cloning machine from $s\ensuremath{\ne}0$ replicas and $k\ensuremath{\ne}0$ orthogonal replicas is higher than that generated by the optimal cloning machine from $s+k$ replicas in case $s+k\ensuremath{\le}300$.

Physical Review AMar 13, 20093 citations

Extremal asymmetric universal cloning machines

Mingming Jiang, Sixia Yu

The trade-offs among various output fidelities of asymmetric universal cloning machines are investigated. First we find out all the attainable optimal output fidelities for the 1 to 3 asymmetric universal cloning machine and it turns out that there are two kinds of extremal machines which have to cooperate in order to achieve some of the optimal output fidelities. Second we construct a family of extremal cloning machines that includes the universal symmetric cloning machine as well as an asymmetric 1 to 1+N cloning machine for qudits with two different output fidelities such that the optimal trade-off between the measurement disturbance and state estimation is attained in the limit of infinite N.The trade-offs among various output fidelities of asymmetric universal cloning machines are investigated. First we find out all the attainable optimal output fidelities for the 1 to 3 asymmetric universal cloning machine and it turns out that there are two kinds of extremal machines which have to cooperate in order to achieve some of the optimal output fidelities. Second we construct a family of extremal cloning machines that includes the universal symmetric cloning machine as well as an asymmetric 1 to 1+N cloning machine for qudits with two different output fidelities such that the optimal trade-off between the measurement disturbance and state estimation is attained in the limit of infinite N.

arXiv:1202.1633Journal of Mathematical PhysicsMay 1, 20108 citations

Asymmetric quantum cloning machines

Nicolas J. Cerf

A family of asymmetric cloning machines for quantum bits and $N$ -dimensional quantum states is introduced. These machines produce two approximate copies of a single quantum state that emerge from two distinct channels. In particular, an asymmetric Pauli cloning machine is defined that makes two imperfect copies of a quantum bit, while the overall input-to-output operation for each copy is a Pauli channel. A no-cloning inequality is derived, characterizing the impossibility of copying imposed by quantum mechanics. If $p$ and $p'$ are the probabilities of the depolarizing channels associated with the two outputs, the domain in $(\\sqrt{p},\\sqrt{p'})$ -space located inside a particular ellipse representing close-to-perfect cloning is forbidden. This ellipse tends to a circle when copying an $N$ -dimensional state with $N\\to\\infty$ , which has a simple semi-classical interpretation. The symmetric Pauli cloning machines are then used to provide an upper bound on the quantum capacity of the Pauli channel of probabilities $p_x$ , $p_y$ and $p_z$ . The capacity is proven to be vanishing if $(\\sqrt{p_x},\\sqrt{p_y},\\sqrt{p_z})$ lies outside an ellipsoid whose pole coincides with the depolarizing channel that underlies the universal cloning machine. Finally, the tradeoff between the quality of the two copies is shown to result from a complementarity akin to Heisenberg uncertainty principle.A family of asymmetric cloning machines for quantum bits and $N$-dimensional quantum states is introduced. These machines produce two approximate copies of a single quantum state that emerge from two distinct channels. In particular, an asymmetric Pauli cloning machine is defined that makes two imperfect copies of a quantum bit, while the overall input-to-output operation for each copy is a Pauli channel. A no-cloning inequality is derived, characterizing the impossibility of copying imposed by quantum mechanics. If $p$ and $p'$ are the probabilities of the depolarizing channels associated with the two outputs, the domain in $(\\sqrt{p},\\sqrt{p'})$-space located inside a particular ellipse representing close-to-perfect cloning is forbidden. This ellipse tends to a circle when copying an $N$-dimensional state with $N\\to\\infty$, which has a simple semi-classical interpretation. The symmetric Pauli cloning machines are then used to provide an upper bound on the quantum capacity of the Pauli channel of probabilities $p_x$, $p_y$ and $p_z$. The capacity is proven to be vanishing if $(\\sqrt{p_x},\\sqrt{p_y},\\sqrt{p_z})$ lies outside an ellipsoid whose pole coincides with the depolarizing channel that underlies the universal cloning machine. Finally, the tradeoff between the quality of the two copies is shown to result from a complementarity akin to Heisenberg uncertainty principle.

Acta Physica Slovaca Reviews and TutorialsJan 1, 19985 citations

A universal cloning machine is derived. The machine produces

c

clones of an unknown qubit from

s

identical replicas of qubit and

k

identical replicas of its orthogonal qubit. For the standard cloning machine, i.e.,

k=0

, the universal-not machine,

s=0

, and some other cases, the optimum machine is well known. The universal cloning machine derived in this paper gives clones whose fidelity is the same value as that for the optimum machine. In the case of sufficiently large

c

, we show that the clone fidelity generated by the cloning machine from $s\ensuremath{\ne}0$ replicas and $k\ensuremath{\ne}0$ orthogonal replicas is higher than that generated by the optimal cloning machine from

s+k

replicas in case $s+k\ensuremath{\le}300$.

A family of asymmetric cloning machines for quantum bits and

N

-dimensional quantum states is introduced. These machines produce two approximate copies of a single quantum state that emerge from two distinct channels. In particular, an asymmetric Pauli cloning machine is defined that makes two imperfect copies of a quantum bit, while the overall input-to-output operation for each copy is a Pauli channel. A no-cloning inequality is derived, characterizing the impossibility of copying imposed by quantum mechanics. If

p

and

p'

are the probabilities of the depolarizing channels associated with the two outputs, the domain in

(\\sqrt{p},\\sqrt{p'})

-space located inside a particular ellipse representing close-to-perfect cloning is forbidden. This ellipse tends to a circle when copying an

N

-dimensional state with

N\\to\\infty

, which has a simple semi-classical interpretation. The symmetric Pauli cloning machines are then used to provide an upper bound on the quantum capacity of the Pauli channel of probabilities

p_x

p_y

and

p_z

. The capacity is proven to be vanishing if

(\\sqrt{p_x},\\sqrt{p_y},\\sqrt{p_z})

lies outside an ellipsoid whose pole coincides with the depolarizing channel that underlies the universal cloning machine. Finally, the tradeoff between the quality of the two copies is shown to result from a complementarity akin to Heisenberg uncertainty principle.