Quantum replication at the Heisenberg limit

Chiribella, Giulio; Yang, Yuxiang; Yao, Andrew Chi-Chih

doi:10.1038/ncomms3915

Cited by 40 publications

(103 citation statements)

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“…sequences of pure states cannot be stretched by any significant amount. The asymptotic no-cloning theorem holds also for non-universal machines designed to copy continuous sets of states, provided that such machines work deterministically [19].The impossibility of universal state cloning suggests similar results for quantum gates. Along this line, a nogo theorem for universal gate cloning was proven in Ref.…”

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confidence: 73%

“…To this purpose, we would have to retrieve the gate U ψ from the input state |ψ -a task whose deterministic execution is forbidden by the no-programming theorem [33]. Since the state |ψ is arbitrary, a symmetry argument precludes the conversion |ψ → U ψ even probabilistically [19].Though gate replication cannot be used for state cloning, it may still provide an advantage in the less demanding task of state generation, which consists in producing M copies of the state |ψ from N uses of the gate U ψ . The advantage does not show up in the universal case, because universal gate replication does not reproduce correctly the action of the gate U ⊗M ψ on the i.i.d.…”

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confidence: 99%

“…The result is interesting not only because it provides an explicit protocol achieving super-replication of maximally entangled states, but also because it allows one to prove the optimality of the gate super-replication protocol: if there existed a protocol producing M N 2 almost perfect copies of a generic unitary gate, such a protocol could be converted into a probabilistic cloning protocol producing M N 2 almost perfect copies of a generic maximally entangled state. Such a protocol is impossible because it would violate the Heisenberg limit for quantum cloning [19]. Even more strongly, since the fidelity of state replication must vanish for M N 2 [19], every gate replication protocol simulating M N 2 uses must have vanishing entanglement fidelity, and, therefore, vanishing fidelity on most input states.…”

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confidence: 99%

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Universal Superreplication of Unitary Gates

2015

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Quantum states obey an asymptotic no-cloning theorem, stating that no deterministic machine can reliably replicate generic sequences of identically prepared pure states. In stark contrast, we show that generic sequences of unitary gates can be replicated deterministically at nearly quadratic rates, with an error vanishing on most inputs except for an exponentially small fraction. The result is not in contradiction with the no-cloning theorem, since the impossibility of deterministically transforming pure states into unitary gates prevents the application of the gate replication protocol to states. In addition to gate replication, we show that N parallel uses of a completely unknown unitary gate can be compressed into a single gate acting on O(log N ) qubits, leading to an exponential reduction of the amount of quantum communication needed to implement the gate remotely.A striking feature of quantum theory is the impossibility of constructing a universal copy machine, which takes as input a quantum system in an arbitrary pure state and produces as output a number of exact replicas [1,2]. Such an impossibility has major implications for quantum error correction [3,4] and cryptographic protocols such as key distribution [5,6], quantum secret sharing [7,8], and quantum money [9][10][11][12].The impossibility of universal copy machines is a hard fact: it equally affects deterministic [13][14][15][16] and probabilistic machines [17][18][19], whose performances coincide with those of deterministic machines when it comes to copying completely unknown pure states [18,19]. A similar no-go result holds when the universal machine is presented a large number N of identical copies and is required to produce a larger number M > N of approximate replicas: if the replicas have non-vanishing overlap with the desired M -copy state, then the number of extra copies must be negligible compared to N [15]. We refer to this fact as the asymptotic no-cloning theorem, expressing the fact that independent and identically distributed (i.i.d.) sequences of pure states cannot be stretched by any significant amount. The asymptotic no-cloning theorem holds also for non-universal machines designed to copy continuous sets of states, provided that such machines work deterministically [19].The impossibility of universal state cloning suggests similar results for quantum gates. Along this line, a nogo theorem for universal gate cloning was proven in Ref. [20], showing that no quantum network can perfectly simulate two uses of an unknown unitary gate by querying it only once. Optimal networks that approximate universal gate cloning were studied in Refs. [20,21]. Very recently, Dür and coauthors [22] considered a non-universal setup designed to clone phase gates, i. e. gates generated by time evolution with a known Hamiltonian. In this scenario, they devised a quantum network that approximately simulates up to N 2 uses of an unknown phase gate while using it only N times, with vanishing error in the large N limit. Such a result establishes the possibi...

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Universal Superreplication of Unitary Gates

2015

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“…The results are plotted in Fig. 5(b) and we can see that F U U exhibits the expected periodic dependence on φ as predicted by the theoretical formula (9). Due to various imperfections, the observed fidelities are smaller than the theoretical prediction, and the dashed line in Fig.…”

Section: Resultsmentioning

confidence: 60%

“…As pointed out in Ref. [9], the observed N 2 limit of the number of achievable almost perfect clones is deeply connected to the Heisenberg limit on quantum phase estimation.…”

Section: Introductionmentioning

confidence: 99%

Experimental replication of single-qubit quantum phase gates

et al. 2016

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We experimentally demonstrate the underlying physical mechanism of the recently proposed protocol for superreplication of quantum phase gates [W. Dür, P. Sekatski, and M. Skotiniotis, Phys. Rev. Lett. 114, 120503 (2015)], which allows to produce up to N 2 high-fidelity replicas from N input copies in the limit of large N . Our implementation of 1 → 2 replication of the single-qubit phase gates is based on linear optics and qubits encoded into states of single photons. We employ the quantum Toffoli gate to imprint information about the structure of an input two-qubit state onto an auxiliary qubit, apply the replicated operation to the auxiliary qubit, and then disentangle the auxiliary qubit from the other qubits by a suitable quantum measurement. We characterize the replication protocol by full quantum process tomography and observe good agreement of the experimental results with theory.

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Approximate Quantum Cloning

Bruß¹,

Macchiavello²

2006

Lectures on Quantum Information

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Quantum replication at the Heisenberg limit

Cited by 40 publications

References 64 publications

Universal Superreplication of Unitary Gates

Universal Superreplication of Unitary Gates

Experimental replication of single-qubit quantum phase gates

Approximate Quantum Cloning

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