The complementary channel is defined on the output space of the extension of the channel Φ, and therefore corresponds to the final state on system K, yet in general will not be quantum error-correctable for an arbitrary subsystem channel. The unitary transformation U Φ corresponds to the dashed and solid boxes in Fig. Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant. The action of the private quantum channel Φ can also be extended to a unitary transformation over a larger Hilbert space, as described by the action of U Φ on systems A B K by introducing the ancillary state | ζ 〉 〈 ζ | K, as described in Eq. ( 17). This operation corresponds to the dotted box in Fig. The accuracy of logical operations on quantum bits (qubits) must be improved for quantum computers to outperform classical ones in useful tasks. The subsystem σ A ⊗ σ B that encodes the arbitrary state of quantum information σ B is prepared by entangling an ancillary pure state mixing ancilla | Θ 〉 〈 Θ | M with a chosen pure state | φ 〉 〈 φ | A via the unitary U M A and tracing out over the mixing ancilla space M. Generalized form of extending a private quantum subsystem channel to a unitary transformation via Stinespring's dilation theorem. Similar to Kraus representations, the term Stinespring representation is often. We also consider the concept of complementarity for the general notion of a private quantum subsystem. In this work we propose and demonstrate a general quantum algorithm to evolve open quantum dynamics on quantum computing devices. current active theory of quantum error correction, which is the subject. The bridge between quantum cryptography and quantum error correction provided by complementary quantum channels motivates the study of a new, more general definition of quantum error-correcting code, and we initiate this study here. These conditions can be regarded as the private analog of the Knill-Laflamme conditions for quantum error correction, and we explore how the conditions simplify in some special cases.
Steinspring quantum error correction code#
Here we prove several previously presented results, including a condition for a given random unitary channel to not have a private subspace (although this does not mean that private communication cannot occur, as was previously demonstrated via private subsystems) and algebraic conditions that characterize when a general quantum subsystem or subspace code is private for a quantum channel. This paper addresses and expands on the contents of the recent Letter discussing private quantum subsystems.
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