There exists a single basis of the state space in which all the “target” subspaces whose projectors commute (in other words, Our solution follows the lines of the “quantum toĬlassical reductions” in. Intuition outlined above, does not always hold in the quantum Union bound from ordinary probability, which is the basis of the Subspace such-and-such.” The problem lies in the fact that the Is “the state of the system has fidelity at least 1 − ϵ to the Statement “such-and-such event holds with probability 1 − ϵ” | ψ ⟩ restricted to those positions, and applying erasureĬorrection should yield a state very close to | ψ ⟩.įormalizing this intuition is more delicate than it would be if On that event, all components of the QECC which pass theĪuthentication test should be “close” to the encoding of With high probability, theĪuthentication keys will be reconstructed correctly conditioned These have been studied more or less explicitly in Sharing schemes which correct any t errors with high Thus, the best classical analogueįor approximate quantum codes are error-tolerant classical secret Schemes which correct t = ⌊ ( n − 1 ) / 2 ⌋ errors (see the Hand, if one allows a small probability of mistaken errorĬorrection, then one can in fact get error-tolerant secret sharing Is optimal for schemes with zero error probability. Reveal no information, then we get t < d, and thus t < n / 3. Schemes are error-tolerant: such a scheme corrects n − d erasuresĪnd hence t = ( n − d ) / 2 errors (this fact was first highlighted for Shamir secret sharing in ). Sharing scheme (ETSS) can recover the secret even when t shares The quantum code construction described here illustrates a furtherĬonnection to classical secret sharing. More generally, the construction illustrates a difference between exact and approximate requirements in quantum cryptography and (yet again) the delicacy of security proofs and impossibility results in the quantum model. Protocols for dishonest-dealer VQSS and secure multi-party Weīelieve the codes could also potentially lead to improved Honest-dealer VQSS scheme for t = ⌊ ( n − 1 ) / 2 ⌋. In particular, the construction directly yields an Secret sharing (VQSS) is impossible when the number of cheaters Highlights an error in a purported proof that verifiable quantum That secret sharing is a better classical analogue to quantumĮrror correction than is classical error correction. The construction has several interesting implications forĬryptography and quantum information theory. Reveal no information about the message, and so they can also be viewedĪs error-tolerant secret sharing schemes. The codes have the property that any t components Sharp distinction between exact and approximate quantum errorĬorrection. The registers (i.e., the coding alphabet). Paper we describe quantum error-correcting codes capable ofĬorrecting up to ⌊ ( n − 1 ) / 2 ⌋ arbitrary errors with fidelityĮxponentially close to 1, at the price of increasing the size of Naively, one might expect thatĬorrecting errors to very high fidelity would only allow small However, this bound only applies to codes which The error bars are obtained through error propagation of the fit parameter uncertainties.It is a standard result in the theory of quantum error-correctingĬodes that no code of length n can fix more than n / 4 arbitraryĮrrors, regardless of the dimension of the coding and encoded QEC+QJT (Fig. 3): the deduced sensitivity from the results with the QEC+QJT strategy in Fig. 3. A sensitivity enhancement of 5.3 dB over TLS (the encoding with the two lowest Fock states) is obtained. d– f Sensitivity of measuring p ( σ p) of the radiometry for the probe states ∣ ψ 1, 3 ⟩, ∣ ψ 1, 5 ⟩, and ∣ ψ 1, 7 ⟩, respectively. The fitted oscillation periods are proportional to n − m. c The measured P g as a function of p t int/ T 1 for the probe states ∣ ψ 1, 3 ⟩, ∣ ψ 1, 5 ⟩, and ∣ ψ 1, 7 ⟩ with a single round of QEC ( M = 1 and t int = M τ int = τ int). The experiment is performed with the probe state ∣ ψ 1, 3 ⟩ = ( ∣ 1 ⟩ + ∣ 3 ⟩ ) / 2 and τ int = 0.1 T 1 for the QEC repetition number M = 1, 5, 10 (from left to right). The purple dots and green triangles correspond to experiments with p = 0 and 0.037, respectively. b The measured P g as a function of the initial phase φ 0. A Experimental sequence for the quantum-enhanced radiometry that senses the excitation population p in the receiver cavity (Fig. 1c) via QEC.
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