Abstract: For respective positive integer value n, performing an outer and inner procedures, for states sufficiently representing coherent-error in a quantum system. Inner procedure creates copies state entangling n-qudits using randomized compiling, and obtains measurements of n-qudits in a basis corresponding to f-states. An outcome bit string forms for the state from measurement. The outer procedure and the forming string repeats, obtaining outcome bit strings for each state. Error-rate is determined for each state using the outcome bit strings for the respective value n. The outer procedure through determining error-rate repeats for different n drawn from positive-integers, determines error-rate for each state for respective values n. For state-S, error-rate fits for each respective value-n of the state to a corresponding quadratic function, the error-rate as dependent variable and n as independent variable.

Abstract: For respective positive integer value n, performing an outer and inner procedures, for states sufficiently representing coherent-error in a quantum system. Inner procedure creates copies state entangling n-qudits using randomized compiling, and obtains measurements of n-qudits in a basis corresponding to f-states. An outcome bit string forms for the state from measurement. The outer procedure and the forming string repeats, obtaining outcome bit strings for each state. Error-rate is determined for each state using the outcome bit strings for the respective value n. The outer procedure through determining error-rate repeats for different n drawn from positive-integers, determines error-rate for each state for respective values n. For state-S, error-rate fits for each respective value-n of the state to a corresponding quadratic function, the error-rate as dependent variable and n as independent variable.

Abstract: This invention provides a quantum key distribution (QKD) system and method for determining initial quantum keys (QKs), including an initial QKA (220) and an initial QKB (230), determining an initial QKA value of a first function applied to said initial QKA, wherein a value of said first function depends upon values of specified information unit of a QK, including bit i (210), determining an initial QKB value of said first function applied to said initial QKB; and forming a revised QKA by depending a value of an information unit of said revised QKA on a value of information unit i of said initial QKA, if said initial QKA value equals said initial QKB value.

Abstract: Systems and methods for providing secure quantum digital signatures. In one embodiment, a digital signature user creates a plurality of identical “public” keys having one or more bits and a corresponding quantum mechanical one-way function. Quantum digital signature recipients use a “swap test” to check the validity of a copy of the key, and compare the test results with others. The quantum digital signature user sends a signed message over any channel, including an insecure channel. The recipients evaluate the signed message, and quantify the number of incorrect keys. The message is deemed valid and original, or forged and/or tampered with, when the number of incorrect keys is less than a lower threshold, or exceeds an upper threshold, respectively. For an intermediate number of incorrect keys, the recipients determine message authenticity by comparing observations. Hardware useful for application of the method is disclosed.

Abstract: This invention provides a quantum key distribution (QKD) system and method for determining initial quantum keys (QKs), including an initial QKA (220) and an initial QKB (230), determining an initial QKA value of a first function applied to said initial QKA, wherein a value of said first function depends upon values of specified information unit of a QK, including bit i (210), determining an initial QKB value of said first function applied to said initial QKB; and forming a revised QKA by depending a value of an information unit of said revised QKA on a value of information unit i of said initial QKA, if said initial QKA value equals said initial QKB value.

Abstract: Systems and methods for providing secure quantum digital signatures. In one embodiment, a digital signature user creates a plurality of identical “public” keys having one or more bits and a corresponding quantum mechanical one-way function. Quantum digital signature recipients use a “swap test” to check the validity of a copy of the key, and compare the test results with others. The quantum digital signature user sends a signed message over any channel, including an insecure channel. The recipients evaluate the signed message, and quantify the number of incorrect keys. The message is deemed valid and original, or forged and/or tampered with, when the number of incorrect keys is less than a lower threshold, or exceeds an upper threshold, respectively. For an intermediate number of incorrect keys, the recipients determine message authenticity by comparing observations. Hardware useful for application of the method is disclosed.

Abstract: A method of forming quantum error-correcting codes by first forming a stabilizer for a Hilbert space. A quantum information processing device can be formed to implement such quantum codes.